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NAME DTPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a tri- angular packed coefficient matrix SYNOPSIS SUBROUTINE DTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO ) CHARACTER DIAG, TRANS, UPLO INTEGER INFO, LDB, LDX, N, NRHS INTEGER IWORK( * ) DOUBLE PRECISION AP( * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * ) PURPOSE DTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a tri- angular packed coefficient matrix. The solution matrix X must be computed by DTPTRS or some other means before entering this routine. DTPRFS does not do iterative refinement because doing so cannot improve the backward error. ARGUMENTS UPLO (input) CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular. TRANS (input) 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 = Tran- spose) DIAG (input) CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular. 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) DOUBLE PRECISION 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. B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS) The 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) DOUBLE PRECISION 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