ZPTRFS(3F) ZPTRFS(3F)
ZPTRFS - improve 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
SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
BERR, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ),
RWORK( * )
COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )
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 (input) 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 (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) DOUBLE PRECISION array, dimension (N)
The n real diagonal elements of the tridiagonal matrix A.
E (input) COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix A (see
UPLO).
DF (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization computed by ZPTTRF.
Page 1
ZPTRFS(3F) ZPTRFS(3F)
EF (input) 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 (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPTTRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) 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 (output) 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 (workspace) COMPLEX*16 array, dimension (N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) 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.
ZPTRFS(3F) ZPTRFS(3F)
ZPTRFS - improve 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
SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
BERR, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ),
RWORK( * )
COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )
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 (input) 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 (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) DOUBLE PRECISION array, dimension (N)
The n real diagonal elements of the tridiagonal matrix A.
E (input) COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix A (see
UPLO).
DF (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization computed by ZPTTRF.
Page 1
ZPTRFS(3F) ZPTRFS(3F)
EF (input) 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 (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPTTRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) 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 (output) 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 (workspace) COMPLEX*16 array, dimension (N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) 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.
PPPPaaaaggggeeee 2222 [ Back ]
|
