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LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
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LAPACK
3.4.0
LAPACK: Linear Algebra PACKage
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Go to the source code of this file.
Functions/Subroutines | |
| subroutine | DPBRFS (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) |
| DPBRFS | |
| subroutine DPBRFS | ( | CHARACTER | UPLO, |
| INTEGER | N, | ||
| INTEGER | KD, | ||
| INTEGER | NRHS, | ||
| DOUBLE PRECISION, dimension( ldab, * ) | AB, | ||
| INTEGER | LDAB, | ||
| DOUBLE PRECISION, dimension( ldafb, * ) | AFB, | ||
| INTEGER | LDAFB, | ||
| DOUBLE PRECISION, dimension( ldb, * ) | B, | ||
| INTEGER | LDB, | ||
| DOUBLE PRECISION, dimension( ldx, * ) | X, | ||
| INTEGER | LDX, | ||
| DOUBLE PRECISION, dimension( * ) | FERR, | ||
| DOUBLE PRECISION, dimension( * ) | BERR, | ||
| DOUBLE PRECISION, dimension( * ) | WORK, | ||
| INTEGER, dimension( * ) | IWORK, | ||
| INTEGER | INFO | ||
| ) |
DPBRFS
Download DPBRFS + dependencies [TGZ] [ZIP] [TXT]DPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution.
| [in] | UPLO |
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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| [in] | N |
N is INTEGER
The order of the matrix A. N >= 0.
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| [in] | KD |
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
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| [in] | NRHS |
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
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| [in] | AB |
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangle of the symmetric band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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| [in] | LDAB |
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
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| [in] | AFB |
AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T of the band matrix A as computed by
DPBTRF, in the same storage format as A (see AB).
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| [in] | LDAFB |
LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.
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| [in] | B |
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.
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| [in] | LDB |
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
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| [in,out] | X |
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DPBTRS.
On exit, the improved solution matrix X.
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| [in] | LDX |
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
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| [out] | FERR |
FERR is 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
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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| [out] | BERR |
BERR is DOUBLE PRECISION 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 solution).
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| [out] | WORK |
WORK is DOUBLE PRECISION array, dimension (3*N)
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| [out] | IWORK |
IWORK is INTEGER array, dimension (N)
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| [out] | INFO |
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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ITMAX is the maximum number of steps of iterative refinement.
Definition at line 189 of file dpbrfs.f.
1.7.6.1 
