sgerq2(l) [redhat man page]
SGERQ2(l) ) SGERQ2(l) NAME
SGERQ2 - compute an RQ factorization of a real m by n matrix A SYNOPSIS
SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO ) INTEGER INFO, LDA, M, N REAL A( LDA, * ), TAU( * ), WORK( * ) PURPOSE
SGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * Q. ARGUMENTS
M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) REAL 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 orthogonal matrix Q as a product of elementary reflectors (see Further Details). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace) REAL array, dimension (M) INFO (output) 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(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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). LAPACK version 3.0 15 June 2000 SGERQ2(l)
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sgerq2.f(3) LAPACK sgerq2.f(3) NAME
sgerq2.f - SYNOPSIS
Functions/Subroutines subroutine sgerq2 (M, N, A, LDA, TAU, WORK, INFO) SGERQ2 Function/Subroutine Documentation subroutine sgerq2 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO) SGERQ2 Purpose: SGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * Q. Parameters: M M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. A A is REAL 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 orthogonal matrix Q as a product of elementary reflectors (see Further Details). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK WORK is REAL array, dimension (M) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Further Details: The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**T where tau is a real scalar, and v is a real vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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). Definition at line 124 of file sgerq2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 sgerq2.f(3)