Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/31/2023
Public

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?orgtr

Generates the real orthogonal matrix Q determined by ?sytrd.

Syntax

lapack_int LAPACKE_sorgtr (int matrix_layout, char uplo, lapack_int n, float* a, lapack_int lda, const float* tau);

lapack_int LAPACKE_dorgtr (int matrix_layout, char uplo, lapack_int n, double* a, lapack_int lda, const double* tau);

Include Files
  • mkl.h
Description

The routine explicitly generates the n-by-n orthogonal matrix Q formed by ?sytrd when reducing a real symmetric matrix A to tridiagonal form: A = Q*T*QT. Use this routine after a call to ?sytrd.

Input Parameters
matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

Must be 'U' or 'L'.

Use the same uplo as supplied to ?sytrd.

n

The order of the matrix Q (n 0).

a, tau

Arrays:

a (size max(1, lda*n)) is the array a as returned by ?sytrd.

tau is the array tau as returned by ?sytrd.

The size of tau must be at least max(1, n-1).

lda

The leading dimension of a; at least max(1, n).

Output Parameters
a

Overwritten by the orthogonal matrix Q.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

Application Notes

The computed matrix Q differs from an exactly orthogonal matrix by a matrix E such that ||E||2 = O(ε), where ε is the machine precision.

The approximate number of floating-point operations is (4/3)n3.

The complex counterpart of this routine is ungtr.