gtrfs - Man Page

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.

Definition at line 207 of file cgtrfs.f.

subroutine dgtrfs (character trans, integer n, integer nrhs, double precision, 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, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

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.

Definition at line 206 of file dgtrfs.f.

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.

Definition at line 206 of file sgtrfs.f.

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, double precision, 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.

Definition at line 207 of file zgtrfs.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK