zsysv.f man page

zsysv.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine zsysv (character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

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

Purpose:

 ZSYSV 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

          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

          A is COMPLEX*16 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
          ZSYTRF.

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 ZSYTRF.  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

          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.

LDB

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

WORK

          WORK is COMPLEX*16 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
          ZSYTRF.
          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:

December 2016

Definition at line 173 of file zsysv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zsysv(3) is an alias of zsysv.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK