## MB01UW

### Computation of matrix expressions alpha H A or alpha A H, over A, H Hessenberg matrix

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To compute one of the matrix products

A : = alpha*op( H ) * A, or A : = alpha*A * op( H ),

where alpha is a scalar, A is an m-by-n matrix, H is an upper
Hessenberg matrix, and op( H ) is one of

op( H ) = H   or   op( H ) = H',  the transpose of H.

```
Specification
```      SUBROUTINE MB01UW( SIDE, TRANS, M, N, ALPHA, H, LDH, A, LDA,
\$                   DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
CHARACTER         SIDE, TRANS
INTEGER           INFO, LDA, LDH, LDWORK, M, N
DOUBLE PRECISION  ALPHA
C     .. Array Arguments ..
DOUBLE PRECISION  A(LDA,*), DWORK(*), H(LDH,*)

```
Arguments

Mode Parameters

```  SIDE    CHARACTER*1
Specifies whether the Hessenberg matrix H appears on the
left or right in the matrix product as follows:
= 'L':  A := alpha*op( H ) * A;
= 'R':  A := alpha*A * op( H ).

TRANS   CHARACTER*1
Specifies the form of op( H ) to be used in the matrix
multiplication as follows:
= 'N':  op( H ) = H;
= 'T':  op( H ) = H';
= 'C':  op( H ) = H'.

```
Input/Output Parameters
```  M       (input) INTEGER
The number of rows of the matrix A.  M >= 0.

N       (input) INTEGER
The number of columns of the matrix A.  N >= 0.

ALPHA   (input) DOUBLE PRECISION
The scalar alpha. When alpha is zero then H is not
referenced and A need not be set before entry.

H       (input) DOUBLE PRECISION array, dimension (LDH,k)
where k is M when SIDE = 'L' and is N when SIDE = 'R'.
On entry with SIDE = 'L', the leading M-by-M upper
Hessenberg part of this array must contain the upper
Hessenberg matrix H.
On entry with SIDE = 'R', the leading N-by-N upper
Hessenberg part of this array must contain the upper
Hessenberg matrix H.
The elements below the subdiagonal are not referenced,
except possibly for those in the first column, which
could be overwritten, but are restored on exit.

LDH     INTEGER
The leading dimension of the array H.  LDH >= max(1,k),
where k is M when SIDE = 'L' and is N when SIDE = 'R'.

A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading M-by-N part of this array must
contain the matrix A.
On exit, the leading M-by-N part of this array contains
the computed product.

LDA     INTEGER
The leading dimension of the array A.  LDA >= max(1,M).

```
Workspace
```  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
On exit, if INFO = 0, alpha <> 0, and LDWORK >= M*N > 0,
DWORK contains a copy of the matrix A, having the leading
dimension M.
This array is not referenced when alpha = 0.

LDWORK  The length of the array DWORK.
LDWORK >= 0,   if  alpha =  0 or MIN(M,N) = 0;
LDWORK >= M-1, if  SIDE  = 'L';
LDWORK >= N-1, if  SIDE  = 'R'.
For maximal efficiency LDWORK should be at least M*N.

```
Error Indicator
```  INFO    INTEGER
= 0:  successful exit;
< 0:  if INFO = -i, the i-th argument had an illegal
value.

```
Method
```  The required matrix product is computed in two steps. In the first
step, the upper triangle of H is used; in the second step, the
contribution of the subdiagonal is added. If the workspace can
accomodate a copy of A, a fast BLAS 3 DTRMM operation is used in
the first step.

```
```  None
```
Example

Program Text

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Program Data
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Program Results
```  None
```