gtsv(3)                    Library Functions Manual                    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.

       Definition at line 123 of file cgtsv.f.

   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.

       Definition at line 126 of file dgtsv.f.

   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.

       Definition at line 126 of file sgtsv.f.

   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.

       Definition at line 123 of file zgtsv.f.

Author
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LAPACK                          Version 3.12.0                         gtsv(3)