dgeqrt3 - recursively compute a QR factorization of a general real matrix using the compact WY representation of Q
RECURSIVE SUBROUTINE DGEQRT3(M, N, A, LDA, T, LDT, INFO) INTEGER INFO, LDA, M, N, LDT DOUBLE PRECISION A(LDA,*), T(LDT,*) RECURSIVE SUBROUTINE DGEQRT3_64(M, N, A, LDA, T, LDT, INFO) INTEGER*8 INFO, LDA, M, N, LDT DOUBLE PRECISION A(LDA,*), T(LDT,*) F95 INTERFACE RECURSIVE SUBROUTINE GEQRT3(M, N, A, LDA, T, LDT, INFO) INTEGER :: M, N, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T RECURSIVE SUBROUTINE GEQRT3_64(M, N, A, LDA, T, LDT, INFO) INTEGER(8) :: M, N, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T C INTERFACE #include <sunperf.h> void dgeqrt3 (int m, int n, double *a, int lda, double *t, int ldt, int *info); void dgeqrt3_64 (long m, long n, double *a, long lda, double *t, long ldt, long *info);
Oracle Solaris Studio Performance Library dgeqrt3(3P) NAME dgeqrt3 - recursively compute a QR factorization of a general real matrix using the compact WY representation of Q SYNOPSIS RECURSIVE SUBROUTINE DGEQRT3(M, N, A, LDA, T, LDT, INFO) INTEGER INFO, LDA, M, N, LDT DOUBLE PRECISION A(LDA,*), T(LDT,*) RECURSIVE SUBROUTINE DGEQRT3_64(M, N, A, LDA, T, LDT, INFO) INTEGER*8 INFO, LDA, M, N, LDT DOUBLE PRECISION A(LDA,*), T(LDT,*) F95 INTERFACE RECURSIVE SUBROUTINE GEQRT3(M, N, A, LDA, T, LDT, INFO) INTEGER :: M, N, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T RECURSIVE SUBROUTINE GEQRT3_64(M, N, A, LDA, T, LDT, INFO) INTEGER(8) :: M, N, LDA, LDT, INFO REAL(8), DIMENSION(:,:) :: A, T C INTERFACE #include <sunperf.h> void dgeqrt3 (int m, int n, double *a, int lda, double *t, int ldt, int *info); void dgeqrt3_64 (long m, long n, double *a, long lda, double *t, long ldt, long *info); PURPOSE dgeqrt3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000. ARGUMENTS M (input) M is INTEGER The number of rows of the matrix A. M >= N. 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 real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. 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,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT (input) LDT is INTEGER The leading dimension of the array T. LDT >= max(1,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. The block reflector H is then given by H = I - V * T * V**T where V**T is the transpose of V. For details of the algorithm, see Elmroth and Gustavson (cited above). 7 Nov 2015 dgeqrt3(3P)