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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/chprfs.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
download | lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.gz lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.bz2 lapack-e1d39294aee16fa6db9ba079b14442358217db71.zip |
Integrating Doxygen in comments
Diffstat (limited to 'SRC/chprfs.f')
-rw-r--r-- | SRC/chprfs.f | 258 |
1 files changed, 173 insertions, 85 deletions
diff --git a/SRC/chprfs.f b/SRC/chprfs.f index a84b3a8e..8f590562 100644 --- a/SRC/chprfs.f +++ b/SRC/chprfs.f @@ -1,12 +1,181 @@ +*> \brief \b CHPRFS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, +* FERR, BERR, WORK, RWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDB, LDX, N, NRHS +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* REAL BERR( * ), FERR( * ), RWORK( * ) +* COMPLEX AFP( * ), AP( * ), B( LDB, * ), WORK( * ), +* $ X( LDX, * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CHPRFS improves the computed solution to a system of linear +*> equations when the coefficient matrix is Hermitian indefinite +*> and packed, and provides error bounds and backward error estimates +*> for the solution. +*> +*>\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] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of right hand sides, i.e., the number of columns +*> of the matrices B and X. NRHS >= 0. +*> \endverbatim +*> +*> \param[in] AP +*> \verbatim +*> AP is COMPLEX 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. +*> \endverbatim +*> +*> \param[in] AFP +*> \verbatim +*> AFP is COMPLEX array, dimension (N*(N+1)/2) +*> The factored form of the matrix A. AFP contains the block +*> diagonal matrix D and the multipliers used to obtain the +*> factor U or L from the factorization A = U*D*U**H or +*> A = L*D*L**H as computed by CHPTRF, stored as a packed +*> triangular matrix. +*> \endverbatim +*> +*> \param[in] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> Details of the interchanges and the block structure of D +*> as determined by CHPTRF. +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is COMPLEX array, dimension (LDB,NRHS) +*> The right hand side matrix B. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array, dimension (LDX,NRHS) +*> On entry, the solution matrix X, as computed by CHPTRS. +*> On exit, the improved solution matrix X. +*> \endverbatim +*> +*> \param[in] LDX +*> \verbatim +*> LDX is INTEGER +*> The leading dimension of the array X. LDX >= max(1,N). +*> \endverbatim +*> +*> \param[out] FERR +*> \verbatim +*> FERR is REAL array, dimension (NRHS) +*> The estimated forward error bound for each solution vector +*> X(j) (the j-th column of the solution matrix X). +*> If XTRUE is the true solution corresponding to X(j), FERR(j) +*> is an estimated upper bound for the magnitude of the largest +*> element in (X(j) - XTRUE) divided by the magnitude of the +*> largest element in X(j). The estimate is as reliable as +*> the estimate for RCOND, and is almost always a slight +*> overestimate of the true error. +*> \endverbatim +*> +*> \param[out] BERR +*> \verbatim +*> BERR is REAL array, dimension (NRHS) +*> The componentwise relative backward error of each solution +*> vector X(j) (i.e., the smallest relative change in +*> any element of A or B that makes X(j) an exact solution). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is REAL 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 +*> \verbatim +*> Internal Parameters +*> =================== +*> \endverbatim +*> \verbatim +*> ITMAX is the maximum number of steps of iterative refinement. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERcomputational +* +* ===================================================================== SUBROUTINE CHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, $ FERR, BERR, WORK, RWORK, 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 -* -* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. +* November 2011 * * .. Scalar Arguments .. CHARACTER UPLO @@ -19,87 +188,6 @@ $ X( LDX, * ) * .. * -* Purpose -* ======= -* -* CHPRFS improves the computed solution to a system of linear -* equations when the coefficient matrix is Hermitian indefinite -* and packed, and provides error bounds and backward error estimates -* for the solution. -* -* 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. -* -* NRHS (input) INTEGER -* The number of right hand sides, i.e., the number of columns -* of the matrices B and X. NRHS >= 0. -* -* AP (input) COMPLEX 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. -* -* AFP (input) COMPLEX array, dimension (N*(N+1)/2) -* The factored form of the matrix A. AFP contains the block -* diagonal matrix D and the multipliers used to obtain the -* factor U or L from the factorization A = U*D*U**H or -* A = L*D*L**H as computed by CHPTRF, stored as a packed -* triangular matrix. -* -* IPIV (input) INTEGER array, dimension (N) -* Details of the interchanges and the block structure of D -* as determined by CHPTRF. -* -* B (input) COMPLEX array, dimension (LDB,NRHS) -* The right hand side matrix B. -* -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1,N). -* -* X (input/output) COMPLEX array, dimension (LDX,NRHS) -* On entry, the solution matrix X, as computed by CHPTRS. -* On exit, the improved solution matrix X. -* -* LDX (input) INTEGER -* The leading dimension of the array X. LDX >= max(1,N). -* -* FERR (output) REAL array, dimension (NRHS) -* The estimated forward error bound for each solution vector -* X(j) (the j-th column of the solution matrix X). -* If XTRUE is the true solution corresponding to X(j), FERR(j) -* is an estimated upper bound for the magnitude of the largest -* element in (X(j) - XTRUE) divided by the magnitude of the -* largest element in X(j). The estimate is as reliable as -* the estimate for RCOND, and is almost always a slight -* overestimate of the true error. -* -* BERR (output) REAL array, dimension (NRHS) -* The componentwise relative backward error of each solution -* vector X(j) (i.e., the smallest relative change in -* any element of A or B that makes X(j) an exact solution). -* -* WORK (workspace) COMPLEX array, dimension (2*N) -* -* RWORK (workspace) REAL array, dimension (N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* -* Internal Parameters -* =================== -* -* ITMAX is the maximum number of steps of iterative refinement. -* * ===================================================================== * * .. Parameters .. |