dgelq2 (3p)

Name

dgelq2 - compute the LQ factorization of a general rectangular matrix using an unblocked algorithm

Synopsis

SUBROUTINE DGELQ2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER INFO, LDA, M, N

DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


SUBROUTINE DGELQ2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


F95 INTERFACE
SUBROUTINE GELQ2(M, N, A, LDA, TAU, WORK, INFO)


INTEGER :: M, N, LDA, INFO

REAL(8), DIMENSION(:,:) :: A

REAL(8), DIMENSION(:) :: TAU, WORK


SUBROUTINE GELQ2_64(M, N, A, LDA, TAU, WORK, INFO)


INTEGER(8) :: M, N, LDA, INFO

REAL(8), DIMENSION(:,:) :: A

REAL(8), DIMENSION(:) :: TAU, WORK


C INTERFACE
#include <sunperf.h>

void dgelq2 (int m, int n, double *a, int lda, double *tau, int *info);


void  dgelq2_64 (long m, long n, double *a, long lda, double *tau, long
*info);

Description

Oracle Solaris Studio Performance Library                           dgelq2(3P)



NAME
       dgelq2  -  compute the LQ factorization of a general rectangular matrix
       using an unblocked algorithm


SYNOPSIS
       SUBROUTINE DGELQ2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER INFO, LDA, M, N

       DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


       SUBROUTINE DGELQ2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

       DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


   F95 INTERFACE
       SUBROUTINE GELQ2(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER :: M, N, LDA, INFO

       REAL(8), DIMENSION(:,:) :: A

       REAL(8), DIMENSION(:) :: TAU, WORK


       SUBROUTINE GELQ2_64(M, N, A, LDA, TAU, WORK, INFO)


       INTEGER(8) :: M, N, LDA, INFO

       REAL(8), DIMENSION(:,:) :: A

       REAL(8), DIMENSION(:) :: TAU, WORK


   C INTERFACE
       #include <sunperf.h>

       void dgelq2 (int m, int n, double *a, int lda, double *tau, int *info);


       void  dgelq2_64 (long m, long n, double *a, long lda, double *tau, long
                 *info);


PURPOSE
       dgelq2 computes an LQ factorization of a real m by n matrix A: A=L*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 DOUBLE PRECISION array, dimension (LDA,N)
                 On entry, the m by n matrix A.
                 On exit, the elements on and below the diagonal of the  array
                 contain  the  m  by min(m,n) lower trapezoidal matrix L (L is
                 lower triangular if m <= n); the elements above the diagonal,
                 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 DOUBLE PRECISION array, dimension (min(M,N))
                 The scalar factors of the elementary reflectors (see  Further
                 Details).


       WORK (output)
                 WORK is DOUBLE PRECISION 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(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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
       A(i,i+1:n), and tau in TAU(i).



                                  7 Nov 2015                        dgelq2(3P)