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

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

11       SUBROUTINE SPTRFS( N,  NRHS,  D, E, DF, EF, B, LDB, X, LDX, FERR, BERR,
12                          WORK, INFO )
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14           INTEGER        INFO, LDB, LDX, N, NRHS
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16           REAL           B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF(
17                          * ), FERR( * ), WORK( * ), X( LDX, * )
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PURPOSE

20       SPTRFS  improves  the computed solution to a system of linear equations
21       when the coefficient matrix is symmetric positive definite and tridiag‐
22       onal,  and  provides  error bounds and backward error estimates for the
23       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) REAL array, dimension (N)
35               The n diagonal elements of the tridiagonal matrix A.
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37       E       (input) REAL array, dimension (N-1)
38               The (n-1) subdiagonal elements of the tridiagonal matrix A.
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40       DF      (input) REAL array, dimension (N)
41               The  n diagonal elements of the diagonal matrix D from the fac‐
42               torization computed by SPTTRF.
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44       EF      (input) REAL array, dimension (N-1)
45               The (n-1) subdiagonal elements of the unit bidiagonal factor  L
46               from the factorization computed by SPTTRF.
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48       B       (input) REAL 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) REAL array, dimension (LDX,NRHS)
55               On  entry,  the  solution  matrix X, as computed by SPTTRS.  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) REAL 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) REAL 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) REAL 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 3.1)    November 2006                       SPTRFS(1)