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341 lines
9.4 KiB
341 lines
9.4 KiB
*> \brief \b CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
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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 CLA_GBRCOND_C + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_gbrcond_c.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/cla_gbrcond_c.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/cla_gbrcond_c.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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* REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
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* LDAFB, IPIV, C, CAPPLY, INFO, WORK,
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* RWORK )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS
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* LOGICAL CAPPLY
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* INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
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* REAL C( * ), RWORK( * )
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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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*> CLA_GBRCOND_C Computes the infinity norm condition number of
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*> op(A) * inv(diag(C)) where C is a REAL vector.
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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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the form of the system of equations:
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*> = 'N': A * X = B (No transpose)
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*> = 'T': A**T * X = B (Transpose)
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*> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
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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 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] AB
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*> \verbatim
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*> AB is COMPLEX array, dimension (LDAB,N)
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*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
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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(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
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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 >= KL+KU+1.
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*> \endverbatim
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*>
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*> \param[in] AFB
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*> \verbatim
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*> AFB is COMPLEX array, dimension (LDAFB,N)
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*> Details of the LU factorization of the band matrix A, as
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*> computed by CGBTRF. U is stored as an upper triangular
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*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
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*> and the multipliers used during the factorization are stored
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*> in rows KL+KU+2 to 2*KL+KU+1.
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*> \endverbatim
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*>
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*> \param[in] LDAFB
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*> \verbatim
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*> LDAFB is INTEGER
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*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices from the factorization A = P*L*U
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*> as computed by CGBTRF; row i of the matrix was interchanged
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*> with row IPIV(i).
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*> \endverbatim
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*>
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*> \param[in] C
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*> \verbatim
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*> C is REAL array, dimension (N)
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*> The vector C in the formula op(A) * inv(diag(C)).
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*> \endverbatim
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*>
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*> \param[in] CAPPLY
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*> \verbatim
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*> CAPPLY is LOGICAL
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*> If .TRUE. then access the vector C in the formula above.
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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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*> i > 0: The ith argument is invalid.
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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 (2*N).
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*> Workspace.
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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 (N).
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*> Workspace.
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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 complexGBcomputational
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*
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* =====================================================================
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REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
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$ LDAFB, IPIV, C, CAPPLY, INFO, WORK,
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$ RWORK )
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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 TRANS
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LOGICAL CAPPLY
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INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
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REAL C( * ), RWORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL NOTRANS
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INTEGER KASE, I, J
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REAL AINVNM, ANORM, TMP
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COMPLEX ZDUM
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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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 CLACN2, CGBTRS, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. Statement Functions ..
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REAL CABS1
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* ..
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* .. Statement Function Definitions ..
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CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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CLA_GBRCOND_C = 0.0E+0
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*
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INFO = 0
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NOTRANS = LSAME( TRANS, 'N' )
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IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
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$ LSAME( TRANS, 'C' ) ) 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( KL.LT.0 .OR. KL.GT.N-1 ) THEN
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INFO = -3
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ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
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INFO = -4
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ELSE IF( LDAB.LT.KL+KU+1 ) THEN
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INFO = -6
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ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CLA_GBRCOND_C', -INFO )
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RETURN
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END IF
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*
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* Compute norm of op(A)*op2(C).
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*
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ANORM = 0.0E+0
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KD = KU + 1
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KE = KL + 1
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IF ( NOTRANS ) THEN
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DO I = 1, N
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TMP = 0.0E+0
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IF ( CAPPLY ) THEN
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DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
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TMP = TMP + CABS1( AB( KD+I-J, J ) ) / C( J )
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END DO
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ELSE
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DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
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TMP = TMP + CABS1( AB( KD+I-J, J ) )
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END DO
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END IF
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RWORK( I ) = TMP
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ANORM = MAX( ANORM, TMP )
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END DO
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ELSE
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DO I = 1, N
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TMP = 0.0E+0
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IF ( CAPPLY ) THEN
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DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
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TMP = TMP + CABS1( AB( KE-I+J, I ) ) / C( J )
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END DO
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ELSE
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DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
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TMP = TMP + CABS1( AB( KE-I+J, I ) )
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END DO
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END IF
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RWORK( I ) = TMP
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ANORM = MAX( ANORM, TMP )
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END DO
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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 ) THEN
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CLA_GBRCOND_C = 1.0E+0
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RETURN
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ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
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RETURN
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END IF
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*
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* Estimate the norm of inv(op(A)).
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*
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AINVNM = 0.0E+0
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*
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KASE = 0
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10 CONTINUE
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CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( KASE.EQ.2 ) THEN
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*
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* Multiply by R.
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*
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DO I = 1, N
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WORK( I ) = WORK( I ) * RWORK( I )
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END DO
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*
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IF ( NOTRANS ) THEN
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CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
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$ IPIV, WORK, N, INFO )
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ELSE
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CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
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$ LDAFB, IPIV, WORK, N, INFO )
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ENDIF
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*
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* Multiply by inv(C).
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*
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IF ( CAPPLY ) THEN
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DO I = 1, N
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WORK( I ) = WORK( I ) * C( I )
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END DO
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END IF
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ELSE
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*
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* Multiply by inv(C**H).
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*
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IF ( CAPPLY ) THEN
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DO I = 1, N
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WORK( I ) = WORK( I ) * C( I )
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END DO
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END IF
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*
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IF ( NOTRANS ) THEN
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CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
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$ LDAFB, IPIV, WORK, N, INFO )
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ELSE
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CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
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$ IPIV, WORK, N, INFO )
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END IF
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*
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* Multiply by R.
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*
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DO I = 1, N
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WORK( I ) = WORK( I ) * RWORK( I )
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END DO
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END IF
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GO TO 10
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM .NE. 0.0E+0 )
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$ CLA_GBRCOND_C = 1.0E+0 / AINVNM
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*
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RETURN
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*
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* End of CLA_GBRCOND_C
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*
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END
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