{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":486,"title":"Surface Fit z(x,y)","description":"Given three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00. \r\n\r\nFor example,\r\n\r\n x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\r\n\r\nthen\r\n\r\n z = x.^2-2*x.*y+3*y.^2-4 \r\n\r\nand\r\n\r\n c = [cxx cxy cyy c00] = [1 -2 3 -4]","description_html":"\u003cp\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre\u003e x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e z = x.^2-2*x.*y+3*y.^2-4 \u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e c = [cxx cxy cyy c00] = [1 -2 3 -4]\u003c/pre\u003e","function_template":"function c = sufit(x,y,z)\r\n  cxx=0;\r\n  cxy=0;\r\n  cyy=0;\r\n  c00=0;\r\n  c=[cxx cxy cyy c00];\r\nend","test_suite":"%%\r\nx= [0 0 1 1 2 2 3 3];\r\ny= [0 1 0 1 0 1 0 1];\r\nz=[-4 -1 -3 -2 0 -1 5 2];\r\nc=[1 -2 3 -4]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,100);\r\ny= rand(1,100);\r\nz=7*x.^2-9*x.*y+11*y.^2-17;\r\nc=[7 -9 11 -17]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,10000);\r\ny= rand(1,10000);\r\nz=17*x.^2-19*x.*y+11*y.^2-13;\r\nc=[17 -19 11 -13]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2012-03-12T19:23:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-12T17:50:33.000Z","updated_at":"2026-04-17T10:38:50.000Z","published_at":"2012-03-19T09:01:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 0  0  1  1  2  2  3  3]\\n y = [ 0  1  0  1  0  1  0  1]\\n z = [-4 -1 -3 -2  0 -1  5  2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z = x.^2-2*x.*y+3*y.^2-4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [cxx cxy cyy c00] = [1 -2 3 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45851,"title":"Least Absolute Deviations (L1-norm) line fit - degree 1","description":"Matlab's polyfit function is very handy to find least-squares regression. It minimizes the (L2-norm) of the estimation errors, by solving a linear system.\r\n\u003chttps://www.mathworks.com/help/matlab/ref/polyfit.html\u003e\r\n\r\nAn often overlooked way to deal with these situations is to use Least Absolute Deviations (LAD) line fitting. It minimizes the L1-norm of the residuals, thus it is less sensitive to outliers that fall far away from the underlying model\r\nhttps://en.wikipedia.org/wiki/Least_absolute_deviations\r\n\r\n- - -\r\n\r\nYou are given two vectors X and Y (coordinates of observations on a plane).\r\nReturn a row vector *P = [a, b]* with the coefficients of the best-fit line, in the L1-norm sense. I.e., find *a* and *b* that minimize *sum( abs( Y - a*X - b ) )* .\r\n\r\n(compare your results with polyfit on the test suite!)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.5px; transform-origin: 407px 112.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMatlab's polyfit function is very handy to find least-squares regression. It minimizes the (L2-norm) of the estimation errors, by solving a linear system.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/polyfit.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://www.mathworks.com/help/matlab/ref/polyfit.html\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u0026gt;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAn often overlooked way to deal with these situations is to use Least Absolute Deviations (LAD) line fitting. It minimizes the L1-norm of the residuals, thus it is less sensitive to outliers that fall far away from the underlying model\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Least_absolute_deviations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Least_absolute_deviations\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e- - -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are given two vectors X and Y (coordinates of observations on a plane). Return a row vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP = [a, b]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e with the coefficients of the best-fit line, in the L1-norm sense. I.e., find\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e that minimize\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003esum( abs( Y - a*X - b ) )\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(compare your results with polyfit on the test suite!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = LADfit(X,Y)\r\nP = polyfit(X,Y,1);\r\nend","test_suite":"%%\r\nX=[-2.8 -4.8 0.9 2.3 3.6 -4.2 -0.7 3.0 0.1 -1.0]';\r\nY=[12.0 6.5 -1.6 -2.1 -2.6 0.1 -1.1 -2.4 -1.3 -1.0]';\r\nP=LADfit(X,Y); % P_correct = [-10/27 -19/15]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 1007/54\r\nassert(res\u003c19)\r\n\r\n%%\r\nX=[1 2 3 4 5]';\r\nY=[1 2 3 4 3]';\r\nP=LADfit(X,Y); % P_correct = [1 0]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 2.0\r\nassert(res\u003c2.1)\r\n\r\n%%\r\nX=[1 2 3 4 5]';\r\nY=[1 0 0 0 0]';\r\nP=LADfit(X,Y); % P_correct = [0 0]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 1.0\r\nassert(res\u003c1.01)\r\n\r\n%%\r\nn=10; % Nr of points\r\nno=2; % Nr of outliers\r\nmax_res = 0;\r\nmax_ratio = 0;\r\nfor cycle=1:10\r\n    rng('shuffle');\r\n    P=(rand(2,1)-0.5)*10; % Generate model\r\n    X=(rand(n,1)-0.5)*2; % Generate X\r\n    Y=polyval(P,X)+(rand(n,1)-0.5);  % Generate Y and add noise\r\n    Y(1:no)=Y(1:no)+(rand(no,1)-0.5)*10; % Add outliers\r\n\r\n    P_lad=LADfit(X,Y);\r\n    P_lin=polyfit(X,Y,1);\r\n\r\n    Y_lad=polyval(P_lad,X);\r\n    res_lad=sum(abs(Y-Y_lad));\r\n\r\n    Y_lin=polyval(P_lin,X);\r\n    res_lin=sum(abs(Y-Y_lin));\r\n\r\n    max_res=max(max_res,res_lad);\r\n    max_ratio=max(max_ratio,res_lad/res_lin);\r\nend\r\nassert(max_res\u003c12.0 \u0026 max_ratio\u003c0.99); % Should be always better than L-2 and under 12.0","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":452188,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2020-11-22T01:25:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-10T07:18:59.000Z","updated_at":"2020-11-22T01:25:26.000Z","published_at":"2020-06-10T07:18:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMatlab's polyfit function is very handy to find least-squares regression. It minimizes the (L2-norm) of the estimation errors, by solving a linear system.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/polyfit.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/help/matlab/ref/polyfit.html\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn often overlooked way to deal with these situations is to use Least Absolute Deviations (LAD) line fitting. It minimizes the L1-norm of the residuals, thus it is less sensitive to outliers that fall far away from the underlying model\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Least_absolute_deviations\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Least_absolute_deviations\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e- - -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given two vectors X and Y (coordinates of observations on a plane). Return a row vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP = [a, b]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the coefficients of the best-fit line, in the L1-norm sense. I.e., find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that minimize\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum( abs( Y - a*X - b ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(compare your results with polyfit on the test suite!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1336,"title":"Geometry: Find Circle given 3 Non-Colinear Points","description":"*This Challenge is to determine the center and radius of a circle given three non-colinear points.*\r\n\r\n*Input:* Points\r\n\r\n*Output:* [xc, yc, r] where [xc,yc] are the center and r is the radius\r\n\r\n*Example:*\r\n\r\nInput: Points = [1 0 ; 0 -1 ; 0 1]\r\n\r\nOutput: [ 0 0 1]\r\n\r\n*Theory/Hint:* The Kasa method provides a best fit circle to a set of points.\r\n\r\n*Future:* 1) Circumscribe 4 points  2) Circumscribe N points  3) The Great Lego Cup Challenge","description_html":"\u003cp\u003e\u003cb\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Points\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/p\u003e\u003cp\u003eOutput: [ 0 0 1]\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory/Hint:\u003c/b\u003e The Kasa method provides a best fit circle to a set of points.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e 1) Circumscribe 4 points  2) Circumscribe N points  3) The Great Lego Cup Challenge\u003c/p\u003e","function_template":"function [xc,yc,r]=find_circle(pts)\r\n xc=0;\r\n yc=0;\r\n r=1;\r\n\r\n","test_suite":"%%\r\nfor tests=1:5\r\n xc_truth=randn;\r\n yc_truth=randn;\r\n r_truth=rand;\r\n rand_ang=randi(360,3,1)+rand(3,1); % Avoid duplicate location via rand(3,1)\r\n pts=[xc_truth+r_truth*cosd(rand_ang) yc_truth+r_truth*sind(rand_ang)]; \r\n\r\n [xc,yc,r]=find_circle(pts);\r\n\r\n %dif=[xc yc r]-[xc_truth yc_truth r_truth]\r\n\r\n assert(max(abs([xc,yc,r]-[xc_truth,yc_truth,r_truth]))\u003c1e-6,...\r\nsprintf('Expect xc %.2f yc %.2f r %.2f  Ans:%.2f %.2f %.2f',...\r\n  xc_truth,yc_truth,r_truth,xc,yc,r))\r\nend","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2017-02-24T17:19:01.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-03-10T17:26:14.000Z","updated_at":"2026-02-16T11:13:15.000Z","published_at":"2013-03-10T18:03:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: [ 0 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory/Hint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The Kasa method provides a best fit circle to a set of points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFuture:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1) Circumscribe 4 points 2) Circumscribe N points 3) The Great Lego Cup Challenge\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":258,"title":"linear least squares fitting","description":"Inputs:\r\n\r\n* |f|: cell-array of function handles\r\n* |x|: column vector of |x| values\r\n* |y|: column vector of |y| values, same length as |x|\r\n\r\nOutput:\r\n\r\n* |a|: column vector of coefficients, same length as |f|\r\n\r\nIn a correct answer the coefficients |a| take values such that the function\r\n\r\n   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)\r\n\r\nminimizes the sum of the squared deviations between |fit(x)| and |y|, i.e.\r\n    sum((fit(x)-y).^2)\r\nis minimal. \r\n\r\nRemarks:\r\n\r\n* The functions will all be vectorized, so e.g. |f{1}(x)| will return results for the whole vector x\r\n* The absolute errors of |a| must be smaller than 1e-6 to pass the tests","description_html":"\u003cp\u003eInputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003ef\u003c/tt\u003e: cell-array of function handles\u003c/li\u003e\u003cli\u003e\u003ctt\u003ex\u003c/tt\u003e: column vector of \u003ctt\u003ex\u003c/tt\u003e values\u003c/li\u003e\u003cli\u003e\u003ctt\u003ey\u003c/tt\u003e: column vector of \u003ctt\u003ey\u003c/tt\u003e values, same length as \u003ctt\u003ex\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutput:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003ea\u003c/tt\u003e: column vector of coefficients, same length as \u003ctt\u003ef\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn a correct answer the coefficients \u003ctt\u003ea\u003c/tt\u003e take values such that the function\u003c/p\u003e\u003cpre\u003e   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)\u003c/pre\u003e\u003cp\u003eminimizes the sum of the squared deviations between \u003ctt\u003efit(x)\u003c/tt\u003e and \u003ctt\u003ey\u003c/tt\u003e, i.e.\r\n    sum((fit(x)-y).^2)\r\nis minimal.\u003c/p\u003e\u003cp\u003eRemarks:\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe functions will all be vectorized, so e.g. \u003ctt\u003ef{1}(x)\u003c/tt\u003e will return results for the whole vector x\u003c/li\u003e\u003cli\u003eThe absolute errors of \u003ctt\u003ea\u003c/tt\u003e must be smaller than 1e-6 to pass the tests\u003c/li\u003e\u003c/ul\u003e","function_template":"function a = fit_coefficients(f,x,y)\r\n  a = zeros(length(f),1);\r\nend","test_suite":"%%% first test: fit to a constant\r\nx = [1,2,3,4]';\r\ny = rand(4,1);\r\nf{1} = @(x) ones(size(x));\r\naref=mean(y);\r\nassert(norm(fit_coefficients(f,x,y)-aref)\u003c1e-6)\r\n\r\n%%% second test: fit to a straight line (linear regression)\r\nx = [1,2,3,4,5]' + randn(5,1);\r\ny = [1,2,3,4,5]' + randn(5,1);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) x;\r\naref(2) = sum((x-mean(x)).*(y-mean(y)))/sum((x-mean(x)).^2);\r\naref(1) = mean(y)-aref(2)*mean(x);\r\nassert(norm(fit_coefficients(f,x,y)-aref')\u003c1e-6)\r\n\r\n%%% third test: polynomial fit\r\nx = [1:15]' + randn(15,1);\r\ny = -10+0.2*x-0.5*x.^2+0.4*x.^3+0.001*log(abs(x)) + 0.2*randn(15,1);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) x;\r\nf{3} = @(x) x.^2;\r\nf{4} = @(x) x.^3;\r\naref = fliplr(polyfit(x,y,3));\r\nassert(norm(fit_coefficients(f,x,y)-aref')\u003c1e-6)\r\n\r\n%%% fourth test: non-polynomial fit (yes, we are that crazy)\r\nx = [0:0.1:2*pi]';\r\ny = 0.123 + 0.456*sin(x).*exp(0.1*x);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) sin(x).*exp(0.1*x);\r\naref=[0.123 0.456]';\r\nassert(norm(fit_coefficients(f,x,y)-aref)\u003c1e-6)","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":165,"test_suite_updated_at":"2013-01-10T10:23:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-04T19:59:00.000Z","updated_at":"2026-04-17T14:21:17.000Z","published_at":"2013-01-09T22:29:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: cell-array of function handles\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values, same length as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of coefficients, same length as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a correct answer the coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e take values such that the function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eminimizes the sum of the squared deviations between\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efit(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, i.e. sum((fit(x)-y).^2) is minimal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemarks:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe functions will all be vectorized, so e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef{1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will return results for the whole vector x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe absolute errors of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e must be smaller than 1e-6 to pass the tests\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45854,"title":"Least Absolute Deviations (L1-norm) line fit - degree n","description":"This is a generalization of Problem 45851 for degree n\r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\u003e\r\n\r\n- - - -\r\n\r\nYou are given two vectors X and Y (coordinates of observations on a plane), and a degree d of the underlying model.\r\nReturn a row vector *P* with the *d+1* coefficients of the best-fit polynomial, in the L1-norm sense. I.e., find *P* of degree *d* that minimizes *sum( abs( Y - polyval(P,X) ) )* .\r\n\r\n(compare your results with polyfit on the test suite!)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.5px 8px; transform-origin: 171.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a generalization of Problem 45851 for degree n\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- - - -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given two vectors X and Y (coordinates of observations on a plane), and a degree d of the underlying model. Return a row vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26px 8px; transform-origin: 26px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ed+1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.5px 8px; transform-origin: 216.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e coefficients of the best-fit polynomial, in the L1-norm sense. I.e., find\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of degree\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that minimizes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5px 8px; transform-origin: 96.