Computes the QR factorization of an M-by-N matrix.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in), | dimension(:,:) | :: | a |
The M-by-N matrix to factor. |
|
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:) | :: | tau |
A MIN(M, N)-element array used to store the scalar factors of the elementary reflectors. |
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | qr |
The M-by-N factored matrix stored such that the elements on and above the diagonal contain the MIN(M, N)-by-N upper trapezoidal matrix ( is upper triangular if M >= N). The elements below the diagonal, along with the array tau, represent the orthogonal matrix as a product of elementary reflectors. |
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | q |
The M-by-M orthogonal matrix . |
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | r |
The M-by-N upper trapezoidal matrix . |
Computes the QR factorization of an M-by-N matrix.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=real64), | intent(in), | dimension(:,:) | :: | a |
The M-by-N matrix to factor. |
|
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:) | :: | tau |
A MIN(M, N)-element array used to store the scalar factors of the elementary reflectors. |
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | qr |
The M-by-N factored matrix stored such that the elements on and above the diagonal contain the MIN(M, N)-by-N upper trapezoidal matrix ( is upper triangular if M >= N). The elements below the diagonal, along with the array tau, represent the orthogonal matrix as a product of elementary reflectors. |
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | q |
The M-by-M orthogonal matrix . |
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | r |
The M-by-N upper trapezoidal matrix . |
Computes the QR factorization of an M-by-N matrix using column pivoting such that .
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in), | dimension(:,:) | :: | a |
The M-by-N matrix to factor. |
|
| integer(kind=int32), | intent(inout), | dimension(:) | :: | jpvt |
On input, an N-element array that if JPVT(I) .ne. 0, the I-th column of A is permuted to the front of A * P; if JPVT(I) = 0, the I-th column of A is a free column. On output, if JPVT(I) = K, then the I-th column of A * P was the K-th column of A. |
|
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:) | :: | tau |
A MIN(M, N)-element array used to store the scalar factors of the elementary reflectors. |
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | qr |
The M-by-N factored matrix stored such that the elements on and above the diagonal contain the MIN(M, N)-by-N upper trapezoidal matrix ( is upper triangular if M >= N). The elements below the diagonal, along with the array tau, represent the orthogonal matrix as a product of elementary reflectors. |
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | q |
The M-by-M orthogonal matrix . |
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | r |
The M-by-N upper trapezoidal matrix . |
| real(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | p |
The N-by-N column-pivot tracking matrix where . |
Computes the QR factorization of an M-by-N matrix using column pivoting such that .
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=real64), | intent(in), | dimension(:,:) | :: | a |
The M-by-N matrix to factor. |
|
| integer(kind=int32), | intent(inout), | dimension(:) | :: | jpvt |
On input, an N-element array that if JPVT(I) .ne. 0, the I-th column of A is permuted to the front of A * P; if JPVT(I) = 0, the I-th column of A is a free column. On output, if JPVT(I) = K, then the I-th column of A * P was the K-th column of A. |
|
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:) | :: | tau |
A MIN(M, N)-element array used to store the scalar factors of the elementary reflectors. |
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | qr |
The M-by-N factored matrix stored such that the elements on and above the diagonal contain the MIN(M, N)-by-N upper trapezoidal matrix ( is upper triangular if M >= N). The elements below the diagonal, along with the array tau, represent the orthogonal matrix as a product of elementary reflectors. |
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | q |
The M-by-M orthogonal matrix . |
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | r |
The M-by-N upper trapezoidal matrix . |
| complex(kind=real64), | intent(out), | optional, | allocatable, target, dimension(:,:) | :: | p |
The N-by-N column-pivot tracking matrix where . |