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

# sorgtr(3lapack)

generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD

## NAME

SORGTR - generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD

## SYNOPSIS

- SUBROUTINE SORGTR(

  UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, LDA, LWORK, N

- REAL

  A( LDA, \* ), TAU( \* ), WORK( \* )

## PURPOSE

SORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD: 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 triangle of A contains elementary reflectors from SSYTRD; = 'L': Lower triangle of A contains elementary reflectors from SSYTRD.

- N (input) INTEGER

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

- A (input/output) REAL array, dimension (LDA,N)

  On entry, the vectors which define the elementary reflectors, as returned by SSYTRD. On exit, the N-by-N orthogonal matrix Q.

- LDA (input) INTEGER

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

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

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

- WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))

  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

- LWORK (input) INTEGER

  The dimension of the array WORK. LWORK \>= max(1,N-1). For optimum performance LWORK \>= (N-1)\*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

- INFO (output) INTEGER

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