zgbrfs
zgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
SUBROUTINE ZGBRFS( TRANSA, N, NSUB, NSUPER, NRHS, A, LDA, AF, LDAF,
* IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZGBRFS_64( TRANSA, N, NSUB, NSUPER, NRHS, A, LDA, AF,
* LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE GBRFS( [TRANSA], [N], NSUB, NSUPER, [NRHS], A, [LDA], AF,
* [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2],
* [INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE GBRFS_64( [TRANSA], [N], NSUB, NSUPER, [NRHS], A, [LDA],
* AF, [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK],
* [WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
#include <sunperf.h>
void zgbrfs(char transa, int n, int nsub, int nsuper, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, int *ipivot, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info);
void zgbrfs_64(char transa, long n, long nsub, long nsuper, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);
zgbrfs improves the computed solution to a system of linear
equations when the coefficient matrix is banded, and provides
error bounds and backward error estimates for the solution.
-
* TRANSA (input)
-
Specifies the form of the system of equations:
-
* N (input)
-
The order of the matrix A. N >= 0.
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* NSUB (input)
-
The number of subdiagonals within the band of A. NSUB >= 0.
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* NSUPER (input)
-
The number of superdiagonals within the band of A. NSUPER >= 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)
-
The original band matrix A, stored in rows 1 to NSUB+NSUPER+1.
The j-th column of A is stored in the j-th column of the
array A as follows:
A(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
-
* LDA (input)
-
The leading dimension of the array A. LDA >= NSUB+NSUPER+1.
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* AF (input)
-
Details of the LU factorization of the band matrix A, as
computed by CGBTRF. U is stored as an upper triangular band
matrix with NSUB+NSUPER superdiagonals in rows 1 to NSUB+NSUPER+1, and
the multipliers used during the factorization are stored in
rows NSUB+NSUPER+2 to 2*NSUB+NSUPER+1.
-
* LDAF (input)
-
The leading dimension of the array AF. LDAF >= 2*NSUB*NSUPER+1.
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* IPIVOT (input)
-
The pivot indices from CGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIVOT(i).
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* 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 CGBTRS.
On exit, the improved solution matrix X.
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* LDX (input)
-
The leading dimension of the array X. LDX >= max(1,N).
-
* FERR (output)
-
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)
-
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)
-