--- rpl/lapack/lapack/zgbcon.f 2010/08/06 15:32:37 1.4 +++ rpl/lapack/lapack/zgbcon.f 2016/08/27 15:34:44 1.14 @@ -1,12 +1,156 @@ +*> \brief \b ZGBCON +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZGBCON + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, +* WORK, RWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER NORM +* INTEGER INFO, KL, KU, LDAB, N +* DOUBLE PRECISION ANORM, RCOND +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION RWORK( * ) +* COMPLEX*16 AB( LDAB, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZGBCON estimates the reciprocal of the condition number of a complex +*> general band matrix A, in either the 1-norm or the infinity-norm, +*> using the LU factorization computed by ZGBTRF. +*> +*> An estimate is obtained for norm(inv(A)), and the reciprocal of the +*> condition number is computed as +*> RCOND = 1 / ( norm(A) * norm(inv(A)) ). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] NORM +*> \verbatim +*> NORM is CHARACTER*1 +*> Specifies whether the 1-norm condition number or the +*> infinity-norm condition number is required: +*> = '1' or 'O': 1-norm; +*> = 'I': Infinity-norm. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> The number of subdiagonals within the band of A. KL >= 0. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> The number of superdiagonals within the band of A. KU >= 0. +*> \endverbatim +*> +*> \param[in] AB +*> \verbatim +*> AB is COMPLEX*16 array, dimension (LDAB,N) +*> Details of the LU factorization of the band matrix A, as +*> computed by ZGBTRF. U is stored as an upper triangular band +*> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and +*> the multipliers used during the factorization are stored in +*> rows KL+KU+2 to 2*KL+KU+1. +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array AB. LDAB >= 2*KL+KU+1. +*> \endverbatim +*> +*> \param[in] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> The pivot indices; for 1 <= i <= N, row i of the matrix was +*> interchanged with row IPIV(i). +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> If NORM = '1' or 'O', the 1-norm of the original matrix A. +*> If NORM = 'I', the infinity-norm of the original matrix A. +*> \endverbatim +*> +*> \param[out] RCOND +*> \verbatim +*> RCOND is DOUBLE PRECISION +*> The reciprocal of the condition number of the matrix A, +*> computed as RCOND = 1/(norm(A) * norm(inv(A))). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is DOUBLE PRECISION array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16GBcomputational +* +* ===================================================================== SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, $ WORK, RWORK, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 -* -* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. +* November 2011 * * .. Scalar Arguments .. CHARACTER NORM @@ -19,65 +163,6 @@ COMPLEX*16 AB( LDAB, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZGBCON estimates the reciprocal of the condition number of a complex -* general band matrix A, in either the 1-norm or the infinity-norm, -* using the LU factorization computed by ZGBTRF. -* -* An estimate is obtained for norm(inv(A)), and the reciprocal of the -* condition number is computed as -* RCOND = 1 / ( norm(A) * norm(inv(A)) ). -* -* Arguments -* ========= -* -* NORM (input) CHARACTER*1 -* Specifies whether the 1-norm condition number or the -* infinity-norm condition number is required: -* = '1' or 'O': 1-norm; -* = 'I': Infinity-norm. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* KL (input) INTEGER -* The number of subdiagonals within the band of A. KL >= 0. -* -* KU (input) INTEGER -* The number of superdiagonals within the band of A. KU >= 0. -* -* AB (input) COMPLEX*16 array, dimension (LDAB,N) -* Details of the LU factorization of the band matrix A, as -* computed by ZGBTRF. U is stored as an upper triangular band -* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and -* the multipliers used during the factorization are stored in -* rows KL+KU+2 to 2*KL+KU+1. -* -* LDAB (input) INTEGER -* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. -* -* IPIV (input) INTEGER array, dimension (N) -* The pivot indices; for 1 <= i <= N, row i of the matrix was -* interchanged with row IPIV(i). -* -* ANORM (input) DOUBLE PRECISION -* If NORM = '1' or 'O', the 1-norm of the original matrix A. -* If NORM = 'I', the infinity-norm of the original matrix A. -* -* RCOND (output) DOUBLE PRECISION -* The reciprocal of the condition number of the matrix A, -* computed as RCOND = 1/(norm(A) * norm(inv(A))). -* -* WORK (workspace) COMPLEX*16 array, dimension (2*N) -* -* RWORK (workspace) DOUBLE PRECISION array, dimension (N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* * ===================================================================== * * .. Parameters .. @@ -187,13 +272,13 @@ $ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO ) ELSE * -* Multiply by inv(U'). +* Multiply by inv(U**H). * CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit', $ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK, $ INFO ) * -* Multiply by inv(L'). +* Multiply by inv(L**H). * IF( LNOTI ) THEN DO 30 J = N - 1, 1, -1