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261 lines
7.6 KiB
261 lines
7.6 KiB
2 years ago
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*> \brief \b CPTEQR
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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 CPTEQR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cpteqr.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/cpteqr.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/cpteqr.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 CPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER COMPZ
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* INTEGER INFO, LDZ, N
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* ..
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* .. Array Arguments ..
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* REAL D( * ), E( * ), WORK( * )
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* COMPLEX Z( LDZ, * )
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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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*> CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
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*> symmetric positive definite tridiagonal matrix by first factoring the
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*> matrix using SPTTRF and then calling CBDSQR to compute the singular
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*> values of the bidiagonal factor.
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*>
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*> This routine computes the eigenvalues of the positive definite
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*> tridiagonal matrix to high relative accuracy. This means that if the
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*> eigenvalues range over many orders of magnitude in size, then the
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*> small eigenvalues and corresponding eigenvectors will be computed
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*> more accurately than, for example, with the standard QR method.
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*>
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*> The eigenvectors of a full or band positive definite Hermitian matrix
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*> can also be found if CHETRD, CHPTRD, or CHBTRD has been used to
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*> reduce this matrix to tridiagonal form. (The reduction to
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*> tridiagonal form, however, may preclude the possibility of obtaining
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*> high relative accuracy in the small eigenvalues of the original
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*> matrix, if these eigenvalues range over many orders of magnitude.)
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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] COMPZ
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*> \verbatim
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*> COMPZ is CHARACTER*1
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*> = 'N': Compute eigenvalues only.
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*> = 'V': Compute eigenvectors of original Hermitian
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*> matrix also. Array Z contains the unitary matrix
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*> used to reduce the original matrix to tridiagonal
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*> form.
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*> = 'I': Compute eigenvectors of tridiagonal matrix also.
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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 order of the matrix. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> On entry, the n diagonal elements of the tridiagonal matrix.
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*> On normal exit, D contains the eigenvalues, in descending
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*> order.
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*> \endverbatim
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*>
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*> \param[in,out] E
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*> \verbatim
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*> E is REAL array, dimension (N-1)
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*> On entry, the (n-1) subdiagonal elements of the tridiagonal
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*> matrix.
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*> On exit, E has been destroyed.
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*> \endverbatim
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*>
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*> \param[in,out] Z
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*> \verbatim
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*> Z is COMPLEX array, dimension (LDZ, N)
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*> On entry, if COMPZ = 'V', the unitary matrix used in the
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*> reduction to tridiagonal form.
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*> On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
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*> original Hermitian matrix;
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*> if COMPZ = 'I', the orthonormal eigenvectors of the
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*> tridiagonal matrix.
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*> If INFO > 0 on exit, Z contains the eigenvectors associated
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*> with only the stored eigenvalues.
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*> If COMPZ = 'N', then Z is not referenced.
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*> \endverbatim
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*>
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*> \param[in] LDZ
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*> \verbatim
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*> LDZ is INTEGER
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*> The leading dimension of the array Z. LDZ >= 1, and if
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*> COMPZ = 'V' or 'I', LDZ >= max(1,N).
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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 REAL array, dimension (4*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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*> > 0: if INFO = i, and i is:
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*> <= N the Cholesky factorization of the matrix could
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*> not be performed because the leading principal
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*> minor of order i was not positive.
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*> > N the SVD algorithm failed to converge;
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*> if INFO = N+i, i off-diagonal elements of the
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*> bidiagonal factor did not converge to zero.
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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 complexPTcomputational
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*
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* =====================================================================
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SUBROUTINE CPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, 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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CHARACTER COMPZ
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INTEGER INFO, LDZ, N
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* ..
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* .. Array Arguments ..
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REAL D( * ), E( * ), WORK( * )
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COMPLEX Z( LDZ, * )
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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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COMPLEX CZERO, CONE
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PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
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$ CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL CBDSQR, CLASET, SPTTRF, XERBLA
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* ..
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* .. Local Arrays ..
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COMPLEX C( 1, 1 ), VT( 1, 1 )
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* ..
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* .. Local Scalars ..
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INTEGER I, ICOMPZ, NRU
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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*
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IF( LSAME( COMPZ, 'N' ) ) THEN
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ICOMPZ = 0
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ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
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ICOMPZ = 1
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ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
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ICOMPZ = 2
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ELSE
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ICOMPZ = -1
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END IF
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IF( ICOMPZ.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( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
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$ N ) ) ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CPTEQR', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( N.EQ.1 ) THEN
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IF( ICOMPZ.GT.0 )
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$ Z( 1, 1 ) = CONE
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RETURN
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END IF
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IF( ICOMPZ.EQ.2 )
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$ CALL CLASET( 'Full', N, N, CZERO, CONE, Z, LDZ )
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*
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* Call SPTTRF to factor the matrix.
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*
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CALL SPTTRF( N, D, E, INFO )
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IF( INFO.NE.0 )
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$ RETURN
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DO 10 I = 1, N
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D( I ) = SQRT( D( I ) )
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10 CONTINUE
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DO 20 I = 1, N - 1
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E( I ) = E( I )*D( I )
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20 CONTINUE
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*
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* Call CBDSQR to compute the singular values/vectors of the
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* bidiagonal factor.
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*
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IF( ICOMPZ.GT.0 ) THEN
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NRU = N
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ELSE
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NRU = 0
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END IF
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CALL CBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1,
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$ WORK, INFO )
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*
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* Square the singular values.
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*
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IF( INFO.EQ.0 ) THEN
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DO 30 I = 1, N
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D( I ) = D( I )*D( I )
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30 CONTINUE
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ELSE
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INFO = N + INFO
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END IF
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*
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RETURN
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*
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* End of CPTEQR
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*
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END
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