norm Interface
-
- experimental
- 474 statements
- Source File
public interface norm
Computes the vector norm of a generic-rank array . (Specification)
Summary
Return one of several scalar norm metrics of a real or complex input array ,
that can have any rank. For generic rank-n arrays, the scalar norm over the whole
array is returned by default. If n>=2 and the optional input dimension dim is specified,
a rank n-1 array is returned with dimension dim collapsed, containing all 1D array norms
evaluated along dimension dim only.
Description
This interface provides methods for computing the vector norm(s) of an array.
Supported data types include real and complex.
Input arrays may have generic rank from 1 to 3.
Norm type input is mandatory, 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'
- Euclidean norm : order = 2 or '2'
- p-norm : integer order, order>=3
- Infinity norm : order = huge(0) or 'inf'
- Minus-infinity norm : order = -huge(0) or '-inf'
Example
real(sp) :: a(3,3), na, rown(3)
a = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9], [3, 3])
! L2 norm: whole matrix
na = norm(a, 2)
! Infinity norm of each row
rown = norm(a, 'inf', dim=2)
Functions
private pure module function stdlib_linalg_norm_1D_order_char_c(a, order) result(nrm)
Scalar norms: complex(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_1D_order_char_d(a, order) result(nrm)
Scalar norms: real(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_1D_order_char_s(a, order) result(nrm)
Scalar norms: real(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_1D_order_char_z(a, order) result(nrm)
Scalar norms: complex(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_char_c(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_char_d(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_char_s(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_char_z(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_int_c(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_int_d(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_int_s(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_1D_order_err_int_z(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_1D_order_int_c(a, order) result(nrm)
Scalar norms: complex(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_1D_order_int_d(a, order) result(nrm)
Scalar norms: real(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_1D_order_int_s(a, order) result(nrm)
Scalar norms: real(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_1D_order_int_z(a, order) result(nrm)
Scalar norms: complex(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:) |
Input 1-d matrix a(:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_char_c(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_char_d(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_char_s(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_char_z(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_char_c(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_char_d(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_char_s(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_char_z(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_int_c(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_int_d(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_int_s(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_2D_order_err_int_z(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_int_c(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_int_d(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_int_s(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_order_int_z(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:) |
Input 2-d matrix a(:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_2D_to_1D_char_c(a, order, dim) result(nrm)
Array norms: complex(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_2D_to_1D_char_d(a, order, dim) result(nrm)
Array norms: real(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_2D_to_1D_char_s(a, order, dim) result(nrm)
Array norms: real(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_2D_to_1D_char_z(a, order, dim) result(nrm)
Array norms: complex(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_char_c(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_char_d(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_char_s(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_char_z(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_int_c(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_int_d(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_int_s(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_2D_to_1D_err_int_z(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_2D_to_1D_int_c(a, order, dim) result(nrm)
Array norms: complex(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_2D_to_1D_int_d(a, order, dim) result(nrm)
Array norms: real(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_2D_to_1D_int_s(a, order, dim) result(nrm)
Array norms: real(sp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_2D_to_1D_int_z(a, order, dim) result(nrm)
Array norms: complex(dp)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_order_char_c(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_order_char_d(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_order_char_s(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_order_char_z(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_char_c(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_char_d(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_char_s(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_char_z(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_int_c(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_int_d(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_int_s(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=sp)
Norm of the matrix.
private module function stdlib_linalg_norm_3D_order_err_int_z(a, order, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_order_int_c(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_order_int_d(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_order_int_s(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=sp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_order_int_z(a, order) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in) | :: | a(:,:,:) |
Input 3-d matrix a(:,:,:) |
||
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
Return Value real(kind=dp)
Norm of the matrix.
private pure module function stdlib_linalg_norm_3D_to_2D_char_c(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_to_2D_char_d(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_to_2D_char_s(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_to_2D_char_z(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_char_c(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_char_d(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_char_s(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_char_z(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| character(len=*), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_int_c(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_int_d(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_int_s(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private module function stdlib_linalg_norm_3D_to_2D_err_int_z(a, order, dim, err) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
||
| type(linalg_state_type), | intent(out) | :: | err |
Output state return flag. |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_to_2D_int_c(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_to_2D_int_d(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_to_2D_int_s(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=sp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).
private pure module function stdlib_linalg_norm_3D_to_2D_int_z(a, order, dim) result(nrm)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(in), | target | :: | a(:,:,:) |
Input matrix a[..] |
|
| integer(kind=ilp), | intent(in) | :: | order |
Order of the matrix norm being computed. |
||
| integer(kind=ilp), | intent(in) | :: | dim |
Dimension the norm is computed along |
Return Value
real(kind=dp), (merge(size(a,1),size(a,2),mask=1
Norm of the matrix. (Same shape as a, with dim dropped).