?orgtr

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?orgtr

Generates the real orthogonal matrix Q determined by ?sytrd .

Syntax

lapack_intLAPACKE_sorgtr ( intmatrix_layout , charuplo , lapack_intn , float*a , lapack_intlda , constfloat*tau );

lapack_intLAPACKE_dorgtr ( intmatrix_layout , charuplo , lapack_intn , double*a , lapack_intlda , constdouble*tau );

Include Files

mkl.h

Description

sorgtr dorgtr orgtr

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*Q^{T} . 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 , work

REAL for sorgtr DOUBLE PRECISION for dorgtr . Arrays:

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

The second dimension of a must be at least max(1, n ).

tau is the array tau as returned by ?sytrd .

The size of tau must be at least max(1, n -1). work is a workspace array, its dimension max(1, lwork) .

lda

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

lwork

The size of the work array ( lwork≥n ).

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 . See Application Notes for the suggested value of lwork .

Output Parameters

a: Overwritten by the orthogonal matrix Q .
work(1): If info = 0 , on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.

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 ungtr .

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?orgtr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes