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version 1.14, 2014/01/27 09:28:21
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*> \brief \b DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. |
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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 DLAQSB + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsb.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/dlaqsb.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/dlaqsb.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 DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER EQUED, UPLO |
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* INTEGER KD, LDAB, N |
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* DOUBLE PRECISION AMAX, SCOND |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), S( * ) |
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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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*> DLAQSB equilibrates a symmetric band matrix A using the scaling |
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*> factors in the vector S. |
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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] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> Specifies whether the upper or lower triangular part of the |
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*> symmetric matrix A is stored. |
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*> = 'U': Upper triangular |
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*> = 'L': Lower triangular |
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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 order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KD |
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*> \verbatim |
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*> KD is INTEGER |
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*> The number of super-diagonals of the matrix A if UPLO = 'U', |
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*> or the number of sub-diagonals if UPLO = 'L'. KD >= 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 DOUBLE PRECISION array, dimension (LDAB,N) |
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*> On entry, the upper or lower triangle of the symmetric band |
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*> matrix A, stored in the first KD+1 rows of the array. The |
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*> j-th column of A is stored in the j-th column of the array AB |
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*> as follows: |
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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*> |
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*> On exit, if INFO = 0, the triangular factor U or L from the |
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*> Cholesky factorization A = U**T*U or A = L*L**T of the band |
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*> matrix A, in the same storage format as A. |
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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 >= KD+1. |
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*> \endverbatim |
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*> |
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*> \param[in] S |
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*> \verbatim |
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*> S is DOUBLE PRECISION array, dimension (N) |
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*> The scale factors for A. |
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*> \endverbatim |
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*> |
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*> \param[in] SCOND |
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*> \verbatim |
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*> SCOND is DOUBLE PRECISION |
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*> Ratio of the smallest S(i) to the largest S(i). |
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*> \endverbatim |
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*> |
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*> \param[in] AMAX |
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*> \verbatim |
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*> AMAX is DOUBLE PRECISION |
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*> Absolute value of largest matrix entry. |
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*> \endverbatim |
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*> |
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*> \param[out] EQUED |
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*> \verbatim |
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*> EQUED is CHARACTER*1 |
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*> Specifies whether or not equilibration was done. |
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*> = 'N': No equilibration. |
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*> = 'Y': Equilibration was done, i.e., A has been replaced by |
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*> diag(S) * A * diag(S). |
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*> \endverbatim |
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* |
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*> \par Internal Parameters: |
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* ========================= |
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*> |
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*> \verbatim |
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*> THRESH is a threshold value used to decide if scaling should be done |
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*> based on the ratio of the scaling factors. If SCOND < THRESH, |
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*> scaling is done. |
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*> |
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*> LARGE and SMALL are threshold values used to decide if scaling should |
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*> be done based on the absolute size of the largest matrix element. |
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*> If AMAX > LARGE or AMAX < SMALL, scaling is done. |
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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 doubleOTHERauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) |
SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.3.1) -- |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- April 2011 -- |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER EQUED, UPLO |
CHARACTER EQUED, UPLO |
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DOUBLE PRECISION AB( LDAB, * ), S( * ) |
DOUBLE PRECISION AB( LDAB, * ), S( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
|
* |
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* DLAQSB equilibrates a symmetric band matrix A using the scaling |
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* factors in the vector S. |
|
* |
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* Arguments |
|
* ========= |
|
* |
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* UPLO (input) CHARACTER*1 |
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* Specifies whether the upper or lower triangular part of the |
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* symmetric matrix A is stored. |
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* = 'U': Upper triangular |
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* = 'L': Lower triangular |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* KD (input) INTEGER |
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* The number of super-diagonals of the matrix A if UPLO = 'U', |
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* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. |
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* |
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* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) |
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* On entry, the upper or lower triangle of the symmetric band |
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* matrix A, stored in the first KD+1 rows of the array. The |
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* j-th column of A is stored in the j-th column of the array AB |
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* as follows: |
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* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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* |
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* On exit, if INFO = 0, the triangular factor U or L from the |
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* Cholesky factorization A = U**T*U or A = L*L**T of the band |
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* matrix A, in the same storage format as A. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= KD+1. |
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* |
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* S (input) DOUBLE PRECISION array, dimension (N) |
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* The scale factors for A. |
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* |
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* SCOND (input) DOUBLE PRECISION |
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* Ratio of the smallest S(i) to the largest S(i). |
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* |
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* AMAX (input) DOUBLE PRECISION |
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* Absolute value of largest matrix entry. |
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* |
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* EQUED (output) CHARACTER*1 |
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* Specifies whether or not equilibration was done. |
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* = 'N': No equilibration. |
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* = 'Y': Equilibration was done, i.e., A has been replaced by |
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* diag(S) * A * diag(S). |
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* |
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* Internal Parameters |
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* =================== |
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* |
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* THRESH is a threshold value used to decide if scaling should be done |
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* based on the ratio of the scaling factors. If SCOND < THRESH, |
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* scaling is done. |
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* |
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* LARGE and SMALL are threshold values used to decide if scaling should |
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* be done based on the absolute size of the largest matrix element. |
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* If AMAX > LARGE or AMAX < SMALL, scaling is done. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |