rescale

Scale range of array elements

Syntax

B = rescale(A)

B = rescale(A,l,u)

B = rescale(___,Name,Value)

Description

B = rescale(A) scales the entries of an array to the interval [0,1]. The output array B is the same size as A.

B = rescale(A,l,u) scales the entries of an array to the interval [l,u].

B = rescale(___,Name,Value) specifies additional parameters for scaling an array for either of the previous syntaxes. For example, rescale(A,'InputMin',5) sets all elements in A that are less than 5 equal to 5 before scaling to the range [0,1].

Examples

Scale to Unit Interval

Scale the entries of a vector to the interval [0,1].

A = 1:5;
B = rescale(A)

B = 1×5

         0    0.2500    0.5000    0.7500    1.0000

Scale to Specified Range

Scale the elements of a vector to the interval [-1,1].

A = 1:5;
B = rescale(A,-1,1)

B = 1×5

   -1.0000   -0.5000         0    0.5000    1.0000

Scale Matrix Columns and Rows

Scale each column of a matrix to the interval [0,1] by specifying the minimum and maximum of each column. rescale scales along the dimension of the input array that corresponds with the shape of the 'InputMin' and 'InputMax' parameter values.

A = magic(3)

A = 3×3

     8     1     6
     3     5     7
     4     9     2

colmin = min(A)

colmin = 1×3

     3     1     2

colmax = max(A)

colmax = 1×3

     8     9     7

Bcol = rescale(A,'InputMin',colmin,'InputMax',colmax)

Bcol = 3×3

    1.0000         0    0.8000
         0    0.5000    1.0000
    0.2000    1.0000         0

Scale each row of A to the interval [0,1].

rowmin = min(A,[],2)

rowmin = 3×1

     1
     3
     2

rowmax = max(A,[],2)

rowmax = 3×1

     8
     7
     9

Brow = rescale(A,'InputMin',rowmin,'InputMax',rowmax)

Brow = 3×3

    1.0000         0    0.7143
         0    0.5000    1.0000
    0.2857    1.0000         0

Input Arguments

A — Input array

scalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array.

• If A has type single, then the output also has type single. Otherwise, the output has type double.

• If A is a scalar, then rescale returns the lower bound of the interval (0 by default) or NaN (when the output range contains Inf).

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

l — Lower bound

0 (default) | scalar | vector | matrix | multidimensional array

Lower bound, specified as a scalar, vector, matrix, or multidimensional array. l must have a size that is compatible with the input array. For example, if A is an M-by-N matrix, then rescale operates along the dimension dictated by the shape of l:

• If l is a scalar, then rescale uses it as the lower bound for all elements of A.

• If l is a 1-by-N row vector, then rescale uses each element as the lower bound for the corresponding column of A.

• If l is an M-by-1 column vector, then rescale uses each element as the lower bound for the corresponding row of A.

For more information on compatible array sizes, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

u — Upper bound

1 (default) | scalar | vector | matrix | multidimensional array

Upper bound, specified as a scalar, vector, matrix, or multidimensional array. u must have a size that is compatible with the input array. For example, if A is an M-by-N matrix, then rescale operates along the dimension dictated by the shape of u:

• If u is a scalar, then rescale uses it as the upper bound for all elements of A.

• If u is a 1-by-N row vector, then rescale uses each element as the upper bound for the corresponding column of A.

• If u is an M-by-1 column vector, then rescale uses each element as the upper bound for the corresponding row of A.

For more information on compatible array sizes, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: B = rescale(A,'InputMin',5,'InputMax',10)

'InputMin' — Minimum of input range

scalar | vector | matrix | multidimensional array

Minimum of input range, specified as a scalar, vector, matrix, or multidimensional array. The default value for an input array A is min(A(:)). Specifying an input range either expands or shrinks the range of the input data. For instance, rescale sets all elements that are less than the specified input minimum to the 'InputMin' value before scaling.

The 'InputMin' value must have a size that is compatible with the input array. For example, if A is an M-by-N matrix, then rescale operates along the dimension dictated by the shape of the input minimum:

• If the input minimum is a scalar, then rescale uses that minimum value for all elements of A.

• If the input minimum is a 1-by-N row vector, then rescale uses each element as the minimum for the corresponding column of A.

• If the input minimum is an M-by-1 column vector, then rescale uses each element as the minimum for the corresponding row of A.

For more information on compatible array sizes, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

'InputMax' — Maximum of input range

scalar | vector | matrix | multidimensional array

Maximum of input range, specified as a scalar, vector, matrix, or multidimensional array. The default value for an input array A is max(A(:)). Specifying an input range either expands or shrinks the range of the input data. For instance, rescale sets all elements that are greater than the specified input maximum to the 'InputMax' value before scaling.

The 'InputMax' value must have a size that is compatible with the input array. For example, if A is an M-by-N matrix, then rescale operates along the dimension dictated by the shape of the input maximum:

• If the input maximum is a scalar, then rescale uses that maximum value for all elements of A.

• If the input maximum is a 1-by-N row vector, then rescale uses each element as the maximum for the corresponding column of A.

• If the input maximum is an M-by-1 column vector, then rescale uses each element as the maximum for the corresponding row of A.

For more information on compatible array sizes, see Compatible Array Sizes for Basic Operations.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Algorithms

B = rescale(A,l,u,'InputMin',inmin,'InputMax',inmax) uses the formula

l + [(A-inmin)./(inmax-inmin)].*(u-l)

to scale the elements of an array A.

• If l and u are not specified, then rescale uses the default values 0 and 1, respectively.

• If the 'InputMin' name-value pair is not specified, then rescale sets its value to the default min(A(:)).

• If the 'InputMax' name-value pair is not specified, then rescale sets its value to the default max(A(:)).

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

• The inputs l and u, and the value of the name-value pairs 'InputMin' and 'InputMax', cannot have more than one row.

For more information, see Tall Arrays.

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