Contents
csprfs - improve the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefin-
ite and packed, and provides error bounds and backward error
estimates for the solution
SUBROUTINE CSPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CSPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE SPRFS(UPLO, [N], [NRHS], A, AF, IPIVOT, B, [LDB], X, [LDX],
FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE SPRFS_64(UPLO, [N], [NRHS], A, AF, IPIVOT, B, [LDB], X,
[LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void csprfs(char uplo, int n, int nrhs, complex *a, complex
*af, int *ipivot, complex *b, int ldb, complex *x,
int ldx, float *ferr, float *berr, int *info);
void csprfs_64(char uplo, long n, long nrhs, complex *a,
complex *af, long *ipivot, complex *b, long ldb,
complex *x, long ldx, float *ferr, float *berr,
long *info);
csprfs improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefin-
ite and packed, and provides error bounds and backward error
estimates for the solution.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number
of columns of the matrices B and X. NRHS >= 0.
A (input) Complex array, dimension (N*(N+1)/2) The upper or
lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of
A is stored in the array A as follows: if UPLO =
'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if
UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for
j<=i<=n.
AF (input)
Complex array, dimension (N*(N+1)/2) The factored
form of the matrix A. AF contains the block diag-
onal 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 CSPTRF,
stored as a packed triangular matrix.
IPIVOT (input)
Integer array, dimension (N) Details of the inter-
changes and the block structure of D as determined
by CSPTRF.
B (input) Complex array, dimension (LDB,NRHS) The right hand
side matrix B.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,N).
X (input/output)
Complex array, dimension (LDX,NRHS) On entry, the
solution matrix X, as computed by CSPTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >=
max(1,N).
FERR (output)
Real array, dimension (NRHS) The estimated forward
error bound for each solution vector X(j) (the j-
th column of the solution matrix X). If XTRUE is
the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of
the largest element in (X(j) - XTRUE) divided by
the magnitude of the largest element in X(j). The
estimate is as reliable as the estimate for RCOND,
and is almost always a slight overestimate of the
true error.
BERR (output)
Real array, dimension (NRHS) The componentwise
relative backward error of each solution vector
X(j) (i.e., the smallest relative change in any
element of A or B that makes X(j) an exact solu-
tion).
WORK (workspace)
Complex array, dimension(2*N)
WORK2 (workspace)
Integer array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value