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003esum( abs( Y - polyval(P,X) ) )\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(compare your results with polyfit on the test suite!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = LADfit(X,Y,d)\r\nP = polyfit(X,Y,d);\r\nend","test_suite":"%%\r\nd=2;\r\nX=[-2 -1 0 1 2 3]';\r\nY=[7.14 -1.87 -0.89 -0.75 2.08 7.86]';\r\nP=LADfit(X,Y,d); % P_correct = [1.387 -1.243 -0.894]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 3.698\r\nassert(res\u003c4.0)\r\n\r\n%%\r\nd=3;\r\nX=[-4 -3 -2 -1 0 1 2 3 4]';\r\nY=[186 408 21 8 2 -4 -21 -57 -121]';\r\nP=LADfit(X,Y,d); % P_correct = [-2.0431 2.1486 -5.6861 -1.8778]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 341.23\r\nassert(res\u003c350)\r\n\r\n%%\r\nd=3;\r\nn=10; % Nr of points\r\nno=2; % Nr of outliers\r\nmax_res = 0;\r\nmax_ratio = 0;\r\nfor cycle=1:10\r\n    rng('shuffle');\r\n    P=(rand(d,1)-0.5)*10; % Generate model\r\n    X=(rand(n,1)-0.5)*10; % Generate X\r\n    Y=polyval(P,X)+(rand(n,1)-0.5)*2;  % Generate Y and add noise\r\n    Y(1:no)=Y(1:no)+(rand(no,1)-0.5)*50; % Add outliers\r\n    P_lad=LADfit(X,Y,d);\r\n    P_lin=polyfit(X,Y,1);\r\n    Y_lad=polyval(P_lad,X);\r\n    res_lad=sum(abs(Y-Y_lad));\r\n    Y_lin=polyval(P_lin,X);\r\n    res_lin=sum(abs(Y-Y_lin));\r\n    max_res=max(max_res,res_lad);\r\n    max_ratio=max(max_ratio,res_lad/res_lin);\r\nend\r\nassert(max_res\u003c50.0 \u0026 max_ratio\u003c0.98); % Should be always better than L-2 and under 50","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":452188,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2021-04-19T10:10:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-10T08:00:01.000Z","updated_at":"2021-04-19T10:10:15.000Z","published_at":"2020-06-10T08:00:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a generalization of Problem 45851 for degree n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e- - - -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given two vectors X and Y (coordinates of observations on a plane), and a degree d of the underlying model. Return a row vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed+1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients of the best-fit polynomial, in the L1-norm sense. I.e., find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that minimizes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum( abs( Y - polyval(P,X) ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(compare your results with polyfit on the test suite!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59516,"title":"Determine aquifer properties: slug test","description":"An important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems 59152, 49473,  and 59147, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity  of the aquifer are determined. \r\nInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement  of water in the well is given as a function of time  by\r\n\r\nwhere  is the initial displacement,  is the radius of the well casing,  is the radius of the well screen,  is the length of the well screen, and  is the effective distance over which the water table returns to its undisturbed level. If the distance  from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness , then \r\n\r\nIf ,\r\n\r\nBouwer and Rice provided the coefficients , , and  in a figure, and Yang and Yeh (2004) fit the curves as functions of :\r\n\r\n\r\n\r\nWrite a function that computes the distance  and determines the hydraulic conductivity  by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1075.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 537.75px; transform-origin: 407px 537.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 8px; transform-origin: 382.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59152\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59152\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e49473\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59147\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4667px 8px; transform-origin: 89.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer are determined. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.933px 8px; transform-origin: 383.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.075px 8px; transform-origin: 152.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of water in the well is given as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"181\" height=\"42\" alt=\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\" style=\"width: 181px; height: 42px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAACXklEQVRYR+1XOy9FQRB2exoqlYKChNB4hJ5GjYhO4vEDSChFSNB71CIevYRSIvGImoKEhoqGnu+TnWTOOXdf13EjcTaZ7N5z5sx8+83szN5SzR8dpT+Kq6YAFhuZgrF/w9gadtoJGUzt+AW/dyFHkGvzrhnzPGQcUqv0P7A+hmwoXS+BoTl2AUu9xtod5mHIg8X6KJ7vq3djWB94kaQUQoHd4rtW8+0i5lWHIw2MzLZD3n4DWD2MvirDPZ6QbOP9lNE/xTwUC4r6IYzFMqDZnYWPrd8Cphk4hBMCtY00uy2OXHTiDWHsGRYajRUfAzPQ2zS6PCQDleRXSChZAu7V1nwM8PSNGH0fuz9iLJYBzW5FZULQ+kKpGYjN4YZKwxgSyncoSRVn/bpxoJtUYWR+tcXuROu7GOuG4pVS9jFwAl1pXetYsz1VPFzAFmB1xVi+xNzn8fKp3rOosrimBze7DHmEsAc/QXjSM53BBUz3Rx8DZIqMcbBpN5VxJjraFr/pgGTalgtYCAPCiC7CNnZ5YutSoCVddvB8WtNrAxbCgLbja/LS1sodCiEggcUGLKYRhzR53uvmIBlm8ExSJlH3bMB8DGi2dBG2XXPEuQtYIo/LAdNhJABXfyRb5xC5q9nqVwiwBGgNzHU13oNzhkNurdRlsk5ApMELi0z+M4iuYz8CpsOT91qKryuUVsbyBqPt5Zb8eYOUvC1X46RcJFqe73aRJ0C5EmmfUmAz/w2qCczWkvqx+y51sL7JqCYw+iO4JQibtwxepzL/UasNLDg1CmDBVBnFgrGCsVgGYvW/AKlmkikkpPNvAAAAAElFTkSuQmCC\" width=\"19\" height=\"20\" alt=\"H0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.6333px 8px; transform-origin: 83.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the initial displacement, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" alt=\"rc\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well casing, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well screen, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"20\" alt=\"Le\" style=\"width: 16px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the length of the well screen, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.475px 8px; transform-origin: 302.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAoCAYAAACWwljjAAACSElEQVRYR+1WOy9FQRCml3h0NAoKEonKIxEKERKtxKMRhXi1QkKUgnhE6RGFQuHxC6g0Eo9SQUEhESoaer5PdmTc3Ht3zrk2buSc5Muee+7szLff7uxMYUGePYV5xqcgIeTbkUShf6fQMlbUBjSlrOwZv/eAI+DKt+oo/1vP0A2c1jjHJNMK3EcJZLW1EnqCw3LndBbjojVAVDsLoTI4fVGOG397mzRpC6ExTNhQ21WH99eoK7faWwgdwFmvc3iIsc/qPI6dhZA+P+MIshknkHWOj1AVHN0pZ9Whskti+AjNwHDBGd9irLWuNK6dj9AxHHc659sYR+MGss7zEXqDoyLnrB8jD3jQJxshKkOF+LwDlUCwdLecIdaxKWd4gbE5qDTOeTaFzmEjRXUF79N/SShuuaCqORHPpBBv432nCKu7pVywxAzlurWZCG3B8YgjdIKxy7NdVPQB4J2VUyeQiZAuF777h2TOAPZL7ARKgQ6gHpgAdN/ELV0CJFuZxad6EekI6XSnMMywbuVExGJZYdFlf8S7ijd5i7MThXXtE7/6Gxu/YqBCnGpCDMCbmBPkMhQ7y6gzUYJLd6BVTCXZ4+J+xfDd1BYi6Wwa8PESEEJUrEQpKueM33eA7748FCGS/ACYoUPAJLAG8MwISWZyu1YnpEJCiCXnERgEeLjZCpPQKjAPDAA/ylFIhaQw67Mlql2DyJzeKtn3kIRYephBknmMSZJ8hoG0nUNoQuspgUlyF8jYBockJLsQaUwI+eRKFEoU8ing+/8TmVRpKTtSZ0oAAAAASUVORK5CYII=\" width=\"18\" height=\"20\" alt=\"Lw\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.0416667px 8px; transform-origin: 0.0416667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"305.5\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\" style=\"width: 305.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAoCAYAAAB6tz31AAADq0lEQVRoQ+2ZOYgVQRCGd3PBI9NAQQ0UFCMPEA1EFEwFj0Q2EK/EQBQUMRBR8cDMC4MNDDxCI41MBI9wgzXQQBCNNNFc/3/petSb41Vt7+t9r4ce+Jn3ZqZrur+uru7qmZwoR1ICk0mtF+MTBXBiJyiAC+DEBBKbLx5cACcmEGd+BYqtgz5ZxS0PvgUDu6HtFUM/8f8p9NLzEqsSGdwnzJPQFmgztBL6AO2w6m4BlvKz+LEh/CHcXdBXy3gH79Phzod23cb5gtVGL+Afoddo7xJ0wzLc0fun0K4HoW3bPKPXA5jx5pcC5jLcUcDP0a5DEEfxJui31U4PYN1rbsPWizO9/wf1XgK9gA572uABLL1Ge27Dnpdn9sxW1PdjqPNpnB966u8BrOOv27Dn5Zk9cxH1vR7qvB5n1yRvAeby5IsC4TacGTxPdV/joX3QZ2hjKEA+98N1Xqo5oAVY95o27KnQsJ9h49jIhR6xq6B/4cWPceaamHPTFegVxFxBlrF9TC3A0mu0LYYX2sDY8qMErN+9Hw1YC52FjkHM5mSe+ovfa6De6sICLLMmoRwJhmIB5VxOEgwCPAhNQzrZEk61UT4IsO61Ws/kTCui7pLJMj1eDU1Bb4IdvbqojfJBgHVa6Mq7IyqeQ5FqolVNkfU8xfAh4OfaNgjwe9yXTR5X3p0DrYg6MqF4FsrR0Q7oGIvfMk81jvI2wLHpMb3e3ACJaCSLjGqS04lW0zwk8ZeeSw/uO9oA617zpsdctjA2mVt4mQGWRIsT2M6K95rZXRvgRzB0IoBo7JkKJHr8N4iZTpd22nSi1RQmJf5KeCAWtp/r5LmjDbBOj631L+G+g7jQ5k7bcmgvxM3pM5BOKRlCbiovYPx6O8adYm1PSvwVJ+S8dQ9iWGkFXI11TYGdhdm73LpjZsQdJj2EZATo1FHs6mtc/iyFVkmFxuwsANvCpMRf3p9pchbtwfJZhAAIbL6HHkICU3bftJdXoXPh3htS831p4uet7UlZaRHwVai2w2ZlcrH1l+AvgOnRy5THS5zm9SeQ+fEwtiKjLpcKMNvFzRH27BR0DroLccgJdK5U9oyx9w6lb1ID5uz6HeKmCCc7fnoi4DvQNegoZH52GUpLR2QkJWCJXzo2i1dzQrjc5dAg/ZkSMCcArhD04pzQeRyHekuZETnXorw2NeC+NSFaROjTkOt71qIQSPySlIATVz0P8wVw4n4qgAvgxAQSmy8eXAAnJpDYfPHgxID/A9fexCkdfIsxAAAAAElFTkSuQmCC\" width=\"44\" height=\"20\" alt=\"Lw = h\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.9px; text-align: left; transform-origin: 384px 21.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\" style=\"width: 203px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.525px 8px; transform-origin: 132.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBouwer and Rice provided the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.15px 8px; transform-origin: 206.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"101\" height=\"20\" alt=\"x = log10(Le/R)\" style=\"width: 101px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"332.5\" height=\"19.5\" alt=\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\" style=\"width: 332.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"342\" height=\"19.5\" alt=\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\" style=\"width: 342px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"351\" height=\"19.5\" alt=\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\" style=\"width: 351px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136px 8px; transform-origin: 136px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.258px 8px; transform-origin: 132.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and determines the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 8px; transform-origin: 83.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 412.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 206.35px; text-align: left; transform-origin: 384px 206.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"455\" height=\"407\" style=\"vertical-align: baseline;width: 455px;height: 407px\" src=\"data:image/png;base64,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\" alt=\"Schematic of the Bouwer-Rice slug test\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h)\r\n%  t = measurement time\r\n%  H = displacement\r\n%  rc = casing radius\r\n%  R = screen radius\r\n%  Le = screen length\r\n%  Lw = distance from undisturbed water table to bottom of well\r\n%  h = initial saturated thickness\r\n  Re = ln(Re/R) = [1.1/ln(Lw/R) + [A+B*ln((h-Lw)/R)]/(Le/R)]^{-1}\r\n  K = rc^2*log(Re/R)*log(H(1)/H)/(2*Le*t);\r\nend","test_suite":"%%\r\nt = 0:2:16;             %  Measurement times (sec)                                                 \r\nrc = 0.05;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 3;                 %  Screen length (m)\r\nLw = 5;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.5 0.645 0.372 0.195 0.13 0.067 0.044 0.023 0.015];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 2.82e-4;\r\nRe_correct = 1.11;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:5:40;             %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 3.5;               %  Screen length (m)\r\nLw = 15;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [0.8 0.404 0.204 0.103 5.21e-2 2.63e-2 1.33e-2 6.72e-3 3.4e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 9.4e-5;\r\nRe_correct = 4.065;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 14;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 0.978 0.562 0.323 0.186 0.107 6.15e-2 3.53e-2 2.03e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 2.179;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 28;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 1.11 0.719 0.467 0.304 0.197 0.128 8.35e-2 5.43e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 5.592;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:60:480;           %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 5;                 %  Screen length (m)\r\nLw = 30;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 30;                 %  Undisturbed saturated thickness (m)\r\nH = [1.3 0.651 0.326 0.163 8.16e-2 4.09e-2 2.05e-2 1.02e-2 5.13e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 7.43e-6;\r\nRe_correct = 5.608;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nfiletext = fileread('BouwerRice.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-30T14:18:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-30T13:54:14.000Z","updated_at":"2026-02-12T15:36:49.000Z","published_at":"2023-12-30T14:04:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59152\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e59152\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e49473\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e59147\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer are determined. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of water in the well is given as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = H_0 \\\\exp\\\\left(-\\\\frac{2 K L_e t}{r_c^2 \\\\ln(R_e/R)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial displacement, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well casing, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well screen, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Le\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the length of the well screen, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{A+B\\\\ln((h-L_w)/R)}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw = h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w = h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{C}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBouwer and Rice provided the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = log10(Le/R)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = \\\\log_{10}(L_e/R)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and determines the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"407\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"455\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Schematic of the Bouwer-Rice slug test\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":486,"title":"Surface Fit z(x,y)","description":"Given three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00. \r\n\r\nFor example,\r\n\r\n x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\r\n\r\nthen\r\n\r\n z = x.^2-2*x.*y+3*y.^2-4 \r\n\r\nand\r\n\r\n c = [cxx cxy cyy c00] = [1 -2 3 -4]","description_html":"\u003cp\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/p\u003e\u003cp\u003eFor example,\u003c/p\u003e\u003cpre\u003e x = [ 0  0  1  1  2  2  3  3]\r\n y = [ 0  1  0  1  0  1  0  1]\r\n z = [-4 -1 -3 -2  0 -1  5  2]\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e z = x.^2-2*x.*y+3*y.^2-4 \u003c/pre\u003e\u003cp\u003eand\u003c/p\u003e\u003cpre\u003e c = [cxx cxy cyy c00] = [1 -2 3 -4]\u003c/pre\u003e","function_template":"function c = sufit(x,y,z)\r\n  cxx=0;\r\n  cxy=0;\r\n  cyy=0;\r\n  c00=0;\r\n  c=[cxx cxy cyy c00];\r\nend","test_suite":"%%\r\nx= [0 0 1 1 2 2 3 3];\r\ny= [0 1 0 1 0 1 0 1];\r\nz=[-4 -1 -3 -2 0 -1 5 2];\r\nc=[1 -2 3 -4]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,100);\r\ny= rand(1,100);\r\nz=7*x.^2-9*x.*y+11*y.^2-17;\r\nc=[7 -9 11 -17]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n%%\r\nx= rand(1,10000);\r\ny= rand(1,10000);\r\nz=17*x.^2-19*x.*y+11*y.^2-13;\r\nc=[17 -19 11 -13]; \r\nassert(isequal(c,round(sufit(x,y,z))))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2012-03-12T19:23:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-12T17:50:33.000Z","updated_at":"2026-04-17T10:38:50.000Z","published_at":"2012-03-19T09:01:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven three vectors x,y,z. Find four coefficients c = [cxx cxy cyy c00], such that z = cxx*x.^2+cxy*x.*y+cyy*y.^2+c00.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 0  0  1  1  2  2  3  3]\\n y = [ 0  1  0  1  0  1  0  1]\\n z = [-4 -1 -3 -2  0 -1  5  2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z = x.^2-2*x.*y+3*y.^2-4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [cxx cxy cyy c00] = [1 -2 3 -4]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45851,"title":"Least Absolute Deviations (L1-norm) line fit - degree 1","description":"Matlab's polyfit function is very handy to find least-squares regression. It minimizes the (L2-norm) of the estimation errors, by solving a linear system.\r\n\u003chttps://www.mathworks.com/help/matlab/ref/polyfit.html\u003e\r\n\r\nAn often overlooked way to deal with these situations is to use Least Absolute Deviations (LAD) line fitting. It minimizes the L1-norm of the residuals, thus it is less sensitive to outliers that fall far away from the underlying model\r\nhttps://en.wikipedia.org/wiki/Least_absolute_deviations\r\n\r\n- - -\r\n\r\nYou are given two vectors X and Y (coordinates of observations on a plane).\r\nReturn a row vector *P = [a, b]* with the coefficients of the best-fit line, in the L1-norm sense. I.e., find *a* and *b* that minimize *sum( abs( Y - a*X - b ) )* .\r\n\r\n(compare your results with polyfit on the test suite!)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 225px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 112.5px; transform-origin: 407px 112.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMatlab's polyfit function is very handy to find least-squares regression. It minimizes the (L2-norm) of the estimation errors, by solving a linear system.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/polyfit.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://www.mathworks.com/help/matlab/ref/polyfit.html\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u0026gt;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAn often overlooked way to deal with these situations is to use Least Absolute Deviations (LAD) line fitting. It minimizes the L1-norm of the residuals, thus it is less sensitive to outliers that fall far away from the underlying model\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Least_absolute_deviations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Least_absolute_deviations\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e- - -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are given two vectors X and Y (coordinates of observations on a plane). Return a row vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP = [a, b]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e with the coefficients of the best-fit line, in the L1-norm sense. I.e., find\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e that minimize\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003esum( abs( Y - a*X - b ) )\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(compare your results with polyfit on the test suite!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = LADfit(X,Y)\r\nP = polyfit(X,Y,1);\r\nend","test_suite":"%%\r\nX=[-2.8 -4.8 0.9 2.3 3.6 -4.2 -0.7 3.0 0.1 -1.0]';\r\nY=[12.0 6.5 -1.6 -2.1 -2.6 0.1 -1.1 -2.4 -1.3 -1.0]';\r\nP=LADfit(X,Y); % P_correct = [-10/27 -19/15]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 1007/54\r\nassert(res\u003c19)\r\n\r\n%%\r\nX=[1 2 3 4 5]';\r\nY=[1 2 3 4 3]';\r\nP=LADfit(X,Y); % P_correct = [1 0]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 2.0\r\nassert(res\u003c2.1)\r\n\r\n%%\r\nX=[1 2 3 4 5]';\r\nY=[1 0 0 0 0]';\r\nP=LADfit(X,Y); % P_correct = [0 0]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 1.0\r\nassert(res\u003c1.01)\r\n\r\n%%\r\nn=10; % Nr of points\r\nno=2; % Nr of outliers\r\nmax_res = 0;\r\nmax_ratio = 0;\r\nfor cycle=1:10\r\n    rng('shuffle');\r\n    P=(rand(2,1)-0.5)*10; % Generate model\r\n    X=(rand(n,1)-0.5)*2; % Generate X\r\n    Y=polyval(P,X)+(rand(n,1)-0.5);  % Generate Y and add noise\r\n    Y(1:no)=Y(1:no)+(rand(no,1)-0.5)*10; % Add outliers\r\n\r\n    P_lad=LADfit(X,Y);\r\n    P_lin=polyfit(X,Y,1);\r\n\r\n    Y_lad=polyval(P_lad,X);\r\n    res_lad=sum(abs(Y-Y_lad));\r\n\r\n    Y_lin=polyval(P_lin,X);\r\n    res_lin=sum(abs(Y-Y_lin));\r\n\r\n    max_res=max(max_res,res_lad);\r\n    max_ratio=max(max_ratio,res_lad/res_lin);\r\nend\r\nassert(max_res\u003c12.0 \u0026 max_ratio\u003c0.99); % Should be always better than L-2 and under 12.0","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":452188,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2020-11-22T01:25:26.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-10T07:18:59.000Z","updated_at":"2020-11-22T01:25:26.000Z","published_at":"2020-06-10T07:18:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMatlab's polyfit function is very handy to find least-squares regression. It minimizes the (L2-norm) of the estimation errors, by solving a linear system.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/polyfit.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/help/matlab/ref/polyfit.html\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn often overlooked way to deal with these situations is to use Least Absolute Deviations (LAD) line fitting. It minimizes the L1-norm of the residuals, thus it is less sensitive to outliers that fall far away from the underlying model\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Least_absolute_deviations\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Least_absolute_deviations\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e- - -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given two vectors X and Y (coordinates of observations on a plane). Return a row vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP = [a, b]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the coefficients of the best-fit line, in the L1-norm sense. I.e., find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that minimize\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum( abs( Y - a*X - b ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(compare your results with polyfit on the test suite!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1336,"title":"Geometry: Find Circle given 3 Non-Colinear Points","description":"*This Challenge is to determine the center and radius of a circle given three non-colinear points.*\r\n\r\n*Input:* Points\r\n\r\n*Output:* [xc, yc, r] where [xc,yc] are the center and r is the radius\r\n\r\n*Example:*\r\n\r\nInput: Points = [1 0 ; 0 -1 ; 0 1]\r\n\r\nOutput: [ 0 0 1]\r\n\r\n*Theory/Hint:* The Kasa method provides a best fit circle to a set of points.\r\n\r\n*Future:* 1) Circumscribe 4 points  2) Circumscribe N points  3) The Great Lego Cup Challenge","description_html":"\u003cp\u003e\u003cb\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Points\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/p\u003e\u003cp\u003eOutput: [ 0 0 1]\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory/Hint:\u003c/b\u003e The Kasa method provides a best fit circle to a set of points.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e 1) Circumscribe 4 points  2) Circumscribe N points  3) The Great Lego Cup Challenge\u003c/p\u003e","function_template":"function [xc,yc,r]=find_circle(pts)\r\n xc=0;\r\n yc=0;\r\n r=1;\r\n\r\n","test_suite":"%%\r\nfor tests=1:5\r\n xc_truth=randn;\r\n yc_truth=randn;\r\n r_truth=rand;\r\n rand_ang=randi(360,3,1)+rand(3,1); % Avoid duplicate location via rand(3,1)\r\n pts=[xc_truth+r_truth*cosd(rand_ang) yc_truth+r_truth*sind(rand_ang)]; \r\n\r\n [xc,yc,r]=find_circle(pts);\r\n\r\n %dif=[xc yc r]-[xc_truth yc_truth r_truth]\r\n\r\n assert(max(abs([xc,yc,r]-[xc_truth,yc_truth,r_truth]))\u003c1e-6,...\r\nsprintf('Expect xc %.2f yc %.2f r %.2f  Ans:%.2f %.2f %.2f',...