No BSD License
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adsmax(f, x, stopit, savit, P...
ADSMAX Alternating directions method for direct search optimization.
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augment(A, alpha)
AUGMENT Augmented system matrix.
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cholp(A, piv)
CHOLP Cholesky factorization with pivoting of a positive semidefinite matrix.
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chop(x, t)
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cod(A, tol)
COD Complete orthogonal decomposition.
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cpltaxes(z)
CPLTAXES Determine suitable AXIS for plot of complex vector.
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dual(x, p)
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fv(B, nk, thmax, noplot)
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gep(A, piv)
GEP Gaussian elimination with pivoting: none, complete, partial or rook.
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gersh(A, noplot)
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gfpp(T, c)
GFPP Matrix giving maximal growth factor for Gaussian elim. with pivoting.
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gj(A, b, piv)
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gqr(A, B, partial)
GQR Generalized QR factorization.
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gs_c(A)
GS_C Classical Gram-Schmidt QR factorization.
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gs_m(A)
GS_M Modified Gram-Schmidt QR factorization.
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ldlt_skew(A)
LDLT_SKEW Block LDL^T factorization for a skew-symmetric matrix.
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ldlt_symm(A, piv)
LDLT_SYMM Block LDL^T factorization for a symmetric indefinite matrix.
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ldlt_sytr(A)
LDLT_SYTR Block LDL^T factorization for a symmetric tridiagonal matrix.
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lse(A, b, B, d, method)
LSE Solve the equality constrained least squares problem.
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makejcf(n, e, m, X)
MAKEJCF A matrix with specified Jordan canonical form.
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matrix(k, n)
MATRIX Test matrices accessed by number.
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matsignt(T)
MATSIGNT Matrix sign function of a triangular matrix.
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mdsmax(fun, x, stopit, savit,...
MDSMAX Multidirectional search method for direct search optimization.
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nmsmax(fun, x, stopit, savit,...
NMSMAX Nelder-Mead simplex method for direct search optimization.
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pnorm(A, p, tol, prnt)
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poldec(A)
POLDEC Polar decomposition.
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ps(A, m, tol, rl, marksize)
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pscont(A, k, npts, ax, levels...
PSCONT Contours and colour pictures of pseudospectra.
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rootm(A,p)
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rschur(n, mu, x, y)
RSCHUR An upper quasi-triangular matrix.
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see(A, k)
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seqcheb(n, k)
SEQCHEB Sequence of points related to Chebyshev polynomials.
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seqm(a, b, n)
SEQM Multiplicative sequence.
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show(x)
SHOW Display signs of matrix elements.
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signm(A)
SIGNM Matrix sign decomposition.
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skewpart(A)
SKEWPART Skew-symmetric (skew-Hermitian) part.
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sparsify(A, p)
SPARSIFY Randomly set matrix elements to zero.
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strassen(A, B, nmin)
STRASSEN Strassen's fast matrix multiplication algorithm.
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strassenw(A, B, nmin)
STRASSENW Strassen's fast matrix multiplication algorithm (Winograd variant).
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sub(A, i, j)
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symmpart(A)
SYMMPART Symmetric (Hermitian) part.
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trap2tri(L)
TRAP2TRI Unitary reduction of trapezoidal matrix to triangular form.
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treshape(x,unit)
TRESHAPE Reshape vector to or from (unit) triangular matrix.
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vand(m, p)
VAND Vandermonde matrix.
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vecperm(m, n)
VECPERM Vec-permutation matrix.
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Contents.m
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mctdemo.m
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readme.m
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View all files
from
The Matrix Computation Toolbox
by Nick Higham
A collection of M-files for carrying out various numerical linear algebra tasks.
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| Contents.m |
% Matrix Computation Toolbox.
% Version 1.2 5-Sep-2002
% Copyright (c) 2002 by N. J. Higham
%
% Demonstration
% mctdemo - Demonstration of Matrix Computation Toolbox.
%
% Test Matrices
% augment - Augmented system matrix.
% gfpp - Matrix giving maximal growth factor for Gaussian elimination
% with partial pivoting.
% makejcf - A matrix with specified Jordan canonical form.
% rschur - An upper quasi-triangular matrix.
% vand - Vandermonde matrix.
% vecperm - Vec-permutation matrix.
%
% Visualization
% fv - Field of values (or numerical range).
% gersh - Gershgorin disks.
% ps - Dot plot of a pseudospectrum.
% pscont - Contours and colour pictures of pseudospectra.
% see - Pictures of a matrix.
%
% Factorizations and Decompositions
% cholp - Cholesky factorization with pivoting of a positive semidefinite
% matrix.
% cod - Complete orthogonal decomposition.
% gep - Gaussian elimination with pivoting: none, complete, partial or
% rook.
% gj - Gauss-Jordan elimination with partial pivoting to solve Ax = b.
% gqr - Generalized QR factorization.
% gs_c - Classical Gram-Schmidt QR factorization.
% gs_m - Modified Gram-Schmidt QR factorization.
% ldlt_skew - Block LDL^T factorization for a skew-symmetric matrix.
% ldlt_symm - Block LDL^T factorization for a symmetric indefinite matrix.
% ldlt_sytr - Block LDL^T factorization for a symmetric tridiagonal
% matrix.
% matsignt - Matrix sign function of a triangular matrix.
% poldec - Polar decomposition.
% signm - Matrix sign decomposition.
% trap2tri - Unitary reduction of trapezoidal matrix to triangular form.
%
% Direct Search Optimization
% adsmax - Alternating directions method.
% mdsmax - Multidirectional search method.
% mmsmax - Nelder-Mead simplex method.
%
% Miscellaneous
% chop - Round matrix elements.
% cpltaxes - Determine suitable AXIS for plot of complex vector.
% dual - Dual vector with respect to Holder p-norm.
% lse - Solve the equality constrained least squares problem.
% matrix - Matrix Computation Toolbox information and matrix access by
% number.
% pnorm - Estimate of matrix p-norm (1 <= p <= inf).
% rootm - P'th root of a matrix.
% seqcheb - Sequence of points related to Chebyshev polynomials.
% seqm - Multiplicative sequence.
% show - Display signs of matrix elements.
% skewpart - Skew-symmetric (skew-Hermitian) part.
% sparsify - Randomly set matrix elements to zero.
% strassen - Strassen's fast matrix multiplication algorithm.
% strassenw - Strassen's fast matrix multiplication algorithm (Winograd
% variant).
% sub - Principal submatrix.
% symmpart - Symmetric (Hermitian) part.
% treshape - Reshape vector to or from (unit) triangular matrix.
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