1CPTRFS(1) LAPACK routine (version 3.2) CPTRFS(1)
2
6 CPTRFS - improves the computed solution to a system of linear equations
7 when the coefficient matrix is Hermitian positive definite and tridiag‐
8 onal, and provides error bounds and backward error estimates for the
9 solution
10
12 SUBROUTINE CPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
13 BERR, WORK, RWORK, INFO )
14 CHARACTER UPLO
16 INTEGER INFO, LDB, LDX, N, NRHS
18 REAL BERR( * ), D( * ), DF( * ), FERR( * ), RWORK( * )
20 COMPLEX B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )
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24 CPTRFS improves the computed solution to a system of linear equations
25 when the coefficient matrix is Hermitian positive definite and tridiag‐
26 onal, and provides error bounds and backward error estimates for the
27 solution.
28
30 UPLO (input) CHARACTER*1
31 Specifies whether the superdiagonal or the subdiagonal of the
32 tridiagonal matrix A is stored and the form of the factoriza‐
33 tion:
34 = 'U': E is the superdiagonal of A, and A = U**H*D*U;
35 = 'L': E is the subdiagonal of A, and A = L*D*L**H. (The two
36 forms are equivalent if A is real.)
37 N (input) INTEGER
39 The order of the matrix A. N >= 0.
40 NRHS (input) INTEGER
42 The number of right hand sides, i.e., the number of columns of
43 the matrix B. NRHS >= 0.
44 D (input) REAL array, dimension (N)
46 The n real diagonal elements of the tridiagonal matrix A.
47 E (input) COMPLEX array, dimension (N-1)
49 The (n-1) off-diagonal elements of the tridiagonal matrix A
50 (see UPLO).
51 DF (input) REAL array, dimension (N)
53 The n diagonal elements of the diagonal matrix D from the fac‐
54 torization computed by CPTTRF.
55 EF (input) COMPLEX array, dimension (N-1)
57 The (n-1) off-diagonal elements of the unit bidiagonal factor U
58 or L from the factorization computed by CPTTRF (see UPLO).
59 B (input) COMPLEX array, dimension (LDB,NRHS)
61 The right hand side matrix B.
62 LDB (input) INTEGER
64 The leading dimension of the array B. LDB >= max(1,N).
65 X (input/output) COMPLEX array, dimension (LDX,NRHS)
67 On entry, the solution matrix X, as computed by CPTTRS. On
68 exit, the improved solution matrix X.
69 LDX (input) INTEGER
71 The leading dimension of the array X. LDX >= max(1,N).
72 FERR (output) REAL array, dimension (NRHS)
74 The forward error bound for each solution vector X(j) (the j-th
75 column of the solution matrix X). If XTRUE is the true solu‐
76 tion corresponding to X(j), FERR(j) is an estimated upper bound
77 for the magnitude of the largest element in (X(j) - XTRUE)
78 divided by the magnitude of the largest element in X(j).
79 BERR (output) REAL array, dimension (NRHS)
81 The componentwise relative backward error of each solution vec‐
82 tor X(j) (i.e., the smallest relative change in any element of
83 A or B that makes X(j) an exact solution).
84 WORK (workspace) COMPLEX array, dimension (N)
86 RWORK (workspace) REAL array, dimension (N)
88 INFO (output) INTEGER
90 = 0: successful exit
91 < 0: if INFO = -i, the i-th argument had an illegal value
92
94 ITMAX is the maximum number of steps of iterative refinement.
95 LAPACK routine (version 3.2) November 2008 CPTRFS(1)