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version 1.8, 2011/07/22 07:38:05 version 1.9, 2011/11/21 20:42:51
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   *> \brief \b DGEQP3
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGEQP3 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqp3.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqp3.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqp3.f"> 
   *> [TXT]</a>
   *> \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 )        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,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N        INTEGER            INFO, LDA, LWORK, M, N
Line 13 Line 164
       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )        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 ..  *     .. Parameters ..
Line 110 Line 189
 *     .. Executable Statements ..  *     .. Executable Statements ..
 *  *
 *     Test input arguments  *     Test input arguments
 *     ====================  *  ====================
 *  *
       INFO = 0        INFO = 0
       LQUERY = ( LWORK.EQ.-1 )        LQUERY = ( LWORK.EQ.-1 )
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       NFXD = NFXD - 1        NFXD = NFXD - 1
 *  *
 *     Factorize fixed columns  *     Factorize fixed columns
 *     =======================  *  =======================
 *  *
 *     Compute the QR factorization of fixed columns and update  *     Compute the QR factorization of fixed columns and update
 *     remaining columns.  *     remaining columns.
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       END IF        END IF
 *  *
 *     Factorize free columns  *     Factorize free columns
 *     ======================  *  ======================
 *  *
       IF( NFXD.LT.MINMN ) THEN        IF( NFXD.LT.MINMN ) THEN
 *  *
Removed from v.1.8  
changed lines
  Added in v.1.9

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