dgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm
SUBROUTINE DGERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) SUBROUTINE DGERQ2_64( M, N, A, LDA, TAU, WORK, INFO ) INTEGER*8 INFO, LDA, M, N DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER :: M, N, LDA, INFO REAL(8), DIMENSION(:,:) :: A REAL(8), DIMENSION(:) :: TAU, WORK SUBROUTINE GERQ2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER(8) :: M, N, LDA, INFO REAL(8), DIMENSION(:,:) :: A REAL(8), DIMENSION(:) :: TAU, WORK C INTERFACE #include <sunperf.h> void dgerq2 (int m, int n, double *a, int lda, double *tau, int *info); void dgerq2_64 (long m, long n, double *a, long lda, double *tau, long *info);
Oracle Solaris Studio Performance Library dgerq2(3P) NAME dgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm SYNOPSIS SUBROUTINE DGERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) SUBROUTINE DGERQ2_64( M, N, A, LDA, TAU, WORK, INFO ) INTEGER*8 INFO, LDA, M, N DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER :: M, N, LDA, INFO REAL(8), DIMENSION(:,:) :: A REAL(8), DIMENSION(:) :: TAU, WORK SUBROUTINE GERQ2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER(8) :: M, N, LDA, INFO REAL(8), DIMENSION(:,:) :: A REAL(8), DIMENSION(:) :: TAU, WORK C INTERFACE #include <sunperf.h> void dgerq2 (int m, int n, double *a, int lda, double *tau, int *info); void dgerq2_64 (long m, long n, double *a, long lda, double *tau, long *info); PURPOSE dgerq2 computes an RQ factorization of a real m by n matrix A: A = R * Q. ARGUMENTS M (input) M is INTEGER The number of rows of the matrix A. M >= 0. N (input) N is INTEGER The number of columns of the matrix A. N >= 0. A (input/output) A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M by N matrix A. On exit, if M <= N, the upper triangle of the subarray A(1:M,N-M+1:N) contains the M by M upper triangular matrix R; if M >= N, the elements on and above the (M-N)-th subdiagonal contain the M by N upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (output) WORK is DOUBLE PRECISION array, dimension (M) INFO (output) INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value FURTHER DETAILS The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**T where tau is a real scalar, and v is a real vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). 7 Nov 2015 dgerq2(3P)