CPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

SUBROUTINE CPTRFS(

UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

CHARACTER UPLO

INTEGER INFO, LDB, LDX, N, NRHS

REAL BERR( * ), D( * ), DF( * ), FERR( * ), RWORK( * )

COMPLEX B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

CPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.

UPLO (input) CHARACTER*1

Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization:

= 'U': E is the superdiagonal of A, and A = U**H*D*U;

= 'L': E is the subdiagonal of A, and A = L*D*L**H. (The two forms are equivalent if A is real.)

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 matrix B. NRHS >= 0.

D (input) REAL array, dimension (N)

The n real diagonal elements of the tridiagonal matrix A.

E (input) COMPLEX array, dimension (N-1)

The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).

DF (input) REAL array, dimension (N)

The n diagonal elements of the diagonal matrix D from the factorization computed by CPTTRF.

EF (input) COMPLEX array, dimension (N-1)

The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by CPTTRF (see UPLO).

B (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)

On entry, the solution matrix X, as computed by CPTTRS. 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 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).

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) COMPLEX array, dimension (N)

RWORK (workspace) REAL array, dimension (N)

INFO (output) 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.