DTPRFS(3)
provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular 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 triangular 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 = Transpose)
 DIAG (input) CHARACTER*1

= 'N': A is nonunit 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 jth column of A is stored in the array
AP as follows:
if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j1)*(2*nj)/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 bound for each solution vector
X(j) (the jth 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (3*N)

 IWORK (workspace) INTEGER array, dimension (N)

 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value