NAME

       lagtm - lagtm: tridiagonal matrix-matrix multiply

SYNOPSIS

   Functions
       subroutine clagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
           CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a
           tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which
           may be 0, 1, or -1.
       subroutine dlagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
           DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a
           tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which
           may be 0, 1, or -1.
       subroutine slagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
           SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a
           tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which
           may be 0, 1, or -1.
       subroutine zlagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
           ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a
           tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which
           may be 0, 1, or -1.

Detailed Description

Function Documentation

   subroutine clagtm (character trans, integer n, integer nrhs, real alpha, complex, dimension( *
       ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( ldx, * )
       x, integer ldx, real beta, complex, dimension( ldb, * ) b, integer ldb)
       CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal
       matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or
       -1.

       Purpose:

            CLAGTM performs a matrix-matrix product of the form

               B := alpha * A * X + beta * B

            where A is a tridiagonal matrix of order N, B and X are N by NRHS
            matrices, and alpha and beta are real scalars, each of which may be
            0., 1., or -1.

       Parameters
           TRANS

                     TRANS is CHARACTER*1
                     Specifies the operation applied to A.
                     = 'N':  No transpose, B := alpha * A * X + beta * B
                     = 'T':  Transpose,    B := alpha * A**T * X + beta * B
                     = 'C':  Conjugate transpose, B := alpha * A**H * X + beta * B

           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 matrices X and B.

           ALPHA

                     ALPHA is REAL
                     The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 0.

           DL

                     DL is COMPLEX array, dimension (N-1)
                     The (n-1) sub-diagonal elements of T.

           D

                     D is COMPLEX array, dimension (N)
                     The diagonal elements of T.

           DU

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

           X

                     X is COMPLEX array, dimension (LDX,NRHS)
                     The N by NRHS matrix X.

           LDX

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

           BETA

                     BETA is REAL
                     The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 1.

           B

                     B is COMPLEX array, dimension (LDB,NRHS)
                     On entry, the N by NRHS matrix B.
                     On exit, B is overwritten by the matrix expression
                     B := alpha * A * X + beta * B.

           LDB

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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine dlagtm (character trans, integer n, integer nrhs, double precision alpha, double
       precision, dimension( * ) dl, double precision, dimension( * ) d, double precision,
       dimension( * ) du, double precision, dimension( ldx, * ) x, integer ldx, double precision
       beta, double precision, dimension( ldb, * ) b, integer ldb)
       DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal
       matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or
       -1.

       Purpose:

            DLAGTM performs a matrix-matrix product of the form

               B := alpha * A * X + beta * B

            where A is a tridiagonal matrix of order N, B and X are N by NRHS
            matrices, and alpha and beta are real scalars, each of which may be
            0., 1., or -1.

       Parameters
           TRANS

                     TRANS is CHARACTER*1
                     Specifies the operation applied to A.
                     = 'N':  No transpose, B := alpha * A * X + beta * B
                     = 'T':  Transpose,    B := alpha * A'* X + beta * B
                     = 'C':  Conjugate transpose = Transpose

           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 matrices X and B.

           ALPHA

                     ALPHA is DOUBLE PRECISION
                     The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 0.

           DL

                     DL is DOUBLE PRECISION array, dimension (N-1)
                     The (n-1) sub-diagonal elements of T.

           D

                     D is DOUBLE PRECISION array, dimension (N)
                     The diagonal elements of T.

           DU

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

           X

                     X is DOUBLE PRECISION array, dimension (LDX,NRHS)
                     The N by NRHS matrix X.

           LDX

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

           BETA

                     BETA is DOUBLE PRECISION
                     The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 1.

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     On entry, the N by NRHS matrix B.
                     On exit, B is overwritten by the matrix expression
                     B := alpha * A * X + beta * B.

           LDB

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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine slagtm (character trans, integer n, integer nrhs, real alpha, real, dimension( * )
       dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldx, * ) x, integer
       ldx, real beta, real, dimension( ldb, * ) b, integer ldb)
       SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal
       matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or
       -1.

       Purpose:

            SLAGTM performs a matrix-matrix product of the form

               B := alpha * A * X + beta * B

            where A is a tridiagonal matrix of order N, B and X are N by NRHS
            matrices, and alpha and beta are real scalars, each of which may be
            0., 1., or -1.

       Parameters
           TRANS

                     TRANS is CHARACTER*1
                     Specifies the operation applied to A.
                     = 'N':  No transpose, B := alpha * A * X + beta * B
                     = 'T':  Transpose,    B := alpha * A'* X + beta * B
                     = 'C':  Conjugate transpose = Transpose

           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 matrices X and B.

           ALPHA

                     ALPHA is REAL
                     The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 0.

           DL

                     DL is REAL array, dimension (N-1)
                     The (n-1) sub-diagonal elements of T.

           D

                     D is REAL array, dimension (N)
                     The diagonal elements of T.

           DU

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

           X

                     X is REAL array, dimension (LDX,NRHS)
                     The N by NRHS matrix X.

           LDX

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

           BETA

                     BETA is REAL
                     The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 1.

           B

                     B is REAL array, dimension (LDB,NRHS)
                     On entry, the N by NRHS matrix B.
                     On exit, B is overwritten by the matrix expression
                     B := alpha * A * X + beta * B.

           LDB

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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine zlagtm (character trans, integer n, integer nrhs, double precision alpha,
       complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * )
       du, complex*16, dimension( ldx, * ) x, integer ldx, double precision beta, complex*16,
       dimension( ldb, * ) b, integer ldb)
       ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal
       matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or
       -1.

       Purpose:

            ZLAGTM performs a matrix-matrix product of the form

               B := alpha * A * X + beta * B

            where A is a tridiagonal matrix of order N, B and X are N by NRHS
            matrices, and alpha and beta are real scalars, each of which may be
            0., 1., or -1.

       Parameters
           TRANS

                     TRANS is CHARACTER*1
                     Specifies the operation applied to A.
                     = 'N':  No transpose, B := alpha * A * X + beta * B
                     = 'T':  Transpose,    B := alpha * A**T * X + beta * B
                     = 'C':  Conjugate transpose, B := alpha * A**H * X + beta * B

           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 matrices X and B.

           ALPHA

                     ALPHA is DOUBLE PRECISION
                     The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 0.

           DL

                     DL is COMPLEX*16 array, dimension (N-1)
                     The (n-1) sub-diagonal elements of T.

           D

                     D is COMPLEX*16 array, dimension (N)
                     The diagonal elements of T.

           DU

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

           X

                     X is COMPLEX*16 array, dimension (LDX,NRHS)
                     The N by NRHS matrix X.

           LDX

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

           BETA

                     BETA is DOUBLE PRECISION
                     The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
                     it is assumed to be 1.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the N by NRHS matrix B.
                     On exit, B is overwritten by the matrix expression
                     B := alpha * A * X + beta * B.

           LDB

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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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