zhprfs
zhprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution
SUBROUTINE ZHPRFS( 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 ZHPRFS_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(*)
SUBROUTINE HPRFS( 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 HPRFS_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
#include <sunperf.h>
void zhprfs(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 zhprfs_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);
zhprfs improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefinite
and packed, and provides error bounds and backward error estimates
for the solution.
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* UPLO (input)
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* N (input)
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The order of the matrix A. N >= 0.
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* NRHS (input)
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The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
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* A (input)
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The upper or lower triangle of the Hermitian 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.
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* AF (input)
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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**H or
A = L*D*L**H as computed by CHPTRF, stored as a packed
triangular matrix.
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* IPIVOT (input)
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Details of the interchanges and the block structure of D
as determined by CHPTRF.
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* B (input)
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The right hand side matrix B.
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* LDB (input)
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The leading dimension of the array B. LDB >= max(1,N).
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* X (input/output)
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On entry, the solution matrix X, as computed by CHPTRS.
On exit, the improved solution matrix X.
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* LDX (input)
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The leading dimension of the array X. LDX >= max(1,N).
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* FERR (output)
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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.
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* BERR (output)
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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 solution).
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* WORK (workspace)
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dimension(2*N)
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* WORK2 (workspace)
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* INFO (output)
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