Contents
zsprfs - 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 ZSPRFS(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZSPRFS_64(UPLO, N, NRHS, A, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION 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(8), DIMENSION(:) :: A, AF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), 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(8), DIMENSION(:) :: A, AF, WORK
COMPLEX(8), DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zsprfs(char uplo, int n, int nrhs, doublecomplex *a,
doublecomplex *af, int *ipivot, doublecomplex *b,
int ldb, doublecomplex *x, int ldx, double *ferr,
double *berr, int *info);
void zsprfs_64(char uplo, long n, long nrhs, doublecomplex
*a, doublecomplex *af, long *ipivot, doublecomplex
*b, long ldb, doublecomplex *x, long ldx, double
*ferr, double *berr, long *info);
zsprfs 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) Double 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)
Double complex array, dimension (N*(N+1)/2) The
factored form of the matrix A. AF contains 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
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) Double 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)
Double 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)
Double precision 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 ele-
ment 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)
Double precision array, dimension (NRHS) The com-
ponentwise relative backward error of each solu-
tion vector X(j) (i.e., the smallest relative
change in any element of A or B that makes X(j) an
exact solution).
WORK (workspace)
Double precision 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