CPTRFS - improve the computed solution to a system of lin
ear equations when the coefficient matrix is Hermitian
positive definite and tridiagonal, and provides error
bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE CPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X,
LDX, FERR, BERR, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
REAL BERR( * ), D( * ), DF( * ), FERR( * ),
RWORK( * )
COMPLEX B( LDB, * ), E( * ), EF( * ), WORK( *
), X( LDX, * )
PURPOSE
CPTRFS improves the computed solution to a system of lin
ear equations when the coefficient matrix is Hermitian
positive definite and tridiagonal, and provides error
bounds and backward error estimates for the solution.
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the superdiagonal or the subdi
agonal 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 (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number
of columns of the matrix B. NRHS >= 0.
D (input) REAL array, dimension (N)
The n real diagonal elements of the tridiagonal
matrix A.
E (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal
matrix A (see UPLO).
DF (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D
EF (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidi
agonal factor U or L from the factorization com
puted by CPTTRF (see UPLO).
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X (input/output) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by
CPTTRS. On exit, the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
FERR (output) REAL 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 (output) 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).
WORK (workspace) COMPLEX array, dimension (N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refine
ment.
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