Developer Reference for Intel® oneAPI Math Kernel Library for C
?orghr
Generates the real orthogonal matrix Q determined by ?gehrd .
Syntax
lapack_intLAPACKE_sorghr ( intmatrix_layout , lapack_intn , lapack_intilo , lapack_intihi , float*a , lapack_intlda , constfloat*tau );
lapack_intLAPACKE_dorghr ( intmatrix_layout , lapack_intn , lapack_intilo , lapack_intihi , double*a , lapack_intlda , constdouble*tau );
Include Files
mkl.h
Description
sorghr dