# dopgtr.f

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

## SYNOPSIS

### Functions/Subroutines

subroutine dopgtr (UPLO, N, AP, TAU, Q, LDQ, WORK, INFO)
DOPGTR

## Function/Subroutine Documentation

### subroutine dopgtr (character UPLO, integer N, double precision, dimension( * ) AP, double precision, dimension( * ) TAU, double precision, dimension( ldq, * ) Q, integer LDQ, double precision, dimension( * ) WORK, integer INFO)

DOPGTR

Purpose:

``` DOPGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
DSPTRD using packed storage:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
= 'U': Upper triangular packed storage used in previous
call to DSPTRD;
= 'L': Lower triangular packed storage used in previous
call to DSPTRD.
```

N

```          N is INTEGER
The order of the matrix Q. N >= 0.
```

AP

```          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The vectors which define the elementary reflectors, as
returned by DSPTRD.
```

TAU

```          TAU is DOUBLE PRECISION array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DSPTRD.
```

Q

```          Q is DOUBLE PRECISION array, dimension (LDQ,N)
The N-by-N orthogonal matrix Q.
```

LDQ

```          LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (N-1)
```

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