dsysv man page on Scientific

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```DSYSV(1)	      LAPACK driver routine (version 3.2)	      DSYSV(1)

NAME
DSYSV - computes the solution to a real system of linear equations  A *
X = B,

SYNOPSIS
SUBROUTINE DSYSV( UPLO, N, NRHS, A, LDA, IPIV,  B,  LDB,	 WORK,	LWORK,
INFO )

CHARACTER	 UPLO

INTEGER	 INFO, LDA, LDB, LWORK, N, NRHS

INTEGER	 IPIV( * )

DOUBLE	 PRECISION A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE
DSYSV computes the solution to a real 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)  tri‐
angular 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.

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

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

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

A       (input/output) DOUBLE PRECISION 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
DSYTRF.

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

IPIV    (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure  of	D,  as
determined  by DSYTRF.  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       (input/output) DOUBLE PRECISION 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     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

WORK	  (workspace/output)   DOUBLE	PRECISION   array,   dimension
(MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The length of WORK.  LWORK >= 1, and for best performance LWORK
>=  max(1,N*NB),	 where NB is the optimal blocksize for DSYTRF.
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    (output) 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.

LAPACK driver routine (version 3November 2008			      DSYSV(1)
```
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