gtsv(3)

NAME
gtsv - gtsv: factor and solve

SYNOPSIS

  Functions

subroutine cgtsv (n, nrhs, dl, d, du, b, ldb, info)
CGTSV computes the solution to system of linear equations A * X = B for GT matrices
subroutine dgtsv (n, nrhs, dl, d, du, b, ldb, info)
DGTSV computes the solution to system of linear equations A * X = B for GT matrices
subroutine sgtsv (n, nrhs, dl, d, du, b, ldb, info)
SGTSV computes the solution to system of linear equations A * X = B for GT matrices
subroutine zgtsv (n, nrhs, dl, d, du, b, ldb, info)
ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

Detailed Description

Function Documentation

  subroutine cgtsv (integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( ldb, * ) b, integer ldb, integer info)

CGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

    !>
    !> CGTSV  solves the equation
    !>
    !>    A*X = B,
    !>
    !> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
    !> partial pivoting.
    !>
    !> Note that the equation  A**T *X = B  may be solved by interchanging the
    !> order of the arguments DU and DL.
    !>

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.
    !>

    DL

    !>          DL is COMPLEX array, dimension (N-1)
    !>          On entry, DL must contain the (n-1) subdiagonal elements of
    !>          A.
    !>          On exit, DL is overwritten by the (n-2) elements of the
    !>          second superdiagonal of the upper triangular matrix U from
    !>          the LU factorization of A, in DL(1), ..., DL(n-2).
    !>

    D

    !>          D is COMPLEX array, dimension (N)
    !>          On entry, D must contain the diagonal elements of A.
    !>          On exit, D is overwritten by the n diagonal elements of U.
    !>

    DU

    !>          DU is COMPLEX array, dimension (N-1)
    !>          On entry, DU must contain the (n-1) superdiagonal elements
    !>          of A.
    !>          On exit, DU is overwritten by the (n-1) elements of the first
    !>          superdiagonal of U.
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
    !>                has not been computed.  The factorization has not been
    !>                completed unless i = N.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dgtsv (integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

    !>
    !> DGTSV  solves the equation
    !>
    !>    A*X = B,
    !>
    !> where A is an n by n tridiagonal matrix, by Gaussian elimination with
    !> partial pivoting.
    !>
    !> Note that the equation  A**T*X = B  may be solved by interchanging the
    !> order of the arguments DU and DL.
    !>

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.
    !>

    DL

    !>          DL is DOUBLE PRECISION array, dimension (N-1)
    !>          On entry, DL must contain the (n-1) sub-diagonal elements of
    !>          A.
    !>
    !>          On exit, DL is overwritten by the (n-2) elements of the
    !>          second super-diagonal of the upper triangular matrix U from
    !>          the LU factorization of A, in DL(1), ..., DL(n-2).
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          On entry, D must contain the diagonal elements of A.
    !>
    !>          On exit, D is overwritten by the n diagonal elements of U.
    !>

    DU

    !>          DU is DOUBLE PRECISION array, dimension (N-1)
    !>          On entry, DU must contain the (n-1) super-diagonal elements
    !>          of A.
    !>
    !>          On exit, DU is overwritten by the (n-1) elements of the first
    !>          super-diagonal of U.
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
    !>          On entry, the N by NRHS matrix of right hand side matrix B.
    !>          On exit, if INFO = 0, the N by NRHS solution matrix X.
    !>

    LDB

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

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, U(i,i) is exactly zero, and the solution
    !>               has not been computed.  The factorization has not been
    !>               completed unless i = N.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sgtsv (integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldb, * ) b, integer ldb, integer info)

SGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

    !>
    !> SGTSV  solves the equation
    !>
    !>    A*X = B,
    !>
    !> where A is an n by n tridiagonal matrix, by Gaussian elimination with
    !> partial pivoting.
    !>
    !> Note that the equation  A**T*X = B  may be solved by interchanging the
    !> order of the arguments DU and DL.
    !>

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.
    !>

    DL

    !>          DL is REAL array, dimension (N-1)
    !>          On entry, DL must contain the (n-1) sub-diagonal elements of
    !>          A.
    !>
    !>          On exit, DL is overwritten by the (n-2) elements of the
    !>          second super-diagonal of the upper triangular matrix U from
    !>          the LU factorization of A, in DL(1), ..., DL(n-2).
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          On entry, D must contain the diagonal elements of A.
    !>
    !>          On exit, D is overwritten by the n diagonal elements of U.
    !>

    DU

    !>          DU is REAL array, dimension (N-1)
    !>          On entry, DU must contain the (n-1) super-diagonal elements
    !>          of A.
    !>
    !>          On exit, DU is overwritten by the (n-1) elements of the first
    !>          super-diagonal of U.
    !>

    B

    !>          B is REAL array, dimension (LDB,NRHS)
    !>          On entry, the N by NRHS matrix of right hand side matrix B.
    !>          On exit, if INFO = 0, the N by NRHS solution matrix X.
    !>

    LDB

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

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, U(i,i) is exactly zero, and the solution
    !>               has not been computed.  The factorization has not been
    !>               completed unless i = N.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zgtsv (integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

Purpose:

    !>
    !> ZGTSV  solves the equation
    !>
    !>    A*X = B,
    !>
    !> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
    !> partial pivoting.
    !>
    !> Note that the equation  A**T *X = B  may be solved by interchanging the
    !> order of the arguments DU and DL.
    !>

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.
    !>

    DL

    !>          DL is COMPLEX*16 array, dimension (N-1)
    !>          On entry, DL must contain the (n-1) subdiagonal elements of
    !>          A.
    !>          On exit, DL is overwritten by the (n-2) elements of the
    !>          second superdiagonal of the upper triangular matrix U from
    !>          the LU factorization of A, in DL(1), ..., DL(n-2).
    !>

    D

    !>          D is COMPLEX*16 array, dimension (N)
    !>          On entry, D must contain the diagonal elements of A.
    !>          On exit, D is overwritten by the n diagonal elements of U.
    !>

    DU

    !>          DU is COMPLEX*16 array, dimension (N-1)
    !>          On entry, DU must contain the (n-1) superdiagonal elements
    !>          of A.
    !>          On exit, DU is overwritten by the (n-1) elements of the first
    !>          superdiagonal of U.
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          On entry, the N-by-NRHS right hand side matrix B.
    !>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDB

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

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
    !>                has not been computed.  The factorization has not been
    !>                completed unless i = N.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

Generated automatically by Doxygen for LAPACK from the source code.