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version 1.12, 2017/06/17 11:06:14
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*> \brief \b DGBEQUB |
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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 DGBEQUB + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbequb.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/dgbequb.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/dgbequb.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 DGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, |
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* AMAX, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, KL, KU, LDAB, M, N |
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* DOUBLE PRECISION AMAX, COLCND, ROWCND |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) |
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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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*> DGBEQUB computes row and column scalings intended to equilibrate an |
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*> M-by-N matrix A and reduce its condition number. R returns the row |
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*> scale factors and C the column scale factors, chosen to try to make |
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*> the largest element in each row and column of the matrix B with |
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*> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most |
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*> the radix. |
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*> |
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*> R(i) and C(j) are restricted to be a power of the radix between |
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*> SMLNUM = smallest safe number and BIGNUM = largest safe number. Use |
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*> of these scaling factors is not guaranteed to reduce the condition |
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*> number of A but works well in practice. |
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*> |
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*> This routine differs from DGEEQU by restricting the scaling factors |
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*> to a power of the radix. Barring over- and underflow, scaling by |
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*> these factors introduces no additional rounding errors. However, the |
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*> scaled entries' magnitudes are no longer approximately 1 but lie |
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*> between sqrt(radix) and 1/sqrt(radix). |
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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] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix A. M >= 0. |
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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 columns of the 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 A. LDAB >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[out] R |
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*> \verbatim |
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*> R is DOUBLE PRECISION array, dimension (M) |
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*> If INFO = 0 or INFO > M, R contains the row scale factors |
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*> for A. |
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*> \endverbatim |
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*> |
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*> \param[out] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (N) |
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*> If INFO = 0, C contains the column scale factors for A. |
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*> \endverbatim |
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*> |
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*> \param[out] ROWCND |
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*> \verbatim |
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*> ROWCND is DOUBLE PRECISION |
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*> If INFO = 0 or INFO > M, ROWCND contains the ratio of the |
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*> smallest R(i) to the largest R(i). If ROWCND >= 0.1 and |
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*> AMAX is neither too large nor too small, it is not worth |
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*> scaling by R. |
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*> \endverbatim |
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*> |
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*> \param[out] COLCND |
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*> \verbatim |
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*> COLCND is DOUBLE PRECISION |
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*> If INFO = 0, COLCND contains the ratio of the smallest |
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*> C(i) to the largest C(i). If COLCND >= 0.1, it is not |
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*> worth scaling by C. |
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*> \endverbatim |
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*> |
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*> \param[out] AMAX |
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*> \verbatim |
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*> AMAX is DOUBLE PRECISION |
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*> Absolute value of largest matrix element. If AMAX is very |
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*> close to overflow or very close to underflow, the matrix |
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*> should be scaled. |
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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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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i, and i is |
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*> <= M: the i-th row of A is exactly zero |
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*> > M: the (i-M)-th column of A is exactly zero |
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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 December 2016 |
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* |
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*> \ingroup doubleGBcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, |
SUBROUTINE DGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, |
$ AMAX, INFO ) |
$ AMAX, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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..-- |
* -- November 2008 -- |
* December 2016 |
* |
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* -- 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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* |
* |
IMPLICIT NONE |
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* .. |
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* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, KL, KU, LDAB, M, N |
INTEGER INFO, KL, KU, LDAB, M, N |
DOUBLE PRECISION AMAX, COLCND, ROWCND |
DOUBLE PRECISION AMAX, COLCND, ROWCND |
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DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) |
DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGBEQUB computes row and column scalings intended to equilibrate an |
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* M-by-N matrix A and reduce its condition number. R returns the row |
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* scale factors and C the column scale factors, chosen to try to make |
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* the largest element in each row and column of the matrix B with |
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* elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most |
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* the radix. |
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* |
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* R(i) and C(j) are restricted to be a power of the radix between |
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* SMLNUM = smallest safe number and BIGNUM = largest safe number. Use |
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* of these scaling factors is not guaranteed to reduce the condition |
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* number of A but works well in practice. |
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* |
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* This routine differs from DGEEQU by restricting the scaling factors |
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* to a power of the radix. Baring over- and underflow, scaling by |
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* these factors introduces no additional rounding errors. However, the |
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* scaled entries' magnitured are no longer approximately 1 but lie |
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* between sqrt(radix) and 1/sqrt(radix). |
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* |
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* Arguments |
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* ========= |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the 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 A. LDAB >= max(1,M). |
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* |
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* R (output) DOUBLE PRECISION array, dimension (M) |
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* If INFO = 0 or INFO > M, R contains the row scale factors |
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* for A. |
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* |
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* C (output) DOUBLE PRECISION array, dimension (N) |
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* If INFO = 0, C contains the column scale factors for A. |
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* |
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* ROWCND (output) DOUBLE PRECISION |
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* If INFO = 0 or INFO > M, ROWCND contains the ratio of the |
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* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and |
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* AMAX is neither too large nor too small, it is not worth |
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* scaling by R. |
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* |
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* COLCND (output) DOUBLE PRECISION |
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* If INFO = 0, COLCND contains the ratio of the smallest |
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* C(i) to the largest C(i). If COLCND >= 0.1, it is not |
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* worth scaling by C. |
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* |
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* AMAX (output) DOUBLE PRECISION |
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* Absolute value of largest matrix element. If AMAX is very |
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* close to overflow or very close to underflow, the matrix |
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* should be scaled. |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: if INFO = i, and i is |
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* <= M: the i-th row of A is exactly zero |
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* > M: the (i-M)-th column of A is exactly zero |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |