Generates the real orthogonal matrix Q determined by ?sptrd.


lapack_int LAPACKE_sopgtr (int matrix_layout, char uplo, lapack_int n, const float* ap, const float* tau, float* q, lapack_int ldq);

lapack_int LAPACKE_dopgtr (int matrix_layout, char uplo, lapack_int n, const double* ap, const double* tau, double* q, lapack_int ldq);

Include Files

  • mkl.h


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

Input Parameters


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


Must be 'U' or 'L'. Use the same uplo as supplied to ?sptrd.


The order of the matrix Q (n 0).

ap, tau

Arrays ap and tau, as returned by ?sptrd.

The size of ap must be at least max(1, n(n+1)/2).

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


The leading dimension of the output array q; at least max(1, n).

Output Parameters


Array, size (size max(1, ldq*n)) .

Contains the computed 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 upgtr.

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