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| zptrfs.f(3) | LAPACK | zptrfs.f(3) | 
NAME¶
zptrfs.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine zptrfs (UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
Function/Subroutine Documentation¶
subroutine zptrfs (characterUPLO, integerN, integerNRHS, double precision, dimension( * )D, complex*16, dimension( * )E, double precision, dimension( * )DF, complex*16, dimension( * )EF, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)¶
ZPTRFS Purpose:ZPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.
UPLO
 
N
 
NRHS
 
D
 
E
 
DF
 
EF
 
B
 
LDB
 
X
 
LDX
 
FERR
 
BERR
 
WORK
 
RWORK
 
INFO
 
Internal Parameters: 
          UPLO is CHARACTER*1
          Specifies whether the superdiagonal or the subdiagonal of the
          tridiagonal matrix A is stored and the form of the
          factorization:
          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
          (The two forms are equivalent if A is real.)
          N is INTEGER
          The order of the matrix A.  N >= 0.
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
          D is DOUBLE PRECISION array, dimension (N)
          The n real diagonal elements of the tridiagonal matrix A.
          E is COMPLEX*16 array, dimension (N-1)
          The (n-1) off-diagonal elements of the tridiagonal matrix A
          (see UPLO).
          DF is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from
          the factorization computed by ZPTTRF.
          EF is COMPLEX*16 array, dimension (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal
          factor U or L from the factorization computed by ZPTTRF
          (see UPLO).
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
          X is COMPLEX*16 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by ZPTTRS.
          On exit, the improved solution matrix X.
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The 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).
          BERR is DOUBLE PRECISION 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).
WORK is COMPLEX*16 array, dimension (N)
RWORK is DOUBLE PRECISION array, dimension (N)
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Author¶
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