zgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm
SUBROUTINE ZGEQL2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) SUBROUTINE ZGEQL2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER*8 INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GEQL2(M, N, A, LDA, TAU, WORK, INFO) INTEGER :: M, N, LDA, INFO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A SUBROUTINE GEQL2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER(8) :: M, N, LDA, INFO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void zgeql2 (int m, int n, doublecomplex *a, int lda, doublecomplex *tau, int *info); void zgeql2_64 (long m, long n, doublecomplex *a, long lda, doublecom- plex *tau, long *info);
Oracle Solaris Studio Performance Library zgeql2(3P) NAME zgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm SYNOPSIS SUBROUTINE ZGEQL2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) SUBROUTINE ZGEQL2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER*8 INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GEQL2(M, N, A, LDA, TAU, WORK, INFO) INTEGER :: M, N, LDA, INFO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A SUBROUTINE GEQL2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER(8) :: M, N, LDA, INFO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void zgeql2 (int m, int n, doublecomplex *a, int lda, doublecomplex *tau, int *info); void zgeql2_64 (long m, long n, doublecomplex *a, long lda, doublecom- plex *tau, long *info); PURPOSE zgeql2 computes a QL factorization of a complex m by n matrix A: A = Q * L. 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 COMPLEX*16 array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m >= n, the lower triangle of the subarray A(m- n+1:m,1:n) contains the n by n lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix L; the remaining elements, with the array TAU, represent the unitary 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 COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (output) WORK is COMPLEX*16 array, dimension (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 Q is represented as a product of elementary reflectors Q = H(k) . . . H(2) H(1), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i). 7 Nov 2015 zgeql2(3P)