Man page - gbrfs(3)

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Manual

gbrfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, *) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr,complex, dimension( * ) work, real, dimension( * ) rwork, integer info)
subroutine dgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integerldb, double precision, dimension( ldx, * ) x, integer ldx, doubleprecision, dimension( * ) ferr, double precision, dimension( * ) berr,double precision, dimension( * ) work, integer, dimension( * ) iwork,integer info)
subroutine sgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,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 zgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab,complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, 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, integerinfo)
Author

NAME

gbrfs - gbrfs: iterative refinement

SYNOPSIS

Functions

subroutine cgbrfs (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CGBRFS
subroutine dgbrfs (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DGBRFS
subroutine sgbrfs (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SGBRFS
subroutine zgbrfs (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZGBRFS

Detailed Description

Function Documentation

subroutine cgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, *) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr,complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CGBRFS

Purpose:

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

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

N

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

KL

KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.

KU

KU is INTEGER
The number of superdiagonals within the band of A. KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

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

AFB

AFB is COMPLEX array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by CGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from CGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).

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 CGBTRS.
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 dgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integerldb, double precision, dimension( ldx, * ) x, integer ldx, doubleprecision, dimension( * ) ferr, double precision, dimension( * ) berr,double precision, dimension( * ) work, integer, dimension( * ) iwork,integer info)

DGBRFS

Purpose:

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

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

N

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

KL

KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.

KU

KU is INTEGER
The number of superdiagonals within the band of A. KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

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

AFB

AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by DGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from DGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).

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 DGBTRS.
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 sgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real,dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,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)

SGBRFS

Purpose:

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

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

N

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

KL

KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.

KU

KU is INTEGER
The number of superdiagonals within the band of A. KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

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

AFB

AFB is REAL array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from SGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).

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 SGBTRS.
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 zgbrfs (character trans, integer n, integer kl, integer ku,integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab,complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,dimension( * ) ipiv, 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, integerinfo)

ZGBRFS

Purpose:

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

Parameters

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

N

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

KL

KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.

KU

KU is INTEGER
The number of superdiagonals within the band of A. KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

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

AFB

AFB is COMPLEX*16 array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by ZGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices from ZGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).

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 ZGBTRS.
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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