Function

NumCosmoMathlapack_dsysvx

Declaration [src] 

gint
ncm_lapack_dsysvx (
  gchar fact,
  gchar uplo,
  gint n,
  gint nrhs,
  gdouble* a,
  gint lda,
  gdouble* af,
  gint ldaf,
  gint* ipiv,
  gdouble* b,
  gint ldb,
  gdouble* x,
  gint ldx,
  gdouble* rcond,
  gdouble* ferr,
  gdouble* berr,
  gdouble* work,
  gint lwork,
  gint* iwork
)

Description [src]

Purpose

DSYSVX uses the diagonal pivoting factorization to compute 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.

Error bounds on the solution and a condition estimate are also provided.

Description

The following steps are performed:

  1. If FACT = ‘N’, the diagonal pivoting method is used to factor A. The form of the factorization is
  2. A = U * D * U**T, if UPLO = ‘U’, or
  3. 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.
  4. If some D(i,i)=0, so that D is exactly singular, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below.
  5. The system of equations is solved for X using the factored form of A.
  6. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.

Parameters

fact

Type: gchar

FACT is CHARACTER*1.

uplo

Type: gchar

UPLO is CHARACTER*1.

n

Type: gint

N is INTEGER.

nrhs

Type: gint

NRHS is INTEGER.

a

Type: gdouble*

A is DOUBLE PRECISION array, dimension (LDA,N).

The data is owned by the caller of the function.
lda

Type: gint

LDA is INTEGER.

af

Type: gdouble*

AF is DOUBLE PRECISION array, dimension (LDAF,N).

The data is owned by the caller of the function.
ldaf

Type: gint

LDA is INTEGER.

ipiv

Type: gint*

IPIV is INTEGER array, dimension (N).

The data is owned by the caller of the function.
b

Type: gdouble*

B is DOUBLE PRECISION array, dimension (LDB,NRHS).

The data is owned by the caller of the function.
ldb

Type: gint

LDB is INTEGER.

x

Type: gdouble*

X is DOUBLE PRECISION array, dimension (LDX,NRHS).

The data is owned by the caller of the function.
ldx

Type: gint

LDX is INTEGER.

rcond

Type: gdouble*

RCOND is DOUBLE PRECISION.

The data is owned by the caller of the function.
ferr

Type: gdouble*

FERR is DOUBLE PRECISION array, dimension (NRHS).

The data is owned by the caller of the function.
berr

Type: gdouble*

BERR is DOUBLE PRECISION array, dimension (NRHS).

The data is owned by the caller of the function.
work

Type: gdouble*

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).

The data is owned by the caller of the function.
lwork

Type: gint

LWORK is INTEGER.

iwork

Type: gint*

IWORK is INTEGER array, dimension (N).

The data is owned by the caller of the function.

Return value

Type: gint

INFO is INTEGER - = 0: successful exit - < 0: if INFO = -i, the i-th argument had an illegal value - > 0: if INFO = i, and i is - <= N: D(i,i) is exactly zero. The factorization has been completed but the factor D is exactly singular, so the solution and error bounds could not be computed. RCOND = 0 is returned. - = N+1: D is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest.