cptrfs
cptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
SUBROUTINE CPTRFS( UPLO, N, NRHS, DIAG, OFFD, DIAGF, OFFDF, B, LDB,
* X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX OFFD(*), OFFDF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
REAL DIAG(*), DIAGF(*), FERR(*), BERR(*), WORK2(*)
SUBROUTINE CPTRFS_64( UPLO, N, NRHS, DIAG, OFFD, DIAGF, OFFDF, B,
* LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
COMPLEX OFFD(*), OFFDF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
REAL DIAG(*), DIAGF(*), FERR(*), BERR(*), WORK2(*)
SUBROUTINE PTRFS( UPLO, [N], [NRHS], DIAG, OFFD, DIAGF, OFFDF, B,
* [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: OFFD, OFFDF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: DIAG, DIAGF, FERR, BERR, WORK2
SUBROUTINE PTRFS_64( UPLO, [N], [NRHS], DIAG, OFFD, DIAGF, OFFDF, B,
* [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: OFFD, OFFDF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
REAL, DIMENSION(:) :: DIAG, DIAGF, FERR, BERR, WORK2
#include <sunperf.h>
void cptrfs(char uplo, int n, int nrhs, float *diag, complex *offd, float *diagf, complex *offdf, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info);
void cptrfs_64(char uplo, long n, long nrhs, float *diag, complex *offd, float *diagf, complex *offdf, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);
cptrfs improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive definite
and tridiagonal, and provides error bounds and backward error
estimates for the solution.
-
* UPLO (input)
-
Specifies whether the superdiagonal or the subdiagonal of the
tridiagonal matrix A is stored and the form of the
factorization:
-
* 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 matrix B. NRHS >= 0.
-
* DIAG (input)
-
The n real diagonal elements of the tridiagonal matrix A.
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* OFFD (input)
-
The (n-1) off-diagonal elements of the tridiagonal matrix A
(see UPLO).
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* DIAGF (input)
-
The n diagonal elements of the diagonal matrix DIAG from
the factorization computed by CPTTRF.
-
* OFFDF (input)
-
The (n-1) off-diagonal elements of the unit bidiagonal
factor U or L from the factorization computed by CPTTRF
(see UPLO).
-
* B (input)
-
The right hand side matrix B.
-
* LDB (input)
-
The leading dimension of the array B. LDB >= max(1,N).
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* X (input/output)
-
On entry, the solution matrix X, as computed by CPTTRS.
On exit, the improved solution matrix X.
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* LDX (input)
-
The leading dimension of the array X. LDX >= max(1,N).
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* FERR (output)
-
The 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).
-
* BERR (output)
-
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).
-
* WORK (workspace)
-
dimension(N)
-
* WORK2 (workspace)
-
-
* INFO (output)
-