.TH "spprfs.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
spprfs.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBspprfs\fP (UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)"
.br
.RI "\fI\fBSPPRFS\fP \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine spprfs (characterUPLO, integerN, integerNRHS, real, dimension( * )AP, real, dimension( * )AFP, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)"

.PP
\fBSPPRFS\fP  
.PP
\fBPurpose: \fP
.RS 4

.PP
.nf
 SPPRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric positive definite
 and packed, and provides error bounds and backward error estimates
 for the solution.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A.  N >= 0.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is REAL array, dimension (N*(N+1)/2)
          The upper or lower triangle of the symmetric matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
.fi
.PP
.br
\fIAFP\fP 
.PP
.nf
          AFP is REAL array, dimension (N*(N+1)/2)
          The triangular factor U or L from the Cholesky factorization
          A = U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF,
          packed columnwise in a linear array in the same format as A
          (see AP).
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,NRHS)
          The right hand side matrix B.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is REAL array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by SPPTRS.
          On exit, the improved solution matrix X.
.fi
.PP
.br
\fILDX\fP 
.PP
.nf
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
.fi
.PP
.br
\fIFERR\fP 
.PP
.nf
          FERR is REAL array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (3*N)
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (N)
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBInternal Parameters: \fP
.RS 4

.PP
.nf
  ITMAX is the maximum number of steps of iterative refinement.
.fi
.PP
 
.RE
.PP
\fBAuthor:\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBDate:\fP
.RS 4
November 2011 
.RE
.PP

.PP
Definition at line 171 of file spprfs\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.