--- rpl/lapack/lapack/zgerq2.f 2011/07/22 07:38:14 1.9 +++ rpl/lapack/lapack/zgerq2.f 2011/11/21 20:43:09 1.10 @@ -1,9 +1,132 @@ +*> \brief \b ZGERQ2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZGERQ2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZGERQ2( M, N, A, LDA, TAU, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZGERQ2 computes an RQ factorization of a complex m by n matrix A: +*> A = R * Q. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> 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). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is COMPLEX*16 array, dimension (min(M,N)) +*> The scalar factors of the elementary reflectors (see Further +*> Details). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (M) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16GEcomputational +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> 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). +*> \endverbatim +*> +* ===================================================================== SUBROUTINE ZGERQ2( M, N, A, LDA, TAU, WORK, INFO ) * -* -- LAPACK routine (version 3.3.1) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N @@ -12,59 +135,6 @@ COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZGERQ2 computes an RQ factorization of a complex 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) 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) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* TAU (output) COMPLEX*16 array, dimension (min(M,N)) -* The scalar factors of the elementary reflectors (see Further -* Details). -* -* WORK (workspace) COMPLEX*16 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 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). -* * ===================================================================== * * .. Parameters ..