version 1.3, 2010/08/13 21:03:47
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version 1.12, 2016/08/27 15:34:24
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*> \brief \b DLA_GBRCOND estimates the Skeel condition number for a general banded matrix. |
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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 DLA_GBRCOND + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbrcond.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/dla_gbrcond.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/dla_gbrcond.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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* DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB, |
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* AFB, LDAFB, IPIV, CMODE, C, |
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* INFO, WORK, IWORK ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER TRANS |
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* INTEGER N, LDAB, LDAFB, INFO, KL, KU, CMODE |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IWORK( * ), IPIV( * ) |
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* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), |
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* $ C( * ) |
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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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*> DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C) |
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*> where op2 is determined by CMODE as follows |
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*> CMODE = 1 op2(C) = C |
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*> CMODE = 0 op2(C) = I |
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*> CMODE = -1 op2(C) = inv(C) |
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*> The Skeel condition number cond(A) = norminf( |inv(A)||A| ) |
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*> is computed by computing scaling factors R such that |
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*> diag(R)*A*op2(C) is row equilibrated and computing the standard |
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*> infinity-norm condition number. |
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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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DGBTRF. 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 DGBTRF; 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] CMODE |
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*> \verbatim |
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*> CMODE is INTEGER |
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*> Determines op2(C) in the formula op(A) * op2(C) as follows: |
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*> CMODE = 1 op2(C) = C |
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*> CMODE = 0 op2(C) = I |
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*> CMODE = -1 op2(C) = inv(C) |
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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 DOUBLE PRECISION array, dimension (N) |
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*> The vector C in the formula op(A) * op2(C). |
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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[in] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (5*N). |
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*> Workspace. |
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*> \endverbatim |
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*> |
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*> \param[in] IWORK |
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*> \verbatim |
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*> IWORK is INTEGER 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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*> \date September 2012 |
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* |
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*> \ingroup doubleGBcomputational |
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* |
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* ===================================================================== |
DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB, |
DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB, |
$ AFB, LDAFB, IPIV, CMODE, C, |
$ AFB, LDAFB, IPIV, CMODE, C, |
$ INFO, WORK, IWORK ) |
$ INFO, WORK, IWORK ) |
* |
* |
* -- LAPACK routine (version 3.2.2) -- |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Jason Riedy of Univ. of California Berkeley. -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- June 2010 -- |
* September 2012 |
* |
* |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley and NAG Ltd. -- |
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* |
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IMPLICIT NONE |
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* .. |
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* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER TRANS |
CHARACTER TRANS |
INTEGER N, LDAB, LDAFB, INFO, KL, KU, CMODE |
INTEGER N, LDAB, LDAFB, INFO, KL, KU, CMODE |
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$ C( * ) |
$ C( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C) |
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* where op2 is determined by CMODE as follows |
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* CMODE = 1 op2(C) = C |
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* CMODE = 0 op2(C) = I |
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* CMODE = -1 op2(C) = inv(C) |
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* The Skeel condition number cond(A) = norminf( |inv(A)||A| ) |
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* is computed by computing scaling factors R such that |
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* diag(R)*A*op2(C) is row equilibrated and computing the standard |
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* infinity-norm condition number. |
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* |
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* Arguments |
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* ========= |
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* |
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* TRANS (input) 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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* |
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* N (input) 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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* |
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* KL (input) INTEGER |
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* The number of subdiagonals within the band of A. KL >= 0. |
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* |
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* KU (input) INTEGER |
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* The number of superdiagonals within the band of A. KU >= 0. |
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* |
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* AB (input) DOUBLE PRECISION 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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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= KL+KU+1. |
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* |
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* AFB (input) DOUBLE PRECISION 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 DGBTRF. 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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* |
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* LDAFB (input) INTEGER |
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* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. |
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* |
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* IPIV (input) 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 DGBTRF; row i of the matrix was interchanged |
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* with row IPIV(i). |
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* |
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* CMODE (input) INTEGER |
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* Determines op2(C) in the formula op(A) * op2(C) as follows: |
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* CMODE = 1 op2(C) = C |
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* CMODE = 0 op2(C) = I |
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* CMODE = -1 op2(C) = inv(C) |
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* |
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* C (input) DOUBLE PRECISION array, dimension (N) |
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* The vector C in the formula op(A) * op2(C). |
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* |
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* INFO (output) INTEGER |
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* = 0: Successful exit. |
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* i > 0: The ith argument is invalid. |
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* |
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* WORK (input) DOUBLE PRECISION array, dimension (5*N). |
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* Workspace. |
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* |
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* IWORK (input) INTEGER array, dimension (N). |
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* Workspace. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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END IF |
END IF |
ELSE |
ELSE |
* |
* |
* Multiply by inv(C'). |
* Multiply by inv(C**T). |
* |
* |
IF ( CMODE .EQ. 1 ) THEN |
IF ( CMODE .EQ. 1 ) THEN |
DO I = 1, N |
DO I = 1, N |