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.

  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.

  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.

  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.

Author

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