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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/cgbequb.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
download | lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.gz lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.bz2 lapack-e1d39294aee16fa6db9ba079b14442358217db71.zip |
Integrating Doxygen in comments
Diffstat (limited to 'SRC/cgbequb.f')
-rw-r--r-- | SRC/cgbequb.f | 238 |
1 files changed, 155 insertions, 83 deletions
diff --git a/SRC/cgbequb.f b/SRC/cgbequb.f index e447ce42..9a03c533 100644 --- a/SRC/cgbequb.f +++ b/SRC/cgbequb.f @@ -1,99 +1,171 @@ - SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, - $ AMAX, INFO ) -* -* -- LAPACK routine (version 3.2) -- -* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- -* -- Jason Riedy of Univ. of California Berkeley. -- -* -- November 2008 -- -* -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley and NAG Ltd. -- -* - IMPLICIT NONE -* .. -* .. Scalar Arguments .. - INTEGER INFO, KL, KU, LDAB, M, N - REAL AMAX, COLCND, ROWCND -* .. -* .. Array Arguments .. - REAL C( * ), R( * ) - COMPLEX AB( LDAB, * ) -* .. -* +*> \brief \b CGBEQUB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, +* AMAX, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, KL, KU, LDAB, M, N +* REAL AMAX, COLCND, ROWCND +* .. +* .. Array Arguments .. +* REAL C( * ), R( * ) +* COMPLEX AB( LDAB, * ) +* .. +* * Purpose * ======= * -* CGBEQUB computes row and column scalings intended to equilibrate an -* M-by-N matrix A and reduce its condition number. R returns the row -* scale factors and C the column scale factors, chosen to try to make -* the largest element in each row and column of the matrix B with -* elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most -* the radix. -* -* R(i) and C(j) are restricted to be a power of the radix between -* SMLNUM = smallest safe number and BIGNUM = largest safe number. Use -* of these scaling factors is not guaranteed to reduce the condition -* number of A but works well in practice. -* -* This routine differs from CGEEQU by restricting the scaling factors -* to a power of the radix. Baring over- and underflow, scaling by -* these factors introduces no additional rounding errors. However, the -* scaled entries' magnitured are no longer approximately 1 but lie -* between sqrt(radix) and 1/sqrt(radix). +*>\details \b Purpose: +*>\verbatim +*> +*> CGBEQUB computes row and column scalings intended to equilibrate an +*> M-by-N matrix A and reduce its condition number. R returns the row +*> scale factors and C the column scale factors, chosen to try to make +*> the largest element in each row and column of the matrix B with +*> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most +*> the radix. +*> +*> R(i) and C(j) are restricted to be a power of the radix between +*> SMLNUM = smallest safe number and BIGNUM = largest safe number. Use +*> of these scaling factors is not guaranteed to reduce the condition +*> number of A but works well in practice. +*> +*> This routine differs from CGEEQU by restricting the scaling factors +*> to a power of the radix. Baring over- and underflow, scaling by +*> these factors introduces no additional rounding errors. However, the +*> scaled entries' magnitured are no longer approximately 1 but lie +*> between sqrt(radix) and 1/sqrt(radix). +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns 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) DOUBLE PRECISION array, dimension (LDAB,N) -* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. -* The j-th column of A is stored in the j-th column of the -* array AB as follows: -* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -* -* LDAB (input) INTEGER -* The leading dimension of the array A. LDAB >= max(1,M). +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns 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 DOUBLE PRECISION array, dimension (LDAB,N) +*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. +*> The j-th column of A is stored in the j-th column of the +*> array AB as follows: +*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array A. LDAB >= max(1,M). +*> \endverbatim +*> +*> \param[out] R +*> \verbatim +*> R is REAL array, dimension (M) +*> If INFO = 0 or INFO > M, R contains the row scale factors +*> for A. +*> \endverbatim +*> +*> \param[out] C +*> \verbatim +*> C is REAL array, dimension (N) +*> If INFO = 0, C contains the column scale factors for A. +*> \endverbatim +*> +*> \param[out] ROWCND +*> \verbatim +*> ROWCND is REAL +*> If INFO = 0 or INFO > M, ROWCND contains the ratio of the +*> smallest R(i) to the largest R(i). If ROWCND >= 0.1 and +*> AMAX is neither too large nor too small, it is not worth +*> scaling by R. +*> \endverbatim +*> +*> \param[out] COLCND +*> \verbatim +*> COLCND is REAL +*> If INFO = 0, COLCND contains the ratio of the smallest +*> C(i) to the largest C(i). If COLCND >= 0.1, it is not +*> worth scaling by C. +*> \endverbatim +*> +*> \param[out] AMAX +*> \verbatim +*> AMAX is REAL +*> Absolute value of largest matrix element. If AMAX is very +*> close to overflow or very close to underflow, the matrix +*> should be scaled. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, and i is +*> <= M: the i-th row of A is exactly zero +*> > M: the (i-M)-th column of A is exactly zero +*> \endverbatim +*> +* +* Authors +* ======= * -* R (output) REAL array, dimension (M) -* If INFO = 0 or INFO > M, R contains the row scale factors -* for A. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* C (output) REAL array, dimension (N) -* If INFO = 0, C contains the column scale factors for A. +*> \date November 2011 * -* ROWCND (output) REAL -* If INFO = 0 or INFO > M, ROWCND contains the ratio of the -* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and -* AMAX is neither too large nor too small, it is not worth -* scaling by R. +*> \ingroup complexGBcomputational * -* COLCND (output) REAL -* If INFO = 0, COLCND contains the ratio of the smallest -* C(i) to the largest C(i). If COLCND >= 0.1, it is not -* worth scaling by C. +* ===================================================================== + SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, + $ AMAX, INFO ) * -* AMAX (output) REAL -* Absolute value of largest matrix element. If AMAX is very -* close to overflow or very close to underflow, the matrix -* should be scaled. +* -- LAPACK computational routine (version 3.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: if INFO = i, and i is -* <= M: the i-th row of A is exactly zero -* > M: the (i-M)-th column of A is exactly zero +* .. Scalar Arguments .. + INTEGER INFO, KL, KU, LDAB, M, N + REAL AMAX, COLCND, ROWCND +* .. +* .. Array Arguments .. + REAL C( * ), R( * ) + COMPLEX AB( LDAB, * ) +* .. * * ===================================================================== * |