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

6       SPORFS - the computed solution to a system of linear equations when the
7       coefficient matrix is symmetric positive definite,
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SYNOPSIS

10       SUBROUTINE SPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF,  B,  LDB,  X,  LDX,
11                          FERR, BERR, WORK, IWORK, INFO )
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13           CHARACTER      UPLO
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15           INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS
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17           INTEGER        IWORK( * )
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19           REAL           A(  LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
20                          FERR( * ), WORK( * ), X( LDX, * )
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PURPOSE

23       SPORFS improves the computed solution to a system of  linear  equations
24       when  the  coefficient  matrix is symmetric positive definite, and pro‐
25       vides error bounds and backward error estimates for the solution.
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ARGUMENTS

29       UPLO    (input) CHARACTER*1
30               = 'U':  Upper triangle of A is stored;
31               = 'L':  Lower triangle of A is stored.
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33       N       (input) INTEGER
34               The order of the matrix A.  N >= 0.
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36       NRHS    (input) INTEGER
37               The number of right hand sides, i.e., the number of columns  of
38               the matrices B and X.  NRHS >= 0.
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40       A       (input) REAL array, dimension (LDA,N)
41               The  symmetric  matrix  A.   If  UPLO = 'U', the leading N-by-N
42               upper triangular part of A contains the upper  triangular  part
43               of the matrix A, and the strictly lower triangular part of A is
44               not referenced.  If UPLO = 'L', the leading N-by-N lower trian‐
45               gular  part  of  A  contains  the  lower triangular part of the
46               matrix A, and the strictly upper triangular part of  A  is  not
47               referenced.
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49       LDA     (input) INTEGER
50               The leading dimension of the array A.  LDA >= max(1,N).
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52       AF      (input) REAL array, dimension (LDAF,N)
53               The  triangular factor U or L from the Cholesky factorization A
54               = U**T*U or A = L*L**T, as computed by SPOTRF.
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56       LDAF    (input) INTEGER
57               The leading dimension of the array AF.  LDAF >= max(1,N).
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59       B       (input) REAL array, dimension (LDB,NRHS)
60               The right hand side matrix B.
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62       LDB     (input) INTEGER
63               The leading dimension of the array B.  LDB >= max(1,N).
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65       X       (input/output) REAL array, dimension (LDX,NRHS)
66               On entry, the solution matrix X, as  computed  by  SPOTRS.   On
67               exit, the improved solution matrix X.
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69       LDX     (input) INTEGER
70               The leading dimension of the array X.  LDX >= max(1,N).
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72       FERR    (output) REAL array, dimension (NRHS)
73               The estimated forward error bound for each solution vector X(j)
74               (the j-th column of the solution matrix X).  If  XTRUE  is  the
75               true  solution  corresponding  to X(j), FERR(j) is an estimated
76               upper bound for the magnitude of the largest element in (X(j) -
77               XTRUE) divided by the magnitude of the largest element in X(j).
78               The estimate is as reliable as the estimate for RCOND,  and  is
79               almost always a slight overestimate of the true error.
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81       BERR    (output) REAL array, dimension (NRHS)
82               The componentwise relative backward error of each solution vec‐
83               tor X(j) (i.e., the smallest relative change in any element  of
84               A or B that makes X(j) an exact solution).
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86       WORK    (workspace) REAL array, dimension (3*N)
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88       IWORK   (workspace) INTEGER array, dimension (N)
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90       INFO    (output) INTEGER
91               = 0:  successful exit
92               < 0:  if INFO = -i, the i-th argument had an illegal value
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PARAMETERS

95       ITMAX is the maximum number of steps of iterative refinement.
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99 LAPACK routine (version 3.1)    November 2006                       SPORFS(1)
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