version 1.3, 2010/08/06 15:28:55
|
version 1.18, 2023/08/07 08:39:26
|
Line 1
|
Line 1
|
|
*> \brief <b> ZHPSV computes the solution to system of linear equations A * X = B for OTHER matrices</b> |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download ZHPSV + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpsv.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpsv.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpsv.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* CHARACTER UPLO |
|
* INTEGER INFO, LDB, N, NRHS |
|
* .. |
|
* .. Array Arguments .. |
|
* INTEGER IPIV( * ) |
|
* COMPLEX*16 AP( * ), B( LDB, * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> ZHPSV computes the solution to a complex system of linear equations |
|
*> A * X = B, |
|
*> where A is an N-by-N Hermitian matrix stored in packed format and X |
|
*> and B are N-by-NRHS matrices. |
|
*> |
|
*> The diagonal pivoting method is used to factor A as |
|
*> A = U * D * U**H, if UPLO = 'U', or |
|
*> A = L * D * L**H, if UPLO = 'L', |
|
*> where U (or L) is a product of permutation and unit upper (lower) |
|
*> triangular matrices, D is Hermitian and block diagonal with 1-by-1 |
|
*> and 2-by-2 diagonal blocks. The factored form of A is then used to |
|
*> solve the system of equations A * X = B. |
|
*> \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 number of linear equations, i.e., 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 matrix B. NRHS >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] AP |
|
*> \verbatim |
|
*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) |
|
*> On entry, 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. |
|
*> See below for further details. |
|
*> |
|
*> On exit, 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 ZHPTRF, stored as |
|
*> a packed triangular matrix in the same storage format as A. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] IPIV |
|
*> \verbatim |
|
*> IPIV is INTEGER array, dimension (N) |
|
*> Details of the interchanges and the block structure of D, as |
|
*> determined by ZHPTRF. If IPIV(k) > 0, then rows and columns |
|
*> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 |
|
*> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, |
|
*> then rows and columns k-1 and -IPIV(k) were interchanged and |
|
*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and |
|
*> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and |
|
*> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 |
|
*> diagonal block. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] B |
|
*> \verbatim |
|
*> B is COMPLEX*16 array, dimension (LDB,NRHS) |
|
*> On entry, the N-by-NRHS right hand side matrix B. |
|
*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDB |
|
*> \verbatim |
|
*> LDB is INTEGER |
|
*> The leading dimension of the array B. LDB >= max(1,N). |
|
*> \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, D(i,i) is exactly zero. The factorization |
|
*> has been completed, but the block diagonal matrix D is |
|
*> exactly singular, so the solution could not be |
|
*> computed. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \ingroup complex16OTHERsolve |
|
* |
|
*> \par Further Details: |
|
* ===================== |
|
*> |
|
*> \verbatim |
|
*> |
|
*> The packed storage scheme is illustrated by the following example |
|
*> when N = 4, UPLO = 'U': |
|
*> |
|
*> Two-dimensional storage of the Hermitian matrix A: |
|
*> |
|
*> a11 a12 a13 a14 |
|
*> a22 a23 a24 |
|
*> a33 a34 (aij = conjg(aji)) |
|
*> a44 |
|
*> |
|
*> Packed storage of the upper triangle of A: |
|
*> |
|
*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] |
|
*> \endverbatim |
|
*> |
|
* ===================================================================== |
SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) |
SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine -- |
* -- 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 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
Line 14
|
Line 173
|
COMPLEX*16 AP( * ), B( LDB, * ) |
COMPLEX*16 AP( * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZHPSV computes the solution to a complex system of linear equations |
|
* A * X = B, |
|
* where A is an N-by-N Hermitian matrix stored in packed format and X |
|
* and B are N-by-NRHS matrices. |
|
* |
|
* The diagonal pivoting method is used to factor A as |
|
* A = U * D * U**H, if UPLO = 'U', or |
|
* A = L * D * L**H, if UPLO = 'L', |
|
* where U (or L) is a product of permutation and unit upper (lower) |
|
* triangular matrices, D is Hermitian and block diagonal with 1-by-1 |
|
* and 2-by-2 diagonal blocks. The factored form of A is then used to |
|
* solve the system of equations A * X = B. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* UPLO (input) CHARACTER*1 |
|
* = 'U': Upper triangle of A is stored; |
|
* = 'L': Lower triangle of A is stored. |
|
* |
|
* N (input) INTEGER |
|
* The number of linear equations, i.e., 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 matrix B. NRHS >= 0. |
|
* |
|
* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) |
|
* On entry, 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. |
|
* See below for further details. |
|
* |
|
* On exit, 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 ZHPTRF, stored as |
|
* a packed triangular matrix in the same storage format as A. |
|
* |
|
* IPIV (output) INTEGER array, dimension (N) |
|
* Details of the interchanges and the block structure of D, as |
|
* determined by ZHPTRF. If IPIV(k) > 0, then rows and columns |
|
* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 |
|
* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, |
|
* then rows and columns k-1 and -IPIV(k) were interchanged and |
|
* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and |
|
* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and |
|
* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 |
|
* diagonal block. |
|
* |
|
* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) |
|
* On entry, the N-by-NRHS right hand side matrix B. |
|
* On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
|
* |
|
* LDB (input) INTEGER |
|
* The leading dimension of the array B. LDB >= max(1,N). |
|
* |
|
* INFO (output) INTEGER |
|
* = 0: successful exit |
|
* < 0: if INFO = -i, the i-th argument had an illegal value |
|
* > 0: if INFO = i, D(i,i) is exactly zero. The factorization |
|
* has been completed, but the block diagonal matrix D is |
|
* exactly singular, so the solution could not be |
|
* computed. |
|
* |
|
* Further Details |
|
* =============== |
|
* |
|
* The packed storage scheme is illustrated by the following example |
|
* when N = 4, UPLO = 'U': |
|
* |
|
* Two-dimensional storage of the Hermitian matrix A: |
|
* |
|
* a11 a12 a13 a14 |
|
* a22 a23 a24 |
|
* a33 a34 (aij = conjg(aji)) |
|
* a44 |
|
* |
|
* Packed storage of the upper triangle of A: |
|
* |
|
* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. External Functions .. |
* .. External Functions .. |
Line 132
|
Line 204
|
RETURN |
RETURN |
END IF |
END IF |
* |
* |
* Compute the factorization A = U*D*U' or A = L*D*L'. |
* Compute the factorization A = U*D*U**H or A = L*D*L**H. |
* |
* |
CALL ZHPTRF( UPLO, N, AP, IPIV, INFO ) |
CALL ZHPTRF( UPLO, N, AP, IPIV, INFO ) |
IF( INFO.EQ.0 ) THEN |
IF( INFO.EQ.0 ) THEN |