version 1.7, 2010/12/21 13:53:55
|
version 1.14, 2016/08/27 15:35:06
|
Line 1
|
Line 1
|
|
*> \brief \b ZSPRFS |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download ZSPRFS + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsprfs.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsprfs.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsprfs.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE ZSPRFS( 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( * ) |
|
* DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) |
|
* COMPLEX*16 AFP( * ), AP( * ), B( LDB, * ), WORK( * ), |
|
* $ X( LDX, * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> ZSPRFS improves the computed solution to a system of linear |
|
*> equations when the coefficient matrix is symmetric 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*16 array, dimension (N*(N+1)/2) |
|
*> The upper or lower triangle of the symmetric 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*16 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**T or |
|
*> A = L*D*L**T as computed by ZSPTRF, 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 ZSPTRF. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] B |
|
*> \verbatim |
|
*> B is COMPLEX*16 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*16 array, dimension (LDX,NRHS) |
|
*> On entry, the solution matrix X, as computed by ZSPTRS. |
|
*> 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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*16 array, dimension (2*N) |
|
*> \endverbatim |
|
*> |
|
*> \param[out] RWORK |
|
*> \verbatim |
|
*> RWORK is DOUBLE PRECISION 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 |
|
* |
|
*> \par Internal Parameters: |
|
* ========================= |
|
*> |
|
*> \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 complex16OTHERcomputational |
|
* |
|
* ===================================================================== |
SUBROUTINE ZSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, |
SUBROUTINE ZSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, |
$ FERR, BERR, WORK, RWORK, INFO ) |
$ FERR, BERR, WORK, RWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- 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..-- |
* November 2006 |
* November 2011 |
* |
|
* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
Line 19
|
Line 196
|
$ X( LDX, * ) |
$ X( LDX, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZSPRFS improves the computed solution to a system of linear |
|
* equations when the coefficient matrix is symmetric 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*16 array, dimension (N*(N+1)/2) |
|
* The upper or lower triangle of the symmetric 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*16 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**T or |
|
* A = L*D*L**T as computed by ZSPTRF, 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 ZSPTRF. |
|
* |
|
* B (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS) |
|
* On entry, the solution matrix X, as computed by ZSPTRS. |
|
* On exit, the improved solution matrix X. |
|
* |
|
* LDX (input) INTEGER |
|
* The leading dimension of the array X. LDX >= max(1,N). |
|
* |
|
* FERR (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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*16 array, dimension (2*N) |
|
* |
|
* RWORK (workspace) DOUBLE PRECISION 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 .. |
* .. Parameters .. |
Line 305
|
Line 401
|
IF( KASE.NE.0 ) THEN |
IF( KASE.NE.0 ) THEN |
IF( KASE.EQ.1 ) THEN |
IF( KASE.EQ.1 ) THEN |
* |
* |
* Multiply by diag(W)*inv(A'). |
* Multiply by diag(W)*inv(A**T). |
* |
* |
CALL ZSPTRS( UPLO, N, 1, AFP, IPIV, WORK, N, INFO ) |
CALL ZSPTRS( UPLO, N, 1, AFP, IPIV, WORK, N, INFO ) |
DO 110 I = 1, N |
DO 110 I = 1, N |