csysv-f(3)

csysv.f –

Synopsis

Functions/Subroutines

subroutine csysv (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
CSYSV computes the solution to system of linear equations A * X = B for SY matrices

Function/Subroutine Documentation

subroutine csysv (characterUPLO, integerN, integerNRHS, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )WORK, integerLWORK, integerINFO)

CSYSV computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

 CSYSV computes the solution to a complex system of linear equations
 A * X = B,
 where A is an N-by-N symmetric matrix 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, and 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.

Parameters:

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangle of A is stored;
 = 'L': Lower triangle of A is stored.

 N is INTEGER
 The number of linear equations, i.e., the order of the
 matrix A. N >= 0.

NRHS

 NRHS is INTEGER
 The number of right hand sides, i.e., the number of columns
 of the matrix B. NRHS >= 0.

 A is COMPLEX array, dimension (LDA,N)
 On entry, the symmetric matrix A. If UPLO = 'U', the leading
 N-by-N upper triangular part of A contains the upper
 triangular part of the matrix A, and the strictly lower
 triangular part of A is not referenced. If UPLO = 'L', the
 leading N-by-N lower triangular part of A contains the lower
 triangular part of the matrix A, and the strictly upper
 triangular part of A is not referenced.
 On exit, if INFO = 0, 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
 CSYTRF.

LDA

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(1,N).

IPIV

 IPIV is INTEGER array, dimension (N)
 Details of the interchanges and the block structure of D, as
 determined by CSYTRF. 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 is COMPLEX 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

 LDB is INTEGER
 The leading dimension of the array B. LDB >= max(1,N).

WORK

 WORK is COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER
 The length of WORK. LWORK >= 1, and for best performance
 LWORK >= max(1,N*NB), where NB is the optimal blocksize for
 CSYTRF.
 for LWORK < N, TRS will be done with Level BLAS 2
 for LWORK >= N, TRS will be done with Level BLAS 3
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates the optimal size of the WORK array, returns
 this value as the first entry of the WORK array, and no error
 message related to LWORK is issued by XERBLA.

INFO

 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 171 of file csysv.f.

Author

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