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csysv_aa.f(3) LAPACK csysv_aa.f(3)

NAME

csysv_aa.f

SYNOPSIS

Functions/Subroutines


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

Function/Subroutine Documentation

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

CSYSV_AA 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.
Aasen's algorithm is used to factor A as
A = U * T * U**T, if UPLO = 'U', or
A = L * T * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is symmetric tridiagonal. 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 REAL 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 tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U*T*U**T or A = L*T*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)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).

B


B is REAL 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 REAL 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 >= MAX(2*N, 3*N-2), and for
the best performance, LWORK >= max(1,N*NB), where NB is
the optimal blocksize for CSYTRF_AA.
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 2017

Definition at line 164 of file csysv_aa.f.

Author

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