CTBRFS (3) - Linux Man Pages
subroutine ctbrfs (characterUPLO, characterTRANS, characterDIAG, integerN, integerKD, integerNRHS, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)
CTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by CTBTRS or some other means before entering this routine. CTBRFS 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)
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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDX,NRHS) The solution matrix X.
LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
FERR is REAL 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 REAL 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 COMPLEX array, dimension (2*N)
RWORK is REAL 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
- November 2011
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