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311 lines
8.8 KiB
311 lines
8.8 KiB
2 years ago
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*> \brief \b CGEQPF
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download CGEQPF + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqpf.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqpf.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqpf.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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* INTEGER JPVT( * )
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* REAL RWORK( * )
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* COMPLEX A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> This routine is deprecated and has been replaced by routine CGEQP3.
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*>
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*> CGEQPF computes a QR factorization with column pivoting of a
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*> complex M-by-N matrix A: A*P = Q*R.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix A. N >= 0
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA,N)
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*> On entry, the M-by-N matrix A.
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*> On exit, the upper triangle of the array contains the
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*> min(M,N)-by-N upper triangular matrix R; the elements
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*> below the diagonal, together with the array TAU,
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*> represent the unitary matrix Q as a product of
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*> min(m,n) elementary reflectors.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[in,out] JPVT
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*> \verbatim
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*> JPVT is INTEGER array, dimension (N)
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*> On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
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*> to the front of A*P (a leading column); if JPVT(i) = 0,
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*> the i-th column of A is a free column.
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*> On exit, if JPVT(i) = k, then the i-th column of A*P
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*> was the k-th column of A.
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*> \endverbatim
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*>
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*> \param[out] TAU
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*> \verbatim
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*> TAU is COMPLEX array, dimension (min(M,N))
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*> The scalar factors of the elementary reflectors.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (2*N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complexGEcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The matrix Q is represented as a product of elementary reflectors
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*>
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*> Q = H(1) H(2) . . . H(n)
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*>
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*> Each H(i) has the form
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*>
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*> H = I - tau * v * v**H
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*>
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*> where tau is a complex scalar, and v is a complex vector with
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*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
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*>
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*> The matrix P is represented in jpvt as follows: If
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*> jpvt(j) = i
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*> then the jth column of P is the ith canonical unit vector.
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*>
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*> Partial column norm updating strategy modified by
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*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
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*> University of Zagreb, Croatia.
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*> -- April 2011 --
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*> For more details see LAPACK Working Note 176.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE CGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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INTEGER JPVT( * )
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REAL RWORK( * )
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COMPLEX A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, ITEMP, J, MA, MN, PVT
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REAL TEMP, TEMP2, TOL3Z
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COMPLEX AII
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEQR2, CLARF, CLARFG, CSWAP, CUNM2R, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, CMPLX, CONJG, MAX, MIN, SQRT
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* ..
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* .. External Functions ..
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INTEGER ISAMAX
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REAL SCNRM2, SLAMCH
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EXTERNAL ISAMAX, SCNRM2, SLAMCH
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CGEQPF', -INFO )
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RETURN
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END IF
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*
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MN = MIN( M, N )
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TOL3Z = SQRT(SLAMCH('Epsilon'))
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*
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* Move initial columns up front
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*
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ITEMP = 1
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DO 10 I = 1, N
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IF( JPVT( I ).NE.0 ) THEN
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IF( I.NE.ITEMP ) THEN
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CALL CSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 )
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JPVT( I ) = JPVT( ITEMP )
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JPVT( ITEMP ) = I
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ELSE
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JPVT( I ) = I
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END IF
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ITEMP = ITEMP + 1
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ELSE
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JPVT( I ) = I
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END IF
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10 CONTINUE
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ITEMP = ITEMP - 1
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*
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* Compute the QR factorization and update remaining columns
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*
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IF( ITEMP.GT.0 ) THEN
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MA = MIN( ITEMP, M )
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CALL CGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
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IF( MA.LT.N ) THEN
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CALL CUNM2R( 'Left', 'Conjugate transpose', M, N-MA, MA, A,
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$ LDA, TAU, A( 1, MA+1 ), LDA, WORK, INFO )
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END IF
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END IF
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*
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IF( ITEMP.LT.MN ) THEN
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*
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* Initialize partial column norms. The first n elements of
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* work store the exact column norms.
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*
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DO 20 I = ITEMP + 1, N
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RWORK( I ) = SCNRM2( M-ITEMP, A( ITEMP+1, I ), 1 )
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RWORK( N+I ) = RWORK( I )
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20 CONTINUE
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*
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* Compute factorization
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*
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DO 40 I = ITEMP + 1, MN
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*
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* Determine ith pivot column and swap if necessary
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*
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PVT = ( I-1 ) + ISAMAX( N-I+1, RWORK( I ), 1 )
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*
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IF( PVT.NE.I ) THEN
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CALL CSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
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ITEMP = JPVT( PVT )
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JPVT( PVT ) = JPVT( I )
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JPVT( I ) = ITEMP
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RWORK( PVT ) = RWORK( I )
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RWORK( N+PVT ) = RWORK( N+I )
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END IF
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*
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* Generate elementary reflector H(i)
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*
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AII = A( I, I )
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CALL CLARFG( M-I+1, AII, A( MIN( I+1, M ), I ), 1,
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$ TAU( I ) )
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A( I, I ) = AII
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*
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IF( I.LT.N ) THEN
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*
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* Apply H(i) to A(i:m,i+1:n) from the left
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*
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AII = A( I, I )
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A( I, I ) = CMPLX( ONE )
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CALL CLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
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$ CONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
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A( I, I ) = AII
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END IF
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*
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* Update partial column norms
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*
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DO 30 J = I + 1, N
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IF( RWORK( J ).NE.ZERO ) THEN
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*
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* NOTE: The following 4 lines follow from the analysis in
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* Lapack Working Note 176.
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*
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TEMP = ABS( A( I, J ) ) / RWORK( J )
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TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
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TEMP2 = TEMP*( RWORK( J ) / RWORK( N+J ) )**2
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IF( TEMP2 .LE. TOL3Z ) THEN
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IF( M-I.GT.0 ) THEN
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RWORK( J ) = SCNRM2( M-I, A( I+1, J ), 1 )
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RWORK( N+J ) = RWORK( J )
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ELSE
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RWORK( J ) = ZERO
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RWORK( N+J ) = ZERO
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END IF
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ELSE
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RWORK( J ) = RWORK( J )*SQRT( TEMP )
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END IF
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END IF
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30 CONTINUE
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*
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40 CONTINUE
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END IF
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RETURN
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*
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* End of CGEQPF
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*
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END
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