1CPTRFS(1)                LAPACK routine (version 3.1)                CPTRFS(1)
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NAME

6       CPTRFS - the computed solution to a system of linear equations when the
7       coefficient matrix is Hermitian positive definite and tridiagonal,  and
8       provides error bounds and backward error estimates for the solution
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SYNOPSIS

11       SUBROUTINE CPTRFS( UPLO,  N,  NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
12                          BERR, WORK, RWORK, INFO )
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14           CHARACTER      UPLO
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16           INTEGER        INFO, LDB, LDX, N, NRHS
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18           REAL           BERR( * ), D( * ), DF( * ), FERR( * ), RWORK( * )
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20           COMPLEX        B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )
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PURPOSE

23       CPTRFS improves the computed solution to a system of  linear  equations
24       when the coefficient matrix is Hermitian positive definite and tridiag‐
25       onal, and provides error bounds and backward error  estimates  for  the
26       solution.
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ARGUMENTS

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.)
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38       N       (input) INTEGER
39               The order of the matrix A.  N >= 0.
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41       NRHS    (input) INTEGER
42               The number of right hand sides, i.e., the number of columns  of
43               the matrix B.  NRHS >= 0.
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45       D       (input) REAL array, dimension (N)
46               The n real diagonal elements of the tridiagonal matrix A.
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48       E       (input) COMPLEX array, dimension (N-1)
49               The  (n-1)  off-diagonal  elements  of the tridiagonal matrix A
50               (see UPLO).
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52       DF      (input) REAL array, dimension (N)
53               The n diagonal elements of the diagonal matrix D from the  fac‐
54               torization computed by CPTTRF.
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56       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).
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60       B       (input) COMPLEX array, dimension (LDB,NRHS)
61               The right hand side matrix B.
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63       LDB     (input) INTEGER
64               The leading dimension of the array B.  LDB >= max(1,N).
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66       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.
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70       LDX     (input) INTEGER
71               The leading dimension of the array X.  LDX >= max(1,N).
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73       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).
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80       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).
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85       WORK    (workspace) COMPLEX array, dimension (N)
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87       RWORK   (workspace) REAL array, dimension (N)
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89       INFO    (output) INTEGER
90               = 0:  successful exit
91               < 0:  if INFO = -i, the i-th argument had an illegal value
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PARAMETERS

94       ITMAX is the maximum number of steps of iterative refinement.
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98 LAPACK routine (version 3.1)    November 2006                       CPTRFS(1)