mnorm Interface
public interface mnorm
Matrix norms: function interface version: experimental
Computes the matrix norm of a generic-rank array . (Specification)
Summary
Return one of several matrix norm metrics of a real or complex input array ,
that can have rank 2 or higher. For rank-2 arrays, the matrix norm is returned.
If rank>2 and the optional input dimensions dim are specified,
a rank n-2 array is returned with dimensions dim(1),dim(2) collapsed, containing all
matrix norms evaluated over the specified dimensions only. dim==[1,2] are assumed as default
dimensions if not specified.
Description
This interface provides methods for computing the matrix norm(s) of an array.
Supported data types include real and complex.
Input arrays must have rank >= 2.
Norm type input is optional, and it is provided via the order argument.
This can be provided as either an integer value or a character string.
Allowed metrics are:
- 1-norm: order = 1 or '1'
- 2-norm: order = 2 or '2'
- Euclidean/Frobenius: order = 'Euclidean','Frobenius', or argument not specified
- Infinity norm: order = huge(0) or 'Inf'
If an invalid norm type is provided, the routine returns an error state.
Example
real(sp) :: a(3,3), na
real(sp) :: b(3,3,4), nb(4) ! Array of 4 3x3 matrices
a = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9], [3, 3])
! Euclidean/Frobenius norm of single matrix
na = mnorm(a)
na = mnorm(a, 'Euclidean')
! 1-norm of each 3x3 matrix in b
nb = mnorm(b, 1, dim=[1,2])
! Infinity-norm
na = mnorm(b, 'inf', dim=[3,2])
Functions
private module function matrix_norm_3D_to_1D_char_c(a, order, dim, err) result(nrm)
Matrix norms: complex(sp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_3D_to_1D_char_d(a, order, dim, err) result(nrm)
Matrix norms: real(dp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_3D_to_1D_char_s(a, order, dim, err) result(nrm)
Matrix norms: real(sp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_3D_to_1D_char_z(a, order, dim, err) result(nrm)
Matrix norms: complex(dp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_3D_to_1D_int_c(a, order, dim, err) result(nrm)
Matrix norms: complex(sp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_3D_to_1D_int_d(a, order, dim, err) result(nrm)
Matrix norms: real(dp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_3D_to_1D_int_s(a, order, dim, err) result(nrm)
Matrix norms: real(sp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_3D_to_1D_int_z(a, order, dim, err) result(nrm)
Matrix norms: complex(dp) higher rank arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | contiguous, target | :: | a(:,:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| integer(kind=ilp), | intent(in), | optional | :: | dim(2) |
[optional] dimensions of the sub-matrices the norms should be evaluated at (default = [1,2]) |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp), allocatable, (:)
Norm of the matrix.
private module function matrix_norm_char_c(a, order, err) result(nrm)
Matrix norms: complex(sp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp)
Norm of the matrix.
private module function matrix_norm_char_d(a, order, err) result(nrm)
Matrix norms: real(dp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp)
Norm of the matrix.
private module function matrix_norm_char_s(a, order, err) result(nrm)
Matrix norms: real(sp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp)
Norm of the matrix.
private module function matrix_norm_char_z(a, order, err) result(nrm)
Matrix norms: complex(dp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp)
Norm of the matrix.
private module function matrix_norm_int_c(a, order, err) result(nrm)
Matrix norms: complex(sp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp)
Norm of the matrix.
private module function matrix_norm_int_d(a, order, err) result(nrm)
Matrix norms: real(dp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp)
Norm of the matrix.
private module function matrix_norm_int_s(a, order, err) result(nrm)
Matrix norms: real(sp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=sp)
Norm of the matrix.
private module function matrix_norm_int_z(a, order, err) result(nrm)
Matrix norms: complex(dp) rank-2 arrays
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a(m,n) |
|
| integer(kind=ilp), | intent(in), | optional | :: | order |
Order of the matrix norm being computed. |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
Return Value real(kind=dp)
Norm of the matrix.