dgeqrt - N matrix A using the compact WY representation of Q
SUBROUTINE DGEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER INFO, LDA, LDT, M, N, NB DOUBLE PRECISION A(LDA,*), T(LDT,*), WORK(*) SUBROUTINE DGEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER*8 INFO, LDA, LDT, M, N, NB DOUBLE PRECISION A(LDA,*), T(LDT,*), WORK(*) F95 INTERFACE SUBROUTINE GEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER :: M, N, NB, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T REAL(8), DIMENSION(:) :: WORK SUBROUTINE GEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER(8) :: M, N, NB, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T REAL(8), DIMENSION(:) :: WORK C INTERFACE #include <sunperf.h> void dgeqrt (int m, int n, int nb, double *a, int lda, double *t, int ldt, int *info); void dgeqrt_64 (long m, long n, long nb, double *a, long lda, double *t, long ldt, long *info);
Oracle Solaris Studio Performance Library dgeqrt(3P) NAME dgeqrt - compute a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q SYNOPSIS SUBROUTINE DGEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER INFO, LDA, LDT, M, N, NB DOUBLE PRECISION A(LDA,*), T(LDT,*), WORK(*) SUBROUTINE DGEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER*8 INFO, LDA, LDT, M, N, NB DOUBLE PRECISION A(LDA,*), T(LDT,*), WORK(*) F95 INTERFACE SUBROUTINE GEQRT(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER :: M, N, NB, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T REAL(8), DIMENSION(:) :: WORK SUBROUTINE GEQRT_64(M, N, NB, A, LDA, T, LDT, WORK, INFO) INTEGER(8) :: M, N, NB, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T REAL(8), DIMENSION(:) :: WORK C INTERFACE #include <sunperf.h> void dgeqrt (int m, int n, int nb, double *a, int lda, double *t, int ldt, int *info); void dgeqrt_64 (long m, long n, long nb, double *a, long lda, double *t, long ldt, long *info); PURPOSE dgeqrt computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of 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. NB (input) NB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1. A (input/output) A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V. LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T (output) T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for fur- ther details. LDT (input) LDT is INTEGER The leading dimension of the array T. LDT >= NB. WORK (output) WORK is DOUBLE PRECISION array, dimension (NB*N) INFO (output) INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value FURTHER DETAILS The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-N matrix T as T = (T1 T2 ... TB). 7 Nov 2015 dgeqrt(3P)