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

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

11       SUBROUTINE CPPRFS( UPLO,  N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR,
12                          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( * ), FERR( * ), RWORK( * )
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20           COMPLEX        AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, *
21                          )
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PURPOSE

24       CPPRFS  improves  the computed solution to a system of linear equations
25       when the coefficient matrix is Hermitian positive definite and  packed,
26       and  provides  error  bounds and backward error estimates for the solu‐
27       tion.
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ARGUMENTS

30       UPLO    (input) CHARACTER*1
31               = 'U':  Upper triangle of A is stored;
32               = 'L':  Lower triangle of A is stored.
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34       N       (input) INTEGER
35               The order of the matrix A.  N >= 0.
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37       NRHS    (input) INTEGER
38               The number of right hand sides, i.e., the number of columns  of
39               the matrices B and X.  NRHS >= 0.
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41       AP      (input) COMPLEX array, dimension (N*(N+1)/2)
42               The  upper  or lower triangle of the Hermitian matrix A, packed
43               columnwise in a linear array.  The j-th column of A  is  stored
44               in  the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
45               A(i,j) for 1<=i<=j; if UPLO = 'L',  AP(i  +  (j-1)*(2n-j)/2)  =
46               A(i,j) for j<=i<=n.
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48       AFP     (input) COMPLEX array, dimension (N*(N+1)/2)
49               The  triangular factor U or L from the Cholesky factorization A
50               = U**H*U or A = L*L**H, as computed  by  SPPTRF/CPPTRF,  packed
51               columnwise in a linear array in the same format as A (see AP).
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53       B       (input) COMPLEX array, dimension (LDB,NRHS)
54               The right hand side matrix B.
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56       LDB     (input) INTEGER
57               The leading dimension of the array B.  LDB >= max(1,N).
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59       X       (input/output) COMPLEX array, dimension (LDX,NRHS)
60               On  entry,  the  solution  matrix X, as computed by CPPTRS.  On
61               exit, the improved solution matrix X.
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63       LDX     (input) INTEGER
64               The leading dimension of the array X.  LDX >= max(1,N).
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66       FERR    (output) REAL array, dimension (NRHS)
67               The estimated forward error bound for each solution vector X(j)
68               (the  j-th  column  of the solution matrix X).  If XTRUE is the
69               true solution corresponding to X(j), FERR(j)  is  an  estimated
70               upper bound for the magnitude of the largest element in (X(j) -
71               XTRUE) divided by the magnitude of the largest element in X(j).
72               The  estimate  is as reliable as the estimate for RCOND, and is
73               almost always a slight overestimate of the true error.
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75       BERR    (output) REAL array, dimension (NRHS)
76               The componentwise relative backward error of each solution vec‐
77               tor  X(j) (i.e., the smallest relative change in any element of
78               A or B that makes X(j) an exact solution).
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80       WORK    (workspace) COMPLEX array, dimension (2*N)
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82       RWORK   (workspace) REAL array, dimension (N)
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84       INFO    (output) INTEGER
85               = 0:  successful exit
86               < 0:  if INFO = -i, the i-th argument had an illegal value
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PARAMETERS

89       ITMAX is the maximum number of steps of iterative refinement.
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93 LAPACK routine (version 3.2)    November 2008                       CPPRFS(1)
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