cgerfs.f (3) - Linux Man Pages
subroutine cgerfs (characterTRANS, integerN, integerNRHS, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldaf, * )AF, integerLDAF, integer, dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)
CGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution.
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)
N is INTEGER The order of the matrix A. N >= 0.
NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
A is COMPLEX array, dimension (LDA,N) The original N-by-N matrix A.
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
AF is COMPLEX array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF.
LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).
IPIV is INTEGER array, dimension (N) The pivot indices from CGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
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) On entry, the solution matrix X, as computed by CGETRS. On exit, the improved 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
ITMAX is the maximum number of steps of iterative refinement.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- November 2011
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