zgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm
SUBROUTINE ZGERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) SUBROUTINE ZGERQ2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER*8 INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER :: M, N, LDA, INFO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A SUBROUTINE GERQ2_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 zgerq2 (int m, int n, doublecomplex *a, int lda, doublecomplex *tau, int *info); void zgerq2_64 (long m, long n, doublecomplex *a, long lda, doublecom- plex *tau, long *info);
Oracle Solaris Studio Performance Library zgerq2(3P) NAME zgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm SYNOPSIS SUBROUTINE ZGERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) SUBROUTINE ZGERQ2_64(M, N, A, LDA, TAU, WORK, INFO) INTEGER*8 INFO, LDA, M, N DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) F95 INTERFACE SUBROUTINE GERQ2(M, N, A, LDA, TAU, WORK, INFO) INTEGER :: M, N, LDA, INFO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A SUBROUTINE GERQ2_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 zgerq2 (int m, int n, doublecomplex *a, int lda, doublecomplex *tau, int *info); void zgerq2_64 (long m, long n, doublecomplex *a, long lda, doublecom- plex *tau, long *info); PURPOSE zgerq2 computes an RQ factorization of a complex 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 COMPLEX*16 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 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 (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 H(2)**H . . . H(k)**H, 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(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 zgerq2(3P)