Man page - gtrfs(3)

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Manual

gtrfs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgtrfs (character trans, integer n, integer nrhs, complex,dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * )du, complex, dimension( * ) dlf, complex, dimension( * ) df, complex,dimension( * ) duf, complex, dimension( * ) du2, 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 dgtrfs (character trans, integer n, integer nrhs, doubleprecision, dimension( * ) dl, double precision, dimension( * ) d,double precision, dimension( * ) du, double precision, dimension( * )dlf, double precision, dimension( * ) df, double precision, dimension(* ) duf, double precision, dimension( * ) du2, integer, dimension( * )ipiv, double precision, dimension( ldb, * ) b, integer ldb, doubleprecision, dimension( ldx, * ) x, integer ldx, double precision,dimension( * ) ferr, double precision, dimension( * ) berr, doubleprecision, dimension( * ) work, integer, dimension( * ) iwork, integerinfo)
subroutine sgtrfs (character trans, integer n, integer nrhs, real,dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du,real, dimension( * ) dlf, real, dimension( * ) df, real, dimension( * )duf, real, dimension( * ) du2, 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 zgtrfs (character trans, integer n, integer nrhs, complex*16,dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension(* ) du, complex*16, dimension( * ) dlf, complex*16, dimension( * ) df,complex*16, dimension( * ) duf, complex*16, dimension( * ) du2,integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b,integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, doubleprecision, dimension( * ) ferr, double precision, dimension( * ) berr,complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)
Author

NAME

gtrfs - gtrfs: iterative refinement

SYNOPSIS

Functions

subroutine cgtrfs (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CGTRFS
subroutine dgtrfs (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DGTRFS
subroutine sgtrfs (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SGTRFS
subroutine zgtrfs (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZGTRFS

Detailed Description

Function Documentation

subroutine cgtrfs (character trans, integer n, integer nrhs, complex,dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * )du, complex, dimension( * ) dlf, complex, dimension( * ) df, complex,dimension( * ) duf, complex, dimension( * ) du2, 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)

CGTRFS

Purpose:

CGTRFS improves the computed solution to a system of linear
equations when the coefficient matrix is tridiagonal, 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.

NRHS

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

DL

DL is COMPLEX array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D

D is COMPLEX array, dimension (N)
The diagonal elements of A.

DU

DU is COMPLEX array, dimension (N-1)
The (n-1) superdiagonal elements of A.

DLF

DLF is COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by CGTTRF.

DF

DF is COMPLEX array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.

DUF

DUF is COMPLEX array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.

DU2

DU2 is COMPLEX array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i). IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.

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 CGTTRS.
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 dgtrfs (character trans, integer n, integer nrhs, doubleprecision, dimension( * ) dl, double precision, dimension( * ) d,double precision, dimension( * ) du, double precision, dimension( * )dlf, double precision, dimension( * ) df, double precision, dimension(* ) duf, double precision, dimension( * ) du2, integer, dimension( * )ipiv, double precision, dimension( ldb, * ) b, integer ldb, doubleprecision, dimension( ldx, * ) x, integer ldx, double precision,dimension( * ) ferr, double precision, dimension( * ) berr, doubleprecision, dimension( * ) work, integer, dimension( * ) iwork, integerinfo)

DGTRFS

Purpose:

DGTRFS improves the computed solution to a system of linear
equations when the coefficient matrix is tridiagonal, 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.

NRHS

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

DL

DL is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D

D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.

DU

DU is DOUBLE PRECISION array, dimension (N-1)
The (n-1) superdiagonal elements of A.

DLF

DLF is DOUBLE PRECISION array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by DGTTRF.

DF

DF is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.

DUF

DUF is DOUBLE PRECISION array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.

DU2

DU2 is DOUBLE PRECISION array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i). IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.

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 DGTTRS.
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 sgtrfs (character trans, integer n, integer nrhs, real,dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du,real, dimension( * ) dlf, real, dimension( * ) df, real, dimension( * )duf, real, dimension( * ) du2, 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)

SGTRFS

Purpose:

SGTRFS improves the computed solution to a system of linear
equations when the coefficient matrix is tridiagonal, 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.

NRHS

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

DL

DL is REAL array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D

D is REAL array, dimension (N)
The diagonal elements of A.

DU

DU is REAL array, dimension (N-1)
The (n-1) superdiagonal elements of A.

DLF

DLF is REAL array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by SGTTRF.

DF

DF is REAL array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.

DUF

DUF is REAL array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.

DU2

DU2 is REAL array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i). IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.

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 SGTTRS.
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 zgtrfs (character trans, integer n, integer nrhs, complex*16,dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension(* ) du, complex*16, dimension( * ) dlf, complex*16, dimension( * ) df,complex*16, dimension( * ) duf, complex*16, dimension( * ) du2,integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b,integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, doubleprecision, dimension( * ) ferr, double precision, dimension( * ) berr,complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)

ZGTRFS

Purpose:

ZGTRFS improves the computed solution to a system of linear
equations when the coefficient matrix is tridiagonal, 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.

NRHS

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

DL

DL is COMPLEX*16 array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D

D is COMPLEX*16 array, dimension (N)
The diagonal elements of A.

DU

DU is COMPLEX*16 array, dimension (N-1)
The (n-1) superdiagonal elements of A.

DLF

DLF is COMPLEX*16 array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by ZGTTRF.

DF

DF is COMPLEX*16 array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.

DUF

DUF is COMPLEX*16 array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.

DU2

DU2 is COMPLEX*16 array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i). IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.

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 ZGTTRS.
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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