# dgemlqt.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dgemlqt.f

## SYNOPSIS

### Functions/Subroutines

subroutine dgemlqt (SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
DGEMLQT

## Function/Subroutine Documentation

### subroutine dgemlqt (character SIDE, character TRANS, integer M, integer N, integer K, integer MB, double precision, dimension( ldv, * ) V, integer LDV, double precision, dimension( ldt, * ) T, integer LDT, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) WORK, integer INFO)

DGEMLQT

Purpose:

``` DGEMLQT overwrites the general real M-by-N matrix C with

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q C            C Q
TRANS = 'T':   Q**T C            C Q**T

where Q is a real orthogonal matrix defined as the product of K
elementary reflectors:

Q = H(1) H(2) . . . H(K) = I - V T V**T

generated using the compact WY representation as returned by DGELQT.

Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
```

Parameters:

SIDE

```          SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
```

TRANS

```          TRANS is CHARACTER*1
= 'N':  No transpose, apply Q;
= 'C':  Transpose, apply Q**T.
```

M

```          M is INTEGER
The number of rows of the matrix C. M >= 0.
```

N

```          N is INTEGER
The number of columns of the matrix C. N >= 0.
```

K

```          K is INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
```

MB

```          MB is INTEGER
The block size used for the storage of T.  K >= MB >= 1.
This must be the same value of MB used to generate T
in DGELQT.
```

V

```          V is DOUBLE PRECISION array, dimension
(LDV,M) if SIDE = 'L',
(LDV,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGELQT in the first K rows of its array argument A.
```

LDV

```          LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).
```

T

```          T is DOUBLE PRECISION array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by DGELQT, stored as a MB-by-K matrix.
```

LDT

```          LDT is INTEGER
The leading dimension of the array T.  LDT >= MB.
```

C

```          C is DOUBLE PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
```

LDC

```          LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
```

WORK

```          WORK is DOUBLE PRECISION array. The dimension of
WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
```

INFO

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

Author:

Univ. of Tennessee

Univ. of California Berkeley