?opgtr

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?opgtr

Generates the real orthogonal matrix Q determined by ?sptrd .

Syntax

lapack_intLAPACKE_sopgtr ( intmatrix_layout , charuplo , lapack_intn , constfloat*ap , constfloat*tau , float*q , lapack_intldq );

lapack_intLAPACKE_dopgtr ( intmatrix_layout , charuplo , lapack_intn , constdouble*ap , constdouble*tau , double*q , lapack_intldq );

Include Files

mkl.h

Description

sopgtr dopgtr opgtr

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*Q^{T} . Use this routine after a call to ?sptrd .

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 ?sptrd .

n

The order of the matrix Q ( n≥ 0 ).

ap , tau: REAL for sopgtr DOUBLE PRECISION for dopgtr . 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).

ldq

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

work: REAL for sopgtr DOUBLE PRECISION for dopgtr . Workspace array, size at least max(1, n -1).

Output Parameters

q

REAL for sopgtr DOUBLE PRECISION for dopgtr .

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

Contains the computed matrix Q . The second dimension of q must be at least max(1, n ).

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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

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

The approximate number of floating-point operations is \((4/3)n^{3}\) .

The complex counterpart of this routine is upgtr .

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?opgtr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes