zsysv_rook (3)  Linux Manuals
NAME
zsysv_rook.f 
SYNOPSIS
Functions/Subroutines
subroutine zsysv_rook (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
Function/Subroutine Documentation
subroutine zsysv_rook (characterUPLO, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )WORK, integerLWORK, integerINFO)
ZSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
Purpose:

ZSYSV_ROOK computes the solution to a complex system of linear equations A * X = B, where A is an NbyN symmetric matrix and X and B are NbyNRHS 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 1by1 and 2by2 diagonal blocks. ZSYTRF_ROOK is called to compute the factorization of a complex symmetric matrix A using the bounded BunchKaufman ("rook") diagonal pivoting method. The factored form of A is then used to solve the system of equations A * X = B by calling ZSYTRS_ROOK.
Parameters:

UPLO
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
NN is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
AA is COMPLEX*16 array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading NbyN 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 NbyN 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 ZSYTRF_ROOK.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIVIPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by ZSYTRF_ROOK. If UPLO = 'U': If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1by1 diagonal block. If IPIV(k) < 0 and IPIV(k1) < 0, then rows and columns k and IPIV(k) were interchanged and rows and columns k1 and IPIV(k1) were inerchaged, D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = 'L': If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1by1 diagonal block. If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and IPIV(k) were interchanged and rows and columns k+1 and IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2by2 diagonal block.
BB is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the NbyNRHS right hand side matrix B. On exit, if INFO = 0, the NbyNRHS solution matrix X.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
WORKWORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK is INTEGER The length of WORK. LWORK >= 1, and for best performance LWORK >= max(1,N*NB), where NB is the optimal blocksize for ZSYTRF_ROOK. TRS will be done with Level 2 BLAS 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.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith 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
Contributors:

November 2011, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester
Definition at line 204 of file zsysv_rook.f.
Author
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