gtrfs(3)

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.

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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