\r\n  xc_truth,yc_truth,r_truth,xc,yc,r))\r\nend","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2017-02-24T17:19:01.000Z","rescore_all_solutions":false,"group_id":20,"created_at":"2013-03-10T17:26:14.000Z","updated_at":"2026-02-16T11:13:15.000Z","published_at":"2013-03-10T18:03:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis Challenge is to determine the center and radius of a circle given three non-colinear points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [xc, yc, r] where [xc,yc] are the center and r is the radius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: Points = [1 0 ; 0 -1 ; 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: [ 0 0 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory/Hint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The Kasa method provides a best fit circle to a set of points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFuture:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1) Circumscribe 4 points 2) Circumscribe N points 3) The Great Lego Cup Challenge\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":258,"title":"linear least squares fitting","description":"Inputs:\r\n\r\n* |f|: cell-array of function handles\r\n* |x|: column vector of |x| values\r\n* |y|: column vector of |y| values, same length as |x|\r\n\r\nOutput:\r\n\r\n* |a|: column vector of coefficients, same length as |f|\r\n\r\nIn a correct answer the coefficients |a| take values such that the function\r\n\r\n   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)\r\n\r\nminimizes the sum of the squared deviations between |fit(x)| and |y|, i.e.\r\n    sum((fit(x)-y).^2)\r\nis minimal. \r\n\r\nRemarks:\r\n\r\n* The functions will all be vectorized, so e.g. |f{1}(x)| will return results for the whole vector x\r\n* The absolute errors of |a| must be smaller than 1e-6 to pass the tests","description_html":"\u003cp\u003eInputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003ef\u003c/tt\u003e: cell-array of function handles\u003c/li\u003e\u003cli\u003e\u003ctt\u003ex\u003c/tt\u003e: column vector of \u003ctt\u003ex\u003c/tt\u003e values\u003c/li\u003e\u003cli\u003e\u003ctt\u003ey\u003c/tt\u003e: column vector of \u003ctt\u003ey\u003c/tt\u003e values, same length as \u003ctt\u003ex\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutput:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003ea\u003c/tt\u003e: column vector of coefficients, same length as \u003ctt\u003ef\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn a correct answer the coefficients \u003ctt\u003ea\u003c/tt\u003e take values such that the function\u003c/p\u003e\u003cpre\u003e   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)\u003c/pre\u003e\u003cp\u003eminimizes the sum of the squared deviations between \u003ctt\u003efit(x)\u003c/tt\u003e and \u003ctt\u003ey\u003c/tt\u003e, i.e.\r\n    sum((fit(x)-y).^2)\r\nis minimal.\u003c/p\u003e\u003cp\u003eRemarks:\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe functions will all be vectorized, so e.g. \u003ctt\u003ef{1}(x)\u003c/tt\u003e will return results for the whole vector x\u003c/li\u003e\u003cli\u003eThe absolute errors of \u003ctt\u003ea\u003c/tt\u003e must be smaller than 1e-6 to pass the tests\u003c/li\u003e\u003c/ul\u003e","function_template":"function a = fit_coefficients(f,x,y)\r\n  a = zeros(length(f),1);\r\nend","test_suite":"%%% first test: fit to a constant\r\nx = [1,2,3,4]';\r\ny = rand(4,1);\r\nf{1} = @(x) ones(size(x));\r\naref=mean(y);\r\nassert(norm(fit_coefficients(f,x,y)-aref)\u003c1e-6)\r\n\r\n%%% second test: fit to a straight line (linear regression)\r\nx = [1,2,3,4,5]' + randn(5,1);\r\ny = [1,2,3,4,5]' + randn(5,1);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) x;\r\naref(2) = sum((x-mean(x)).*(y-mean(y)))/sum((x-mean(x)).^2);\r\naref(1) = mean(y)-aref(2)*mean(x);\r\nassert(norm(fit_coefficients(f,x,y)-aref')\u003c1e-6)\r\n\r\n%%% third test: polynomial fit\r\nx = [1:15]' + randn(15,1);\r\ny = -10+0.2*x-0.5*x.^2+0.4*x.^3+0.001*log(abs(x)) + 0.2*randn(15,1);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) x;\r\nf{3} = @(x) x.^2;\r\nf{4} = @(x) x.^3;\r\naref = fliplr(polyfit(x,y,3));\r\nassert(norm(fit_coefficients(f,x,y)-aref')\u003c1e-6)\r\n\r\n%%% fourth test: non-polynomial fit (yes, we are that crazy)\r\nx = [0:0.1:2*pi]';\r\ny = 0.123 + 0.456*sin(x).*exp(0.1*x);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) sin(x).*exp(0.1*x);\r\naref=[0.123 0.456]';\r\nassert(norm(fit_coefficients(f,x,y)-aref)\u003c1e-6)","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":165,"test_suite_updated_at":"2013-01-10T10:23:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-04T19:59:00.000Z","updated_at":"2026-04-17T14:21:17.000Z","published_at":"2013-01-09T22:29:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: cell-array of function handles\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values, same length as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of coefficients, same length as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a correct answer the coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e take values such that the function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eminimizes the sum of the squared deviations between\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efit(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, i.e. sum((fit(x)-y).^2) is minimal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemarks:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe functions will all be vectorized, so e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef{1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will return results for the whole vector x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe absolute errors of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e must be smaller than 1e-6 to pass the tests\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45854,"title":"Least Absolute Deviations (L1-norm) line fit - degree n","description":"This is a generalization of Problem 45851 for degree n\r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\u003e\r\n\r\n- - - -\r\n\r\nYou are given two vectors X and Y (coordinates of observations on a plane), and a degree d of the underlying model.\r\nReturn a row vector *P* with the *d+1* coefficients of the best-fit polynomial, in the L1-norm sense. I.e., find *P* of degree *d* that minimizes *sum( abs( Y - polyval(P,X) ) )* .\r\n\r\n(compare your results with polyfit on the test suite!)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.5px 8px; transform-origin: 171.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a generalization of Problem 45851 for degree n\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e- - - -\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given two vectors X and Y (coordinates of observations on a plane), and a degree d of the underlying model. Return a row vector\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26px 8px; transform-origin: 26px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ed+1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 216.5px 8px; transform-origin: 216.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e coefficients of the best-fit polynomial, in the L1-norm sense. I.e., find\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of degree\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that minimizes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5px 8px; transform-origin: 96.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003esum( abs( Y - polyval(P,X) ) )\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 161px 8px; transform-origin: 161px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(compare your results with polyfit on the test suite!)