ptrfs(3)

NAME
ptrfs - ptrfs: iterative refinement

SYNOPSIS

  Functions
subroutine cptrfs (uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CPTRFS
subroutine dptrfs (n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, info)
DPTRFS
subroutine sptrfs (n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, info)
SPTRFS
subroutine zptrfs (uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZPTRFS

Detailed Description

Function Documentation

  subroutine cptrfs (character uplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, real, dimension( * ) df, complex, dimension( * ) ef, 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)

CPTRFS

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the superdiagonal or the subdiagonal of the
              tridiagonal matrix A is stored and the form of the
              factorization:
              = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
              = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
              (The two forms are equivalent if A is real.)

    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.

    D

              D is REAL array, dimension (N)
              The n real diagonal elements of the tridiagonal matrix A.

    E

              E is COMPLEX array, dimension (N-1)
              The (n-1) off-diagonal elements of the tridiagonal matrix A
              (see UPLO).

    DF

              DF is REAL array, dimension (N)
              The n diagonal elements of the diagonal matrix D from
              the factorization computed by CPTTRF.

    EF

              EF is COMPLEX array, dimension (N-1)
              The (n-1) off-diagonal elements of the unit bidiagonal
              factor U or L from the factorization computed by CPTTRF
              (see UPLO).

    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 CPTTRS.
              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 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).

    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 (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 181 of file cptrfs.f.

  subroutine dptrfs (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) df, double precision, dimension( * ) ef, 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 info)

DPTRFS

Purpose:

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

Parameters
    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.

    D

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

    E

              E is DOUBLE PRECISION array, dimension (N-1)
              The (n-1) subdiagonal elements of the tridiagonal matrix A.

    DF

              DF is DOUBLE PRECISION array, dimension (N)
              The n diagonal elements of the diagonal matrix D from the
              factorization computed by DPTTRF.

    EF

              EF is DOUBLE PRECISION array, dimension (N-1)
              The (n-1) subdiagonal elements of the unit bidiagonal factor
              L from the factorization computed by DPTTRF.

    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 DPTTRS.
              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 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).

    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 (2*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 161 of file dptrfs.f.

  subroutine sptrfs (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) df, real, dimension( * ) ef, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer info)

SPTRFS

Purpose:

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

Parameters
    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.

    D

              D is REAL array, dimension (N)
              The n diagonal elements of the tridiagonal matrix A.

    E

              E is REAL array, dimension (N-1)
              The (n-1) subdiagonal elements of the tridiagonal matrix A.

    DF

              DF is REAL array, dimension (N)
              The n diagonal elements of the diagonal matrix D from the
              factorization computed by SPTTRF.

    EF

              EF is REAL array, dimension (N-1)
              The (n-1) subdiagonal elements of the unit bidiagonal factor
              L from the factorization computed by SPTTRF.

    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 SPTTRS.
              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 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).

    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 (2*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 161 of file sptrfs.f.

  subroutine zptrfs (character uplo, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, double precision, dimension( * ) df, complex*16, dimension( * ) ef, 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)

ZPTRFS

Purpose:

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

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the superdiagonal or the subdiagonal of the
              tridiagonal matrix A is stored and the form of the
              factorization:
              = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
              = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
              (The two forms are equivalent if A is real.)

    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.

    D

              D is DOUBLE PRECISION array, dimension (N)
              The n real diagonal elements of the tridiagonal matrix A.

    E

              E is COMPLEX*16 array, dimension (N-1)
              The (n-1) off-diagonal elements of the tridiagonal matrix A
              (see UPLO).

    DF

              DF is DOUBLE PRECISION array, dimension (N)
              The n diagonal elements of the diagonal matrix D from
              the factorization computed by ZPTTRF.

    EF

              EF is COMPLEX*16 array, dimension (N-1)
              The (n-1) off-diagonal elements of the unit bidiagonal
              factor U or L from the factorization computed by ZPTTRF
              (see UPLO).

    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 ZPTTRS.
              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 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).

    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 (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 181 of file zptrfs.f.

Author

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