1DTPRFS(1) LAPACK routine (version 3.1) DTPRFS(1)
2
6 DTPRFS - error bounds and backward error estimates for the solution to
7 a system of linear equations with a triangular packed coefficient
8 matrix
9
11 SUBROUTINE DTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
12 FERR, BERR, WORK, IWORK, INFO )
13 CHARACTER DIAG, TRANS, UPLO
15 INTEGER INFO, LDB, LDX, N, NRHS
17 INTEGER IWORK( * )
19 DOUBLE PRECISION AP( * ), B( LDB, * ), BERR( * ), FERR( *
21 ), WORK( * ), X( LDX, * )
22
24 DTPRFS provides error bounds and backward error estimates for the solu‐
25 tion to a system of linear equations with a triangular packed coeffi‐
26 cient matrix.
27 The solution matrix X must be computed by DTPTRS or some other means
29 before entering this routine. DTPRFS does not do iterative refinement
30 because doing so cannot improve the backward error.
31
34 UPLO (input) CHARACTER*1
35 = 'U': A is upper triangular;
36 = 'L': A is lower triangular.
37 TRANS (input) CHARACTER*1
39 Specifies the form of the system of equations:
40 = 'N': A * X = B (No transpose)
41 = 'T': A**T * X = B (Transpose)
42 = 'C': A**H * X = B (Conjugate transpose = Transpose)
43 DIAG (input) CHARACTER*1
45 = 'N': A is non-unit triangular;
46 = 'U': A is unit triangular.
47 N (input) INTEGER
49 The order of the matrix A. N >= 0.
50 NRHS (input) INTEGER
52 The number of right hand sides, i.e., the number of columns of
53 the matrices B and X. NRHS >= 0.
54 AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
56 The upper or lower triangular matrix A, packed columnwise in a
57 linear array. The j-th column of A is stored in the array AP
58 as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for
59 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for
60 j<=i<=n. If DIAG = 'U', the diagonal elements of A are not
61 referenced and are assumed to be 1.
62 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
64 The right hand side matrix B.
65 LDB (input) INTEGER
67 The leading dimension of the array B. LDB >= max(1,N).
68 X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
70 The solution matrix X.
71 LDX (input) INTEGER
73 The leading dimension of the array X. LDX >= max(1,N).
74 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
76 The estimated forward error bound for each solution vector X(j)
77 (the j-th column of the solution matrix X). If XTRUE is the
78 true solution corresponding to X(j), FERR(j) is an estimated
79 upper bound for the magnitude of the largest element in (X(j) -
80 XTRUE) divided by the magnitude of the largest element in X(j).
81 The estimate is as reliable as the estimate for RCOND, and is
82 almost always a slight overestimate of the true error.
83 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
85 The componentwise relative backward error of each solution vec‐
86 tor X(j) (i.e., the smallest relative change in any element of
87 A or B that makes X(j) an exact solution).
88 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
90 IWORK (workspace) INTEGER array, dimension (N)
92 INFO (output) INTEGER
94 = 0: successful exit
95 < 0: if INFO = -i, the i-th argument had an illegal value
96 LAPACK routine (version 3.1) November 2006 DTPRFS(1)