--- rpl/lapack/lapack/dgeqp3.f 2011/07/22 07:38:05 1.8 +++ rpl/lapack/lapack/dgeqp3.f 2011/11/21 20:42:51 1.9 @@ -1,9 +1,160 @@ +*> \brief \b DGEQP3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DGEQP3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, LWORK, M, N +* .. +* .. Array Arguments .. +* INTEGER JPVT( * ) +* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGEQP3 computes a QR factorization with column pivoting of a +*> matrix A: A*P = Q*R using Level 3 BLAS. +*> \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 DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the M-by-N matrix A. +*> On exit, the upper triangle of the array contains the +*> min(M,N)-by-N upper trapezoidal matrix R; the elements below +*> the diagonal, together with the array TAU, represent the +*> orthogonal matrix Q as a product of min(M,N) elementary +*> reflectors. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[in,out] JPVT +*> \verbatim +*> JPVT is INTEGER array, dimension (N) +*> On entry, if JPVT(J).ne.0, the J-th column of A is permuted +*> to the front of A*P (a leading column); if JPVT(J)=0, +*> the J-th column of A is a free column. +*> On exit, if JPVT(J)=K, then the J-th column of A*P was the +*> the K-th column of A. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION array, dimension (min(M,N)) +*> The scalar factors of the elementary reflectors. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +*> On exit, if INFO=0, WORK(1) returns the optimal LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. LWORK >= 3*N+1. +*> For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB +*> is the optimal blocksize. +*> +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> \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 doubleGEcomputational +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> 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/complex scalar, and v is a real/complex vector +*> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in +*> A(i+1:m,i), and tau in TAU(i). +*> \endverbatim +* +*> \par Contributors: +* ================== +*> +*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain +*> X. Sun, Computer Science Dept., Duke University, USA +*> +* ===================================================================== SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, 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, LWORK, M, N @@ -13,78 +164,6 @@ DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DGEQP3 computes a QR factorization with column pivoting of a -* matrix A: A*P = Q*R using Level 3 BLAS. -* -* 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) DOUBLE PRECISION array, dimension (LDA,N) -* On entry, the M-by-N matrix A. -* On exit, the upper triangle of the array contains the -* min(M,N)-by-N upper trapezoidal matrix R; the elements below -* the diagonal, together with the array TAU, represent the -* orthogonal matrix Q as a product of min(M,N) elementary -* reflectors. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* JPVT (input/output) INTEGER array, dimension (N) -* On entry, if JPVT(J).ne.0, the J-th column of A is permuted -* to the front of A*P (a leading column); if JPVT(J)=0, -* the J-th column of A is a free column. -* On exit, if JPVT(J)=K, then the J-th column of A*P was the -* the K-th column of A. -* -* TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) -* The scalar factors of the elementary reflectors. -* -* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -* On exit, if INFO=0, WORK(1) returns the optimal LWORK. -* -* LWORK (input) INTEGER -* The dimension of the array WORK. LWORK >= 3*N+1. -* For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB -* is the optimal blocksize. -* -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the optimal size of the WORK array, returns -* this value as the first entry of the WORK array, and no error -* message related to LWORK is issued by XERBLA. -* -* 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**T -* -* where tau is a real/complex scalar, and v is a real/complex vector -* with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in -* A(i+1:m,i), and tau in TAU(i). -* -* Based on contributions by -* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain -* X. Sun, Computer Science Dept., Duke University, USA -* * ===================================================================== * * .. Parameters .. @@ -110,7 +189,7 @@ * .. Executable Statements .. * * Test input arguments -* ==================== +* ==================== * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) @@ -172,7 +251,7 @@ NFXD = NFXD - 1 * * Factorize fixed columns -* ======================= +* ======================= * * Compute the QR factorization of fixed columns and update * remaining columns. @@ -192,7 +271,7 @@ END IF * * Factorize free columns -* ====================== +* ====================== * IF( NFXD.LT.MINMN ) THEN *