sggqrf
sggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B.
SUBROUTINE SGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, LWORK,
* INFO)
INTEGER N, M, P, LDA, LDB, LWORK, INFO
REAL A(LDA,*), TAUA(*), B(LDB,*), TAUB(*), WORK(*)
SUBROUTINE SGGQRF_64( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
* LWORK, INFO)
INTEGER*8 N, M, P, LDA, LDB, LWORK, INFO
REAL A(LDA,*), TAUA(*), B(LDB,*), TAUB(*), WORK(*)
SUBROUTINE GGQRF( [N], [M], [P], A, [LDA], TAUA, B, [LDB], TAUB,
* [WORK], [LWORK], [INFO])
INTEGER :: N, M, P, LDA, LDB, LWORK, INFO
REAL, DIMENSION(:) :: TAUA, TAUB, WORK
REAL, DIMENSION(:,:) :: A, B
SUBROUTINE GGQRF_64( [N], [M], [P], A, [LDA], TAUA, B, [LDB], TAUB,
* [WORK], [LWORK], [INFO])
INTEGER(8) :: N, M, P, LDA, LDB, LWORK, INFO
REAL, DIMENSION(:) :: TAUA, TAUB, WORK
REAL, DIMENSION(:,:) :: A, B
#include <sunperf.h>
void sggqrf(int n, int m, int p, float *a, int lda, float *taua, float *b, int ldb, float *taub, int *info);
void sggqrf_64(long n, long m, long p, float *a, long lda, float *taua, float *b, long ldb, float *taub, long *info);
sggqrf computes a generalized QR factorization of an N-by-M matrix A
and an N-by-P matrix B:
A = Q*R, B = Q*T*Z,
where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
matrix, and R and T assume one of the forms:
if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
( 0 ) N-M N M-N
M
where R11 is upper triangular, and
if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,
P-N N ( T21 ) P
P
where T12 or T21 is upper triangular.
In particular, if B is square and nonsingular, the GQR factorization
of A and B implicitly gives the QR factorization of inv(B)*A:
inv(B)*A = Z'*(inv(T)*R)
where inv(B) denotes the inverse of the matrix B, and Z' denotes the
transpose of the matrix Z.
-
* N (input)
-
The number of rows of the matrices A and B. N >= 0.
-
* M (input)
-
The number of columns of the matrix A. M >= 0.
-
* P (input)
-
The number of columns of the matrix B. P >= 0.
-
* A (input/output)
-
On entry, the N-by-M matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(N,M)-by-M upper trapezoidal matrix R (R is
upper triangular if N >= M); the elements below the diagonal,
with the array TAUA, represent the orthogonal matrix Q as a
product of min(N,M) elementary reflectors (see Further
Details).
-
* LDA (input)
-
The leading dimension of the array A. LDA >= max(1,N).
-
* TAUA (output)
-
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Q (see Further Details).
-
* B (input/output)
-
On entry, the N-by-P matrix B.
On exit, if N <= P, the upper triangle of the subarray
B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
if N > P, the elements on and above the (N-P)-th subdiagonal
contain the N-by-P upper trapezoidal matrix T; the remaining
elements, with the array TAUB, represent the orthogonal
matrix Z as a product of elementary reflectors (see Further
Details).
-
* LDB (input)
-
The leading dimension of the array B. LDB >= max(1,N).
-
* TAUB (output)
-
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Z (see Further Details).
-
* WORK (workspace)
-
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-
* LWORK (input)
-
The dimension of the array WORK. LWORK >= max(1,N,M,P).
For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
where NB1 is the optimal blocksize for the QR factorization
of an N-by-M matrix, NB2 is the optimal blocksize for the
RQ factorization of an N-by-P matrix, and NB3 is the optimal
blocksize for a call of SORMQR.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
-
* INFO (output)
-