solve_lstsq Interface
-
- experimental
- 102 statements
- Source File
public interface solve_lstsq
Computes the squares solution to system . (Specification)
Summary
Subroutine interface for computing least squares, i.e. the 2-norm minimizing solution.
Description
This interface provides methods for computing the least squares of a linear matrix system using
a subroutine. Supported data types include real and complex. If pre-allocated work spaces
are provided, no internal memory allocations take place when using this interface.
Note
The solution is based on LAPACK's singular value decomposition *GELSD methods.
Subroutines
private module subroutine stdlib_linalg_c_solve_lstsq_many(a, b, x, real_storage, int_storage, cmpl_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| complex(kind=sp), | intent(in) | :: | b(:,:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| complex(kind=sp), | intent(inout), | contiguous, target | :: | x(:,:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=sp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| complex(kind=sp), | intent(inout), | optional, | target | :: | cmpl_storage(:) |
[optional] complex working storage space |
| real(kind=sp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=sp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_c_solve_lstsq_one(a, b, x, real_storage, int_storage, cmpl_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| complex(kind=sp), | intent(in) | :: | b(:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| complex(kind=sp), | intent(inout), | contiguous, target | :: | x(:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=sp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| complex(kind=sp), | intent(inout), | optional, | target | :: | cmpl_storage(:) |
[optional] complex working storage space |
| real(kind=sp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=sp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_d_solve_lstsq_many(a, b, x, real_storage, int_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| real(kind=dp), | intent(in) | :: | b(:,:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| real(kind=dp), | intent(inout), | contiguous, target | :: | x(:,:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=dp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| real(kind=dp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=dp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_d_solve_lstsq_one(a, b, x, real_storage, int_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| real(kind=dp), | intent(in) | :: | b(:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| real(kind=dp), | intent(inout), | contiguous, target | :: | x(:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=dp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| real(kind=dp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=dp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_s_solve_lstsq_many(a, b, x, real_storage, int_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| real(kind=sp), | intent(in) | :: | b(:,:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| real(kind=sp), | intent(inout), | contiguous, target | :: | x(:,:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=sp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| real(kind=sp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=sp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_s_solve_lstsq_one(a, b, x, real_storage, int_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| real(kind=sp), | intent(in) | :: | b(:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| real(kind=sp), | intent(inout), | contiguous, target | :: | x(:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=sp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| real(kind=sp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=sp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_z_solve_lstsq_many(a, b, x, real_storage, int_storage, cmpl_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| complex(kind=dp), | intent(in) | :: | b(:,:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| complex(kind=dp), | intent(inout), | contiguous, target | :: | x(:,:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=dp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| complex(kind=dp), | intent(inout), | optional, | target | :: | cmpl_storage(:) |
[optional] complex working storage space |
| real(kind=dp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=dp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_z_solve_lstsq_one(a, b, x, real_storage, int_storage, cmpl_storage, cond, singvals, overwrite_a, rank, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[n,n] |
|
| complex(kind=dp), | intent(in) | :: | b(:) |
Right hand side vector or array, b[n] or b[n,nrhs] |
||
| complex(kind=dp), | intent(inout), | contiguous, target | :: | x(:) |
Result array/matrix x[n] or x[n,nrhs] |
|
| real(kind=dp), | intent(inout), | optional, | target | :: | real_storage(:) |
[optional] real working storage space |
| integer(kind=ilp), | intent(inout), | optional, | target | :: | int_storage(:) |
[optional] integer working storage space |
| complex(kind=dp), | intent(inout), | optional, | target | :: | cmpl_storage(:) |
[optional] complex working storage space |
| real(kind=dp), | intent(in), | optional | :: | cond |
[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0. |
|
| real(kind=dp), | intent(out), | optional, | target | :: | singvals(:) |
[optional] list of singular values [min(m,n)], in descending magnitude order, returned by the SVD |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A,b data be overwritten and destroyed? |
|
| integer(kind=ilp), | intent(out), | optional | :: | rank |
[optional] Return rank of A |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |