Man page - pbrfs(3)

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Manual

pbrfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cpbrfs (character uplo, integer n, integer kd, integer nrhs,complex, dimension( ldab, * ) ab, integer ldab, complex, dimension(ldafb, * ) afb, integer ldafb, complex, dimension( ldb, * ) b, integerldb, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * )ferr, real, dimension( * ) berr, complex, dimension( * ) work, real,dimension( * ) rwork, integer info)
subroutine dpbrfs (character uplo, integer n, integer kd, integer nrhs,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( ldafb, * ) afb, integer ldafb, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, *) x, integer ldx, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, double precision, dimension( * ) work,integer, dimension( * ) iwork, integer info)
subroutine spbrfs (character uplo, integer n, integer kd, integer nrhs,real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, *) afb, integer ldafb, real, dimension( ldb, * ) b, integer ldb, real,dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,dimension( * ) berr, real, dimension( * ) work, integer, dimension( * )iwork, integer info)
subroutine zpbrfs (character uplo, integer n, integer kd, integer nrhs,complex*16, dimension( ldab, * ) ab, integer ldab, complex*16,dimension( ldafb, * ) afb, integer ldafb, complex*16, dimension( ldb, *) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx,double precision, dimension( * ) ferr, double precision, dimension( * )berr, complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)
Author

NAME

pbrfs - pbrfs: iterative refinement

SYNOPSIS

Functions

subroutine cpbrfs (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CPBRFS
subroutine dpbrfs (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DPBRFS
subroutine spbrfs (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SPBRFS
subroutine zpbrfs (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZPBRFS

Detailed Description

Function Documentation

subroutine cpbrfs (character uplo, integer n, integer kd, integer nrhs,complex, dimension( ldab, * ) ab, integer ldab, complex, dimension(ldafb, * ) afb, integer ldafb, complex, dimension( ldb, * ) b, integerldb, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * )ferr, real, dimension( * ) berr, complex, dimension( * ) work, real,dimension( * ) rwork, integer info)

CPBRFS

Purpose:

CPBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive definite
and banded, and provides error bounds and backward error estimates
for the solution.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

AFB

AFB is COMPLEX array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A as computed by
CPBTRF, in the same storage format as A (see AB).

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

B

B is COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X

X is COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CPBTRS.
On exit, the improved solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

FERR

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.

BERR

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).

WORK

WORK is COMPLEX array, dimension (2*N)

RWORK

RWORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dpbrfs (character uplo, integer n, integer kd, integer nrhs,double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( ldafb, * ) afb, integer ldafb, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, *) x, integer ldx, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, double precision, dimension( * ) work,integer, dimension( * ) iwork, integer info)

DPBRFS

Purpose:

DPBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric positive definite
and banded, and provides error bounds and backward error estimates
for the solution.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangle of the symmetric band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

AFB

AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T of the band matrix A as computed by
DPBTRF, in the same storage format as A (see AB).

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X

X is DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DPBTRS.
On exit, the improved solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

FERR

FERR is DOUBLE PRECISION 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.

BERR

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

WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine spbrfs (character uplo, integer n, integer kd, integer nrhs,real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, *) afb, integer ldafb, real, dimension( ldb, * ) b, integer ldb, real,dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,dimension( * ) berr, real, dimension( * ) work, integer, dimension( * )iwork, integer info)

SPBRFS

Purpose:

SPBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric positive definite
and banded, and provides error bounds and backward error estimates
for the solution.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.

AB

AB is REAL array, dimension (LDAB,N)
The upper or lower triangle of the symmetric band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

AFB

AFB is REAL array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T of the band matrix A as computed by
SPBTRF, in the same storage format as A (see AB).

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

B

B is REAL array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X

X is REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPBTRS.
On exit, the improved solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

FERR

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.

BERR

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).

WORK

WORK is REAL array, dimension (3*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zpbrfs (character uplo, integer n, integer kd, integer nrhs,complex*16, dimension( ldab, * ) ab, integer ldab, complex*16,dimension( ldafb, * ) afb, integer ldafb, complex*16, dimension( ldb, *) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx,double precision, dimension( * ) ferr, double precision, dimension( * )berr, complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)

ZPBRFS

Purpose:

ZPBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive definite
and banded, and provides error bounds and backward error estimates
for the solution.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

AFB

AFB is COMPLEX*16 array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A as computed by
ZPBTRF, in the same storage format as A (see AB).

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X

X is COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPBTRS.
On exit, the improved solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

FERR

FERR is DOUBLE PRECISION 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.

BERR

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

WORK is COMPLEX*16 array, dimension (2*N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Internal Parameters:

ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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