1CTPRFS(1) LAPACK routine (version 3.1) CTPRFS(1)
2
6 CTPRFS - 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 CTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
12 FERR, BERR, WORK, RWORK, INFO )
13 CHARACTER DIAG, TRANS, UPLO
15 INTEGER INFO, LDB, LDX, N, NRHS
17 REAL BERR( * ), FERR( * ), RWORK( * )
19 COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
21
23 CTPRFS provides error bounds and backward error estimates for the solu‐
24 tion to a system of linear equations with a triangular packed coeffi‐
25 cient matrix.
26 The solution matrix X must be computed by CTPTRS or some other means
28 before entering this routine. CTPRFS does not do iterative refinement
29 because doing so cannot improve the backward error.
30
33 UPLO (input) CHARACTER*1
34 = 'U': A is upper triangular;
35 = 'L': A is lower triangular.
36 TRANS (input) CHARACTER*1
38 Specifies the form of the system of equations:
39 = 'N': A * X = B (No transpose)
40 = 'T': A**T * X = B (Transpose)
41 = 'C': A**H * X = B (Conjugate transpose)
42 DIAG (input) CHARACTER*1
44 = 'N': A is non-unit triangular;
45 = 'U': A is unit triangular.
46 N (input) INTEGER
48 The order of the matrix A. N >= 0.
49 NRHS (input) INTEGER
51 The number of right hand sides, i.e., the number of columns of
52 the matrices B and X. NRHS >= 0.
53 AP (input) COMPLEX array, dimension (N*(N+1)/2)
55 The upper or lower triangular matrix A, packed columnwise in a
56 linear array. The j-th column of A is stored in the array AP
57 as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for
58 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
59 j<=i<=n. If DIAG = 'U', the diagonal elements of A are not
60 referenced and are assumed to be 1.
61 B (input) COMPLEX array, dimension (LDB,NRHS)
63 The right hand side matrix B.
64 LDB (input) INTEGER
66 The leading dimension of the array B. LDB >= max(1,N).
67 X (input) COMPLEX array, dimension (LDX,NRHS)
69 The solution matrix X.
70 LDX (input) INTEGER
72 The leading dimension of the array X. LDX >= max(1,N).
73 FERR (output) REAL array, dimension (NRHS)
75 The estimated forward error bound for each solution vector X(j)
76 (the j-th column of the solution matrix X). If XTRUE is the
77 true solution corresponding to X(j), FERR(j) is an estimated
78 upper bound for the magnitude of the largest element in (X(j) -
79 XTRUE) divided by the magnitude of the largest element in X(j).
80 The estimate is as reliable as the estimate for RCOND, and is
81 almost always a slight overestimate of the true error.
82 BERR (output) REAL array, dimension (NRHS)
84 The componentwise relative backward error of each solution vec‐
85 tor X(j) (i.e., the smallest relative change in any element of
86 A or B that makes X(j) an exact solution).
87 WORK (workspace) COMPLEX array, dimension (2*N)
89 RWORK (workspace) REAL array, dimension (N)
91 INFO (output) INTEGER
93 = 0: successful exit
94 < 0: if INFO = -i, the i-th argument had an illegal value
95 LAPACK routine (version 3.1) November 2006 CTPRFS(1)