Computes the singular value decomposition of an M-by-N matrix such that where is an M-by-M orthogonal matrix, is an M-by-N diagonal matrix containing the singular values, and is an N-by-N orthogonal matrix.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(inout), | dimension(:,:) | :: | a |
On input, the M-by-N matrix to factor. The matrix is overwritten on output. |
|
| real(kind=real64), | intent(out), | dimension(:) | :: | s |
A MIN(M, N)-element array containing the singular values of a sorted in descending order. |
|
| real(kind=real64), | intent(out), | optional, | dimension(:,:) | :: | u |
An optional argument, that if supplied, is used to contain the orthogonal matrix from the decomposition. The matrix contains the left singular vectors, and can be either M-by-M (all left singular vectors are computed), or M-by-MIN(M,N) (only the first MIN(M, N) left singular vectors are computed). |
| real(kind=real64), | intent(out), | optional, | dimension(:,:) | :: | vt |
An optional argument, that if supplied, is used to contain the transpose of the N-by-N orthogonal matrix . The matrix contains the right singular vectors. |
| real(kind=real64), | intent(out), | optional, | target, dimension(:) | :: | work |
An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork. |
| integer(kind=int32), | intent(out), | optional | :: | olwork |
An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations. |
|
| class(errors), | intent(inout), | optional, | target | :: | err |
The error object to be updated. |
Computes the singular value decomposition of an M-by-N matrix such that where is an M-by-M orthogonal matrix, is an M-by-N diagonal matrix containing the singular values, and is an N-by-N orthogonal matrix.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=real64), | intent(inout), | dimension(:,:) | :: | a |
On input, the M-by-N matrix to factor. The matrix is overwritten on output. |
|
| real(kind=real64), | intent(out), | dimension(:) | :: | s |
A MIN(M, N)-element array containing the singular values of a sorted in descending order. |
|
| complex(kind=real64), | intent(out), | optional, | dimension(:,:) | :: | u |
An optional argument, that if supplied, is used to contain the orthogonal matrix from the decomposition. The matrix contains the left singular vectors, and can be either M-by-M (all left singular vectors are computed), or M-by-MIN(M,N) (only the first MIN(M, N) left singular vectors are computed). |
| complex(kind=real64), | intent(out), | optional, | dimension(:,:) | :: | vt |
An optional argument, that if supplied, is used to contain the conjugate transpose of the N-by-N orthogonal matrix . The matrix contains the right singular vectors. |
| complex(kind=real64), | intent(out), | optional, | target, dimension(:) | :: | work |
An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork. |
| integer(kind=int32), | intent(out), | optional | :: | olwork |
An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations. |
|
| real(kind=real64), | intent(out), | optional, | target, dimension(:) | :: | rwork |
An optional input, that if provided, prevents any local memory allocation for real-valued workspaces. If not provided, the memory required is allocated within. If provided, the length of the array must be at least 5 * MIN(M, N). |
| class(errors), | intent(inout), | optional, | target | :: | err |
The error object to be updated. |