subroutine dtbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
LDX, FERR, BERR, WORK, IWORK, INFO)
subroutine dtbrfs (characterUPLO, characterTRANS, characterDIAG, integerN,
integerKD, integerNRHS, double precision, dimension( ldab, * )AB,
integerLDAB, double precision, dimension( ldb, * )B, integerLDB, double
precision, dimension( ldx, * )X, integerLDX, double precision,
dimension( * )FERR, double precision, dimension( * )BERR, double
precision, dimension( * )WORK, integer, dimension( * )IWORK,
DTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
The solution matrix X must be computed by DTBTRS or some other
means before entering this routine. DTBRFS does not do iterative
refinement because doing so cannot improve the backward error.
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N is INTEGER
The order of the matrix A. N >= 0.
KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular 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).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X is DOUBLE PRECISION array, dimension (LDX,NRHS)
The solution matrix X.
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
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.
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).
WORK is DOUBLE PRECISION array, dimension (3*N)
IWORK is INTEGER array, dimension (N)
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
Definition at line 188 of file dtbrfs.f.
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