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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine ctprfs | ( | character | UPLO, |
character | TRANS, | ||
character | DIAG, | ||
integer | N, | ||
integer | NRHS, | ||
complex, dimension( * ) | AP, | ||
complex, dimension( ldb, * ) | B, | ||
integer | LDB, | ||
complex, dimension( ldx, * ) | X, | ||
integer | LDX, | ||
real, dimension( * ) | FERR, | ||
real, dimension( * ) | BERR, | ||
complex, dimension( * ) | WORK, | ||
real, dimension( * ) | RWORK, | ||
integer | INFO | ||
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CTPRFS
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CTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by CTPTRS or some other means before entering this routine. CTPRFS does not do iterative refinement because doing so cannot improve the backward error.
[in] | UPLO | UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. |
[in] | TRANS | 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) |
[in] | DIAG | DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[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. |
[in] | AP | AP is COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. |
[in] | B | B is COMPLEX array, dimension (LDB,NRHS) The right hand side matrix B. |
[in] | LDB | LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). |
[in] | X | X is COMPLEX array, dimension (LDX,NRHS) The solution matrix X. |
[in] | LDX | LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). |
[out] | FERR | 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. |
[out] | BERR | 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). |
[out] | WORK | WORK is COMPLEX array, dimension (2*N) |
[out] | RWORK | RWORK is REAL array, dimension (N) |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value |
Definition at line 176 of file ctprfs.f.