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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/zppequ.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
download | lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.gz lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.bz2 lapack-e1d39294aee16fa6db9ba079b14442358217db71.zip |
Integrating Doxygen in comments
Diffstat (limited to 'SRC/zppequ.f')
-rw-r--r-- | SRC/zppequ.f | 160 |
1 files changed, 111 insertions, 49 deletions
diff --git a/SRC/zppequ.f b/SRC/zppequ.f index 92478f9a..c1de9f48 100644 --- a/SRC/zppequ.f +++ b/SRC/zppequ.f @@ -1,9 +1,118 @@ +*> \brief \b ZPPEQU +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, N +* DOUBLE PRECISION AMAX, SCOND +* .. +* .. Array Arguments .. +* DOUBLE PRECISION S( * ) +* COMPLEX*16 AP( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZPPEQU computes row and column scalings intended to equilibrate a +*> Hermitian positive definite matrix A in packed storage and reduce +*> its condition number (with respect to the two-norm). S contains the +*> scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix +*> B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal. +*> This choice of S puts the condition number of B within a factor N of +*> the smallest possible condition number over all possible diagonal +*> scalings. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) +*> The upper or lower triangle of the Hermitian matrix A, packed +*> columnwise in a linear array. The j-th column of A is stored +*> in the array AP as follows: +*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension (N) +*> If INFO = 0, S contains the scale factors for A. +*> \endverbatim +*> +*> \param[out] SCOND +*> \verbatim +*> SCOND is DOUBLE PRECISION +*> If INFO = 0, S contains the ratio of the smallest S(i) to +*> the largest S(i). If SCOND >= 0.1 and AMAX is neither too +*> large nor too small, it is not worth scaling by S. +*> \endverbatim +*> +*> \param[out] AMAX +*> \verbatim +*> AMAX is DOUBLE PRECISION +*> 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, the i-th diagonal element is nonpositive. +*> \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 ZPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- 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 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER UPLO @@ -15,53 +124,6 @@ COMPLEX*16 AP( * ) * .. * -* Purpose -* ======= -* -* ZPPEQU computes row and column scalings intended to equilibrate a -* Hermitian positive definite matrix A in packed storage and reduce -* its condition number (with respect to the two-norm). S contains the -* scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix -* B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal. -* This choice of S puts the condition number of B within a factor N of -* the smallest possible condition number over all possible diagonal -* scalings. -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) -* The upper or lower triangle of the Hermitian matrix A, packed -* columnwise in a linear array. The j-th column of A is stored -* in the array AP as follows: -* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -* -* S (output) DOUBLE PRECISION array, dimension (N) -* If INFO = 0, S contains the scale factors for A. -* -* SCOND (output) DOUBLE PRECISION -* If INFO = 0, S contains the ratio of the smallest S(i) to -* the largest S(i). If SCOND >= 0.1 and AMAX is neither too -* large nor too small, it is not worth scaling by S. -* -* AMAX (output) DOUBLE PRECISION -* Absolute value of largest matrix element. If AMAX is very -* close to overflow or very close to underflow, the matrix -* should be scaled. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: if INFO = i, the i-th diagonal element is nonpositive. -* * ===================================================================== * * .. Parameters .. |