LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine csprfs | ( | character | UPLO, |
integer | N, | ||
integer | NRHS, | ||
complex, dimension( * ) | AP, | ||
complex, dimension( * ) | AFP, | ||
integer, dimension( * ) | IPIV, | ||
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 | ||
) |
CSPRFS
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CSPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, 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. |
[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 triangle of the symmetric 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. |
[in] | AFP | AFP is COMPLEX array, dimension (N*(N+1)/2) The factored form of the matrix A. AFP contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as a packed triangular matrix. |
[in] | IPIV | IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSPTRF. |
[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,out] | X | X is COMPLEX array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by CSPTRS. On exit, the improved 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 |
ITMAX is the maximum number of steps of iterative refinement.
Definition at line 182 of file csprfs.f.