---
name: "sopgtr"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/sopgtr/3lapack"
---

# sopgtr(3lapack)

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 SSPTRD using packed storage

## NAME

SOPGTR - 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 SSPTRD using packed storage

## SYNOPSIS

- SUBROUTINE SOPGTR(

  UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, LDQ, N

- REAL

  AP( \* ), Q( LDQ, \* ), TAU( \* ), WORK( \* )

## PURPOSE

SOPGTR 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 SSPTRD 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).\

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= 'U': Upper triangular packed storage used in previous call to SSPTRD; = 'L': Lower triangular packed storage used in previous call to SSPTRD.

- N (input) INTEGER

  The order of the matrix Q. N \>= 0.

- AP (input) REAL array, dimension (N\*(N+1)/2)

  The vectors which define the elementary reflectors, as returned by SSPTRD.

- TAU (input) REAL array, dimension (N-1)

  TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSPTRD.

- Q (output) REAL array, dimension (LDQ,N)

  The N-by-N orthogonal matrix Q.

- LDQ (input) INTEGER

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

- WORK (workspace) REAL array, dimension (N-1)

  - INFO (output) INTEGER

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