1DPTRFS(1)                LAPACK routine (version 3.2)                DPTRFS(1)
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NAME

6       DPTRFS - improves the computed solution to a system of linear equations
7       when the coefficient matrix is symmetric positive definite and tridiag‐
8       onal,  and  provides  error bounds and backward error estimates for the
9       solution
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SYNOPSIS

12       SUBROUTINE DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX,  FERR,  BERR,
13                          WORK, INFO )
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15           INTEGER        INFO, LDB, LDX, N, NRHS
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17           DOUBLE         PRECISION  B(  LDB, * ), BERR( * ), D( * ), DF( * ),
18                          E( * ), EF( * ), FERR( * ), WORK( * ), X( LDX, * )
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PURPOSE

21       DPTRFS improves the computed solution to a system of  linear  equations
22       when the coefficient matrix is symmetric positive definite and tridiag‐
23       onal, and provides error bounds and backward error  estimates  for  the
24       solution.
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ARGUMENTS

27       N       (input) INTEGER
28               The order of the matrix A.  N >= 0.
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30       NRHS    (input) INTEGER
31               The  number of right hand sides, i.e., the number of columns of
32               the matrix B.  NRHS >= 0.
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34       D       (input) DOUBLE PRECISION array, dimension (N)
35               The n diagonal elements of the tridiagonal matrix A.
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37       E       (input) DOUBLE PRECISION array, dimension (N-1)
38               The (n-1) subdiagonal elements of the tridiagonal matrix A.
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40       DF      (input) DOUBLE PRECISION array, dimension (N)
41               The n diagonal elements of the diagonal matrix D from the  fac‐
42               torization computed by DPTTRF.
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44       EF      (input) DOUBLE PRECISION array, dimension (N-1)
45               The  (n-1) subdiagonal elements of the unit bidiagonal factor L
46               from the factorization computed by DPTTRF.
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48       B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
49               The right hand side matrix B.
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51       LDB     (input) INTEGER
52               The leading dimension of the array B.  LDB >= max(1,N).
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54       X       (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
55               On entry, the solution matrix X, as  computed  by  DPTTRS.   On
56               exit, the improved solution matrix X.
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58       LDX     (input) INTEGER
59               The leading dimension of the array X.  LDX >= max(1,N).
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61       FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
62               The forward error bound for each solution vector X(j) (the j-th
63               column of the solution matrix X).  If XTRUE is the  true  solu‐
64               tion corresponding to X(j), FERR(j) is an estimated upper bound
65               for the magnitude of the largest  element  in  (X(j)  -  XTRUE)
66               divided by the magnitude of the largest element in X(j).
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68       BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
69               The componentwise relative backward error of each solution vec‐
70               tor X(j) (i.e., the smallest relative change in any element  of
71               A or B that makes X(j) an exact solution).
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73       WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
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75       INFO    (output) INTEGER
76               = 0:  successful exit
77               < 0:  if INFO = -i, the i-th argument had an illegal value
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PARAMETERS

80       ITMAX is the maximum number of steps of iterative refinement.
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84 LAPACK routine (version 3.2)    November 2008                       DPTRFS(1)