gtts2(3)

NAME
gtts2 - gtts2: triangular solve using factor

SYNOPSIS

  Functions
subroutine cgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
subroutine dgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
subroutine sgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
subroutine zgtts2 (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Detailed Description

Function Documentation

  subroutine cgtts2 (integer itrans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb)

CGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

     CGTTS2 solves one of the systems of equations
        A * X = B,  A**T * X = B,  or  A**H * X = B,
     with a tridiagonal matrix A using the LU factorization computed
     by CGTTRF.

Parameters
    ITRANS

              ITRANS is INTEGER
              Specifies the form of the system of equations.
              = 0:  A * X = B     (No transpose)
              = 1:  A**T * X = B  (Transpose)
              = 2:  A**H * X = B  (Conjugate transpose)

    N

              N is INTEGER
              The order of the matrix A.

    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) multipliers that define the matrix L from the
              LU factorization of A.

    D

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

    DU

              DU is COMPLEX array, dimension (N-1)
              The (n-1) elements of the first super-diagonal of U.

    DU2

              DU2 is COMPLEX array, dimension (N-2)
              The (n-2) elements of the second super-diagonal 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)
              On entry, the matrix of right hand side vectors B.
              On exit, B is overwritten by the solution vectors X.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file cgtts2.f.

  subroutine dgtts2 (integer itrans, integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb)

DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

     DGTTS2 solves one of the systems of equations
        A*X = B  or  A**T*X = B,
     with a tridiagonal matrix A using the LU factorization computed
     by DGTTRF.

Parameters
    ITRANS

              ITRANS is INTEGER
              Specifies the form of the system of equations.
              = 0:  A * X = B  (No transpose)
              = 1:  A**T* X = B  (Transpose)
              = 2:  A**T* X = B  (Conjugate transpose = Transpose)

    N

              N is INTEGER
              The order of the matrix A.

    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) multipliers that define the matrix L from the
              LU factorization of A.

    D

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

    DU

              DU is DOUBLE PRECISION array, dimension (N-1)
              The (n-1) elements of the first super-diagonal of U.

    DU2

              DU2 is DOUBLE PRECISION array, dimension (N-2)
              The (n-2) elements of the second super-diagonal 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)
              On entry, the matrix of right hand side vectors B.
              On exit, B is overwritten by the solution vectors X.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file dgtts2.f.

  subroutine sgtts2 (integer itrans, integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb)

SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

     SGTTS2 solves one of the systems of equations
        A*X = B  or  A**T*X = B,
     with a tridiagonal matrix A using the LU factorization computed
     by SGTTRF.

Parameters
    ITRANS

              ITRANS is INTEGER
              Specifies the form of the system of equations.
              = 0:  A * X = B  (No transpose)
              = 1:  A**T* X = B  (Transpose)
              = 2:  A**T* X = B  (Conjugate transpose = Transpose)

    N

              N is INTEGER
              The order of the matrix A.

    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) multipliers that define the matrix L from the
              LU factorization of A.

    D

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

    DU

              DU is REAL array, dimension (N-1)
              The (n-1) elements of the first super-diagonal of U.

    DU2

              DU2 is REAL array, dimension (N-2)
              The (n-2) elements of the second super-diagonal 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)
              On entry, the matrix of right hand side vectors B.
              On exit, B is overwritten by the solution vectors X.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file sgtts2.f.

  subroutine zgtts2 (integer itrans, integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb)

ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Purpose:

     ZGTTS2 solves one of the systems of equations
        A * X = B,  A**T * X = B,  or  A**H * X = B,
     with a tridiagonal matrix A using the LU factorization computed
     by ZGTTRF.

Parameters
    ITRANS

              ITRANS is INTEGER
              Specifies the form of the system of equations.
              = 0:  A * X = B     (No transpose)
              = 1:  A**T * X = B  (Transpose)
              = 2:  A**H * X = B  (Conjugate transpose)

    N

              N is INTEGER
              The order of the matrix A.

    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) multipliers that define the matrix L from the
              LU factorization of A.

    D

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

    DU

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

    DU2

              DU2 is COMPLEX*16 array, dimension (N-2)
              The (n-2) elements of the second super-diagonal 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)
              On entry, the matrix of right hand side vectors B.
              On exit, B is overwritten by the solution vectors X.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 127 of file zgtts2.f.

Author

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