- SUBROUTINE SPPRFS(
- UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
- CHARACTER UPLO
- INTEGER INFO, LDB, LDX, N, NRHS
- INTEGER IWORK( * )
- REAL AFP( * ), AP( * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
PURPOSESPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution.
- UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
- N (input) INTEGER
- The order of the matrix A. N >= 0.
- NRHS (input) INTEGER
- The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
- AP (input) REAL 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
- AFP (input) REAL array, dimension (N*(N+1)/2)
- The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF, packed columnwise in a linear array in the same format as A (see AP).
- B (input) REAL array, dimension (LDB,NRHS)
- The right hand side matrix B.
- LDB (input) INTEGER
- The leading dimension of the array B. LDB >= max(1,N).
- X (input/output) REAL array, dimension (LDX,NRHS)
- On entry, the solution matrix X, as computed by SPPTRS. On exit, the improved solution matrix X.
- LDX (input) INTEGER
- The leading dimension of the array X. LDX >= max(1,N).
- FERR (output) 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 (output) 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 (workspace) REAL array, dimension (3*N)
- IWORK (workspace) INTEGER array, dimension (N)
- INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
PARAMETERSITMAX is the maximum number of steps of iterative refinement.