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = LADfit(X,Y,d)\r\nP = polyfit(X,Y,d);\r\nend","test_suite":"%%\r\nd=2;\r\nX=[-2 -1 0 1 2 3]';\r\nY=[7.14 -1.87 -0.89 -0.75 2.08 7.86]';\r\nP=LADfit(X,Y,d); % P_correct = [1.387 -1.243 -0.894]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 3.698\r\nassert(res\u003c4.0)\r\n\r\n%%\r\nd=3;\r\nX=[-4 -3 -2 -1 0 1 2 3 4]';\r\nY=[186 408 21 8 2 -4 -21 -57 -121]';\r\nP=LADfit(X,Y,d); % P_correct = [-2.0431 2.1486 -5.6861 -1.8778]\r\nres=sum(abs(Y-polyval(P,X))); % Optimal residual = 341.23\r\nassert(res\u003c350)\r\n\r\n%%\r\nd=3;\r\nn=10; % Nr of points\r\nno=2; % Nr of outliers\r\nmax_res = 0;\r\nmax_ratio = 0;\r\nfor cycle=1:10\r\n    rng('shuffle');\r\n    P=(rand(d,1)-0.5)*10; % Generate model\r\n    X=(rand(n,1)-0.5)*10; % Generate X\r\n    Y=polyval(P,X)+(rand(n,1)-0.5)*2;  % Generate Y and add noise\r\n    Y(1:no)=Y(1:no)+(rand(no,1)-0.5)*50; % Add outliers\r\n    P_lad=LADfit(X,Y,d);\r\n    P_lin=polyfit(X,Y,1);\r\n    Y_lad=polyval(P_lad,X);\r\n    res_lad=sum(abs(Y-Y_lad));\r\n    Y_lin=polyval(P_lin,X);\r\n    res_lin=sum(abs(Y-Y_lin));\r\n    max_res=max(max_res,res_lad);\r\n    max_ratio=max(max_ratio,res_lad/res_lin);\r\nend\r\nassert(max_res\u003c50.0 \u0026 max_ratio\u003c0.98); % Should be always better than L-2 and under 50","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":452188,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2021-04-19T10:10:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-10T08:00:01.000Z","updated_at":"2021-04-19T10:10:15.000Z","published_at":"2020-06-10T08:00:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a generalization of Problem 45851 for degree n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e- - - -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given two vectors X and Y (coordinates of observations on a plane), and a degree d of the underlying model. Return a row vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed+1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients of the best-fit polynomial, in the L1-norm sense. I.e., find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of degree\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that minimizes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum( abs( Y - polyval(P,X) ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(compare your results with polyfit on the test suite!)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59516,"title":"Determine aquifer properties: slug test","description":"An important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems 59152, 49473,  and 59147, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity  of the aquifer are determined. \r\nInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement  of water in the well is given as a function of time  by\r\n\r\nwhere  is the initial displacement,  is the radius of the well casing,  is the radius of the well screen,  is the length of the well screen, and  is the effective distance over which the water table returns to its undisturbed level. If the distance  from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness , then \r\n\r\nIf ,\r\n\r\nBouwer and Rice provided the coefficients , , and  in a figure, and Yang and Yeh (2004) fit the curves as functions of :\r\n\r\n\r\n\r\nWrite a function that computes the distance  and determines the hydraulic conductivity  by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1075.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 537.75px; transform-origin: 407px 537.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 8px; transform-origin: 382.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59152\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59152\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e49473\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59147\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4667px 8px; transform-origin: 89.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer are determined. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.933px 8px; transform-origin: 383.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.075px 8px; transform-origin: 152.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of water in the well is given as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"181\" height=\"42\" alt=\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\" style=\"width: 181px; height: 42px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"H0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.6333px 8px; transform-origin: 83.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the initial displacement, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" alt=\"rc\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well casing, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well screen, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"20\" alt=\"Le\" style=\"width: 16px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the length of the well screen, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAoCAYAAABw65OnAAACXElEQVRYR+1XOy8FQRi9t1cIFYVIKEgkKuEHCJXoPGqJV6Ik4QeQUGm8Eo0KhUQjIRKVxKNSUZCgoKKh5xyZ7+a7Y3Z29tpNrmQ3Odm5O+ObM9/jfKNYqIKnWAUcCjkJiULuiX/liU2wHQAaPFX0ibkjYBs4qaTaQnKiDobflHFuNA08AH3AKtBm5jnXn5RICAna/FKGRzDeU79J8gmoMd8W8F5KQiSERBcMXimj9Ri/W5uQ1JD5dod3e9oklmFw1hi9xLvHsYFe84r5xrRJXMBgtzG6gvecYwPtiSiikbxCwqHzgUlnV4CdE1NYs5GmJ4ZhbNcYpJs7rHwggXNAqmMfY5Kwc8bLKc4T1IlxRz4wWXuBGUA0ZAvj+aQEaDuOxK06pes0jP8hcApcJwmBXusj0YKF92pxK8YUqA9ANMGVI4m5+EhMwtq6sahrX4eoIoW0WfpI6LJjvCfMH9viFRfSWM/4DLyopLOlWudKYpkO9UScVLMKFh1VE3tq14IoT8RtYndWSdpUSRzDGts0nyipDlkTRCrKE77WLYZtNfU1LZY7u2wz0AlQ5Eq64iKhQ8EN7aTUp9OaEdUz2GE5x07MnsKG2ASUSGsSdP+YYaw34vWNekF9oFjpR2sGv7OUuamskzIXgiKA7DH05M/z5xq3SOmfInbS2llxO8AzMAqUmlyWJERnqKqPQC1wBvxq81mRELez/Q8C3uaWFQnmF0vYddVjWMpIZUWCuSGVo5NyDd9vgLIrYpYkeGLeNeTSw4o4APS/C5lXh6dwyqey9EROItgDsjAPR1V54htUynUpQju3qgAAAABJRU5ErkJggg==\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.475px 8px; transform-origin: 302.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"Lw\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.0416667px 8px; transform-origin: 0.0416667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"305.5\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\" style=\"width: 305.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"20\" alt=\"Lw = h\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.9px; text-align: left; transform-origin: 384px 21.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\" style=\"width: 203px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.525px 8px; transform-origin: 132.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBouwer and Rice provided the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.15px 8px; transform-origin: 206.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMoAAAAoCAYAAAC/6WUhAAAJW0lEQVR4Xu2cW+jlUxTHZ97J7YkHpswDueca0ZBLiSTlnhQNHiQPJjxIHhBK8uASNUmuSVIKhYhcHtzjgRoST27xzvqM3xpr1uy1f3vvc86v85+zf7X6n//57dtv7f1d+7vWXr+zfl2/uga6BkY1sH60RC/QNdA1sK4DpS+CroECDXSgFCipF5lUA2dLb7+LfDJpryOddaAs02wsfiz7ShfXidyz+K6ae/hZaj68wDEeLG0fJ/J8zQg7UGq0tbbLApLXRG5cNmtt1Hq8fP5YZD+R3xao7vuk7YNELintY9WAooqpsialylzicoDkfZGrlhgkqO8xkQ0i50ygS10DRWDZ3YGiVGOTKP5kkT1E3phoIiaY6+IuPpSS74psydSAkkDLrhTZ35X7aKh/74It/V/S/i0ij46M8265f+4wn1HRX+TGqyLsHt8HhdDL1pH+tlddBaDAR88cJoBnXjWgsFBY/AcUwgrj8qspi74uWzBA6A7L/oQIlKiEdlH+OTPO++WzAvl6+cz/GEau20VSfhlU7y2Ro0UiMG1vYHcHil0b/wz/rBJQWPQ/iIxZaasndpbvzBcnyOcpIlBVVEjGRHTsdTNO79f4+9Fz0C/gPMkqwX/uQMlpZ+3fq91NeGJrqaEvh4uUWPhZtKWAvlYaKfUfb5OyUDCub0UOTQyACJrSyMflM9TSXwqorEHoQJllepe/Lpz/mWCBRKNnoV483Jxq94Uq3SFSSg8ZHv7FicM4oVkp/8uWeUHKRI47gHovc79Tr+Vf680j1J3hUmmh1ErTmbXCN8j/Oce6eXCuIhRqWyWglUrTFFEyQO0v+ywRmKiDfggO7Bk9UN9RdtYM/BzLdNTw9YHDX6wNiyZHQaAPt4qcNtQ5TP7+JPKFyAMiU/B8+zSEWjeL1JxJeP9ko9TPOrnRwqr4Xvus8YWs//G39JUKAPgyZ2TmQGlcOIYcUJh4tuDTRU4VgetZC8P9R4YycNmabbNCj3MrOubMq7I8l7VcOLKwek6xl4z2gmFCWAAAzIdap6IzSjtqjCEUiDnlgvefIrJo/wT9cr6T8jGiyVcjwP2UPjWaNRb10vYVVOEOmlMilfcRIe/mJRE6VUDowqCjQ4beSqyPj0S0oiAK9+XaywFFF0jkFOIUEzniSlEZ5fV+e7eOMRz5yUGfU+wu+Cdfi2SjOU5hUCDmiCtyflvnLKr3jdx4SqQmrYY6uu6szhn7RSKXD+uV3QaHf6xtXZchPSu1NhbBbOVYnT9EiCJgOQFOyeQvI1A04oIhiABozxZQvuWy9l6qvvLkqXYSXZAYBg4Ka4ACuNQK1/o2LQDSlJUSI6vt+3Me3y/z84HIyyJvipRSR/QVOvylQLGWUZ2mKQ6hWpQf1Yl2FEs3cjzZRoPsIrLgTwFFrbQH2DyfLdVWLVB00WpbNb5N67O0pKyk6CHGmhwxvUrXtR13Vl+lDXqLOnqS2aq5BdaLgGJ3yxxQrK/it3s9+EoBRWnbsgPF0svanah12tht7xKpiaxZg2XpoaVjrdQ8fO5SoKAIHUjE41uVNVW9CCg21p4Dit05LI2yljilaF2AOeqlgZEjRRmRU8uufrMIOVvni5DHlMvdqt1RSs4l5jlXtSkr2rcN+dqd3RqyWqDrRhD6ZTVAUSRPbRnnNTklQIni8YwhAgr3cmBT6pXi/Jq0SdQH53QsmKDjo95XIl+KRJm2LKgfRUp9lJJziXnNBe3UpqxQx4evLT30vktLuHlmZ9474bkFlVPmMjrzlnLktuycL6LvenBSjCHRmD1Wjjaj03HqEVlkAQCoFFB0cXgrqRY0crprwsMtaSuM6yyRGtqka6MlZYW6Y2krNmqXO2D0a1TnNgxglOwoNrFOY+w1g7CDWkag2EWS27KtE5kyFBoyx4pznsL1uQgZsWMRQdVLCijqQ3laoHWiMasBKIkojZ1LpIwfOwIJlzn6FxlNze4NT8KDimNA8IAvPdsb1VUJUOy7DOqn2MnhoQmrLfpgKrdTldzLnaNY3htFe5R6phaz7ihbGy1sDii6M6SsnT5TaszqO5WEeWsdYR1vDb2xc9SSskJ9G76OWE1JGb9eGM8RIiGwUkBBwVxYQeWRmr5hLQ91AcmFImshVJwDit3pUrF03VXRCwdaPq+IhcZVc7psJysHFB13Dii5XKdssp8MwvP+MWDpqTcL0mcWazbHMXJvgwhnGZ6aqS9RCzLPRiKDZtdoLhHS6h8dZ1mSB4qN4MC1yVU6T0QPbfzW9qe7bztfps9WyZHDbKmVT9XhXXPyvlKhTJ9TxGm4XlAThOtFkYiCzQqUaHFDKXiW3MtQ1kdjnFHkh7VBGvzm4Xn8ItQoFvScF6jIeyObwVM//Aze2y+lRapLS7v4LgKKPw8ao54679lyHig2Pwl6dYWIP9lUKhDdXyaA8DykMPjXRgFLKm1CkyIJv3Lhb2AMtonkXin1kxjpYOydiBSIS3aUCCi5F7c03UMXfu282V1MF5sFD3QW3fl8sdqUFdq+WkRT6nWc6CoKkVsqicEHvJEvxXrGl0y9q7JDJyU+Sq0CV7E8Vgzg3SlyrFEAWcjq2LMjkSCZohy5HUU5d4565ehS63lF6TwqdSMPkORZcgOfFeF5/Y9ZaNkxK1/a96zlinXTgTKrqv97GejBweql3omwPbDzvCPik/QW4czbflvOLEo1Y4McHIbuLfKZCL6CD/DwHcaj9GyndAwt5XS3Tfmcu7TXgdKi4v/rYCFZFKVZuiwUfsxAF662lAOK+hDe2czVST1V8S+OVKpEI4ZjQQCapWxtykrlcIqLV+mjA6VYr8mCegBW8j6O0rPUOx65RT924FiT1wRA3xZpOSSMNKU+lKdTjBsapruKPuMUyZZjs1qthw6UMZXm7/tM1oekuD1TYnvn55KuESGPK/oBOo0m1qawEGwgUFFzhkVffkebRQsayFBHXt/0hGLZY4NF0r+a8de8FrKj3Q6UGhWny9q4faoEURfCy3oWZcvoucNN8qV9ESkVStYfYHhayrIIidQQhq0ByexPu2sLNn2Hu0RDXxHxfhhBiZpfWVnEWJvb7EBpVt1OFbFSvDa9ScSmr3wq/6+FrIX5aCHfCjR17E3DKcbR1EcHSpPaeqVV00AHyqrNeH/eJg10oDSprVdaNQ10oKzajPfnbdJAB0qT2nqlVdNAB8qqzXh/3iYN/Av404xHdxwSBQAAAABJRU5ErkJggg==\" width=\"101\" height=\"20\" alt=\"x = log10(Le/R)\" style=\"width: 101px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"332.5\" height=\"19.5\" alt=\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\" style=\"width: 332.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"342\" height=\"19.5\" alt=\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\" style=\"width: 342px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"351\" height=\"19.5\" alt=\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\" style=\"width: 351px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136px 8px; transform-origin: 136px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.258px 8px; transform-origin: 132.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and determines the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 8px; transform-origin: 83.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 412.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 206.35px; text-align: left; transform-origin: 384px 206.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"455\" height=\"407\" style=\"vertical-align: baseline;width: 455px;height: 407px\" src=\"data:image/png;base64,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\" alt=\"Schematic of the Bouwer-Rice slug test\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h)\r\n%  t = measurement time\r\n%  H = displacement\r\n%  rc = casing radius\r\n%  R = screen radius\r\n%  Le = screen length\r\n%  Lw = distance from undisturbed water table to bottom of well\r\n%  h = initial saturated thickness\r\n  Re = ln(Re/R) = [1.1/ln(Lw/R) + [A+B*ln((h-Lw)/R)]/(Le/R)]^{-1}\r\n  K = rc^2*log(Re/R)*log(H(1)/H)/(2*Le*t);\r\nend","test_suite":"%%\r\nt = 0:2:16;             %  Measurement times (sec)                                                 \r\nrc = 0.05;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 3;                 %  Screen length (m)\r\nLw = 5;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.5 0.645 0.372 0.195 0.13 0.067 0.044 0.023 0.015];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 2.82e-4;\r\nRe_correct = 1.11;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:5:40;             %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 3.5;               %  Screen length (m)\r\nLw = 15;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [0.8 0.404 0.204 0.103 5.21e-2 2.63e-2 1.33e-2 6.72e-3 3.4e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 9.4e-5;\r\nRe_correct = 4.065;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 14;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 0.978 0.562 0.323 0.186 0.107 6.15e-2 3.53e-2 2.03e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 2.179;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 28;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 1.11 0.719 0.467 0.304 0.197 0.128 8.35e-2 5.43e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 5.592;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:60:480;           %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 5;                 %  Screen length (m)\r\nLw = 30;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 30;                 %  Undisturbed saturated thickness (m)\r\nH = [1.3 0.651 0.326 0.163 8.16e-2 4.09e-2 2.05e-2 1.02e-2 5.13e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 7.43e-6;\r\nRe_correct = 5.608;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nfiletext = fileread('BouwerRice.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-30T14:18:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-30T13:54:14.000Z","updated_at":"2026-02-12T15:36:49.000Z","published_at":"2023-12-30T14:04:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59152\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e59152\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e49473\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e59147\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer are determined. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of water in the well is given as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = H_0 \\\\exp\\\\left(-\\\\frac{2 K L_e t}{r_c^2 \\\\ln(R_e/R)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial displacement, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well casing, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well screen, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Le\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the length of the well screen, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{A+B\\\\ln((h-L_w)/R)}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw = h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w = h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{C}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBouwer and Rice provided the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = log10(Le/R)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = \\\\log_{10}(L_e/R)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and determines the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"407\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"455\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Schematic of the Bouwer-Rice slug test\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"fit\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"fit\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"fit\"","","\"","fit","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fbf309cb728\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fbf309cb688\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fbf309cadc8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fbf309cb9a8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fbf309cb908\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fbf309cb868\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fbf309cb7c8\u003e":"tag:\"fit\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fbf309cb7c8\u003e":"tag:\"fit\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"fit\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"fit\"","","\"","fit","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fbf309cb728\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fbf309cb688\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fbf309cadc8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fbf309cb9a8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fbf309cb908\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fbf309cb868\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fbf309cb7c8\u003e":"tag:\"fit\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fbf309cb7c8\u003e":"tag:\"fit\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":486,"difficulty_rating":"easy-medium"},{"id":45851,"difficulty_rating":"easy-medium"},{"id":1336,"difficulty_rating":"medium"},{"id":258,"difficulty_rating":"medium"},{"id":45854,"difficulty_rating":"medium"},{"id":59516,"difficulty_rating":"medium-hard"}]}}