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NAME ZPTRFS - 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 SYNOPSIS SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDB, LDX, N, NRHS DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ), RWORK( * ) COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * ) PURPOSE ZPTRFS 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. ARGUMENTS UPLO (input) CHARACTER*1 Specifies whether the superdiagonal or the subdiago- nal 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) DOUBLE PRECISION array, dimension (N) The n real diagonal elements of the tridiagonal matrix A. E (input) COMPLEX*16 array, dimension (N-1) The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO). DF (input) DOUBLE PRECISION array, dimension (N) The n diagonal elements of the diagonal matrix D from the factorization computed by ZPTTRF. EF (input) COMPLEX*16 array, dimension (N-1) The (n-1) off-diagonal elements of the unit bidiago- nal factor U or L from the factorization computed by ZPTTRF (see UPLO). B (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZPTTRS. On exit, the improved solution matrix X. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). FERR (output) DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution, FERR(j) bounds the magnitude of the largest entry in (X(j) - XTRUE) divided by the magnitude of the largest entry in X(j). The quality of the error bound depends on the quality of the estimate of norm(inv(A)) computed in the code; if the estimate of norm(inv(A)) is accu- rate, the error bound is guaranteed. BERR (output) DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any entry of A or B that makes X(j) an exact solution). WORK (workspace) COMPLEX*16 array, dimension (N) RWORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value PARAMETERS ITMAX is the maximum number of steps of iterative refinement.