*> \brief ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZSPSV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZSPSV( 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 *> *> ZSPSV computes the solution to a complex system of linear equations *> A * X = B, *> where A is an N-by-N symmetric 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**T, if UPLO = 'U', or *> A = L * D * L**T, if UPLO = 'L', *> where U (or L) is a product of permutation and unit upper (lower) *> triangular matrices, D is symmetric 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 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)*(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**T or A = L*D*L**T as computed by ZSPTRF, 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 ZSPTRF. 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 symmetric matrix A: *> *> a11 a12 a13 a14 *> a22 a23 a24 *> a33 a34 (aij = aji) *> a44 *> *> Packed storage of the upper triangle of A: *> *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] *> \endverbatim *> * ===================================================================== SUBROUTINE ZSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) * * -- LAPACK driver routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 AP( * ), B( LDB, * ) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZSPTRF, ZSPTRS * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZSPSV ', -INFO ) RETURN END IF * * Compute the factorization A = U*D*U**T or A = L*D*L**T. * CALL ZSPTRF( UPLO, N, AP, IPIV, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL ZSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) * END IF RETURN * * End of ZSPSV * END