sgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm
SUBROUTINE SGEQL2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N REAL A(LDA,*), TAU(*), WORK(*) SUBROUTINE SGEQL2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER*8 INFO, LDA, M, N REAL A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GEQL2(M, N, A, LDA, TAU, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: M, N, LDA, INFO REAL, DIMENSION(:) :: TAU, WORK SUBROUTINE GEQL2_64(M, N, A, LDA, TAU, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: M, N, LDA, INFO REAL, DIMENSION(:) :: TAU, WORK C INTERFACE #include <sunperf.h> void sgeql2 (int m, int n, float *a, int lda, float *tau, int *info); void sgeql2_64 (long m, long n, float *a, long lda, float *tau, long *info);
Oracle Solaris Studio Performance Library sgeql2(3P) NAME sgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm SYNOPSIS SUBROUTINE SGEQL2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N REAL A(LDA,*), TAU(*), WORK(*) SUBROUTINE SGEQL2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER*8 INFO, LDA, M, N REAL A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GEQL2(M, N, A, LDA, TAU, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: M, N, LDA, INFO REAL, DIMENSION(:) :: TAU, WORK SUBROUTINE GEQL2_64(M, N, A, LDA, TAU, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: M, N, LDA, INFO REAL, DIMENSION(:) :: TAU, WORK C INTERFACE #include <sunperf.h> void sgeql2 (int m, int n, float *a, int lda, float *tau, int *info); void sgeql2_64 (long m, long n, float *a, long lda, float *tau, long *info); PURPOSE sgeql2 computes a QL factorization of a real 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 REAL 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 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (output) WORK is REAL 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**T 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 sgeql2(3P)