--- rpl/lapack/lapack/dgeqr2.f 2010/08/06 15:28:36 1.3 +++ rpl/lapack/lapack/dgeqr2.f 2014/01/27 09:28:16 1.15 @@ -1,9 +1,130 @@ +*> \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DGEQR2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGEQR2 computes a QR factorization of a real m by n matrix A: +*> A = Q * R. +*> \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 elements on and above the diagonal of the array +*> contain the min(m,n) by n upper trapezoidal matrix R (R is +*> upper triangular if m >= n); the elements below the diagonal, +*> with the array TAU, represent the orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N)) +*> The scalar factors of the elementary reflectors (see Further +*> Details). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (N) +*> \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 September 2012 +* +*> \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 scalar, and v is a real 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 +*> +* ===================================================================== SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine (version 3.4.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* September 2012 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N @@ -12,57 +133,6 @@ DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DGEQR2 computes a QR factorization of a real m by n matrix A: -* A = Q * R. -* -* 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 elements on and above the diagonal of the array -* contain the min(m,n) by n upper trapezoidal matrix R (R is -* upper triangular if m >= n); the elements below the diagonal, -* 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) DOUBLE PRECISION array, dimension (min(M,N)) -* The scalar factors of the elementary reflectors (see Further -* Details). -* -* WORK (workspace) DOUBLE PRECISION array, dimension (N) -* -* 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(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). -* * ===================================================================== * * .. Parameters .. @@ -74,7 +144,7 @@ DOUBLE PRECISION AII * .. * .. External Subroutines .. - EXTERNAL DLARF, DLARFP, XERBLA + EXTERNAL DLARF, DLARFG, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN @@ -102,7 +172,7 @@ * * Generate elementary reflector H(i) to annihilate A(i+1:m,i) * - CALL DLARFP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, + CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, $ TAU( I ) ) IF( I.LT.N ) THEN *