--- rpl/lapack/lapack/zpbcon.f 2011/07/22 07:38:18 1.8 +++ rpl/lapack/lapack/zpbcon.f 2011/11/21 20:43:18 1.9 @@ -1,12 +1,142 @@ +*> \brief \b ZPBCON +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZPBCON + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, +* RWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, KD, LDAB, N +* DOUBLE PRECISION ANORM, RCOND +* .. +* .. Array Arguments .. +* DOUBLE PRECISION RWORK( * ) +* COMPLEX*16 AB( LDAB, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZPBCON estimates the reciprocal of the condition number (in the +*> 1-norm) of a complex Hermitian positive definite band matrix using +*> the Cholesky factorization A = U**H*U or A = L*L**H computed by +*> ZPBTRF. +*> +*> An estimate is obtained for norm(inv(A)), and the reciprocal of the +*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangular factor stored in AB; +*> = 'L': Lower triangular factor stored in AB. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] KD +*> \verbatim +*> KD is INTEGER +*> The number of superdiagonals of the matrix A if UPLO = 'U', +*> or the number of sub-diagonals if UPLO = 'L'. KD >= 0. +*> \endverbatim +*> +*> \param[in] AB +*> \verbatim +*> AB is COMPLEX*16 array, dimension (LDAB,N) +*> The triangular factor U or L from the Cholesky factorization +*> A = U**H*U or A = L*L**H of the band matrix A, stored in the +*> first KD+1 rows of the array. The j-th column of U or L is +*> stored in the j-th column of the array AB as follows: +*> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; +*> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array AB. LDAB >= KD+1. +*> \endverbatim +*> +*> \param[in] ANORM +*> \verbatim +*> ANORM is DOUBLE PRECISION +*> The 1-norm (or infinity-norm) of the Hermitian band 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/(ANORM * AINVNM), where AINVNM is an +*> estimate of the 1-norm of inv(A) computed in this routine. +*> \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 complex16OTHERcomputational +* +* ===================================================================== SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, $ RWORK, INFO ) * -* -- LAPACK routine (version 3.3.1) -- +* -- 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..-- -* -- April 2011 -- -* -* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. +* November 2011 * * .. Scalar Arguments .. CHARACTER UPLO @@ -18,58 +148,6 @@ COMPLEX*16 AB( LDAB, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZPBCON estimates the reciprocal of the condition number (in the -* 1-norm) of a complex Hermitian positive definite band matrix using -* the Cholesky factorization A = U**H*U or A = L*L**H computed by -* ZPBTRF. -* -* An estimate is obtained for norm(inv(A)), and the reciprocal of the -* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangular factor stored in AB; -* = 'L': Lower triangular factor stored in AB. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* KD (input) INTEGER -* The number of superdiagonals of the matrix A if UPLO = 'U', -* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. -* -* AB (input) COMPLEX*16 array, dimension (LDAB,N) -* The triangular factor U or L from the Cholesky factorization -* A = U**H*U or A = L*L**H of the band matrix A, stored in the -* first KD+1 rows of the array. The j-th column of U or L is -* stored in the j-th column of the array AB as follows: -* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; -* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). -* -* LDAB (input) INTEGER -* The leading dimension of the array AB. LDAB >= KD+1. -* -* ANORM (input) DOUBLE PRECISION -* The 1-norm (or infinity-norm) of the Hermitian band matrix A. -* -* RCOND (output) DOUBLE PRECISION -* The reciprocal of the condition number of the matrix A, -* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an -* estimate of the 1-norm of inv(A) computed in this routine. -* -* 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 ..