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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: performs a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N,

```NAME
LAPACK-3  - performs a matrix-vector 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

SYNOPSIS
SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX,  BETA,  B,
LDB )

CHARACTER      TRANS

INTEGER        LDB, LDX, N, NRHS

DOUBLE         PRECISION ALPHA, BETA

COMPLEX*16     B( LDB, * ), D( * ), DL( * ), DU( * ), X( LDX, * )

PURPOSE
ZLAGTM performs a matrix-vector product of the form

ARGUMENTS
TRANS   (input) 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       (input) INTEGER
The order of the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B.

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

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

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

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

X       (input) COMPLEX*16 array, dimension (LDX,NRHS)
The N by NRHS matrix X.
LDX     (input) INTEGER
The leading dimension of the array X.  LDX >= max(N,1).

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

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

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```