removed lapack 3.6.0
This commit is contained in:
Werner Saar
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*> \brief <b> ZGBSV computes the solution to system of linear equations A * X = B for GB matrices</b> (simple driver)
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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 ZGBSV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbsv.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/zgbsv.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/zgbsv.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 ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX*16 AB( LDAB, * ), B( LDB, * )
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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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*> ZGBSV computes the solution to a complex system of linear equations
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*> A * X = B, where A is a band matrix of order N with KL subdiagonals
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*> and KU superdiagonals, and X and B are N-by-NRHS matrices.
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*>
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*> The LU decomposition with partial pivoting and row interchanges is
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*> used to factor A as A = L * U, where L is a product of permutation
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*> and unit lower triangular matrices with KL subdiagonals, and U is
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*> upper triangular with KL+KU superdiagonals. The factored form of A
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*> is then used to solve the system of equations A * X = B.
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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] N
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*> \verbatim
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*> N is INTEGER
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*> The number of linear equations, i.e., the order of the
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*> matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KL
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*> \verbatim
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*> KL is INTEGER
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*> The number of subdiagonals within the band of A. KL >= 0.
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*> \endverbatim
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*>
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*> \param[in] KU
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*> \verbatim
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*> KU is INTEGER
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*> The number of superdiagonals within the band of A. KU >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, i.e., the number of columns
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*> of the matrix B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] AB
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*> \verbatim
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*> AB is COMPLEX*16 array, dimension (LDAB,N)
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*> On entry, the matrix A in band storage, in rows KL+1 to
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*> 2*KL+KU+1; rows 1 to KL of the array need not be set.
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*> The j-th column of A is stored in the j-th column of the
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*> array AB as follows:
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*> AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
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*> On exit, details of the factorization: U is stored as an
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*> upper triangular band matrix with KL+KU superdiagonals in
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*> rows 1 to KL+KU+1, and the multipliers used during the
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*> factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
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*> See below for further details.
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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*> \endverbatim
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*>
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*> \param[out] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices that define the permutation matrix P;
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*> row i of the matrix was interchanged with row IPIV(i).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (LDB,NRHS)
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*> On entry, the N-by-NRHS right hand side matrix B.
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*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,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, U(i,i) is exactly zero. The factorization
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*> has been completed, but the factor U is exactly
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*> singular, and the solution has not been computed.
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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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*> \date November 2011
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*
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*> \ingroup complex16GBsolve
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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 band storage scheme is illustrated by the following example, when
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*> M = N = 6, KL = 2, KU = 1:
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*>
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*> On entry: On exit:
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*>
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*> * * * + + + * * * u14 u25 u36
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*> * * + + + + * * u13 u24 u35 u46
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*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
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*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
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*> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
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*> a31 a42 a53 a64 * * m31 m42 m53 m64 * *
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*>
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*> Array elements marked * are not used by the routine; elements marked
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*> + need not be set on entry, but are required by the routine to store
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*> elements of U because of fill-in resulting from the row interchanges.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
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*
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* -- LAPACK driver routine (version 3.4.0) --
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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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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX*16 AB( LDAB, * ), B( LDB, * )
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* ..
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*
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* =====================================================================
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*
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZGBTRF, ZGBTRS
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( KL.LT.0 ) THEN
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INFO = -2
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ELSE IF( KU.LT.0 ) THEN
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INFO = -3
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZGBSV ', -INFO )
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RETURN
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END IF
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*
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* Compute the LU factorization of the band matrix A.
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*
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CALL ZGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
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IF( INFO.EQ.0 ) THEN
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*
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* Solve the system A*X = B, overwriting B with X.
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*
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CALL ZGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
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$ B, LDB, INFO )
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END IF
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RETURN
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*
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* End of ZGBSV
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*
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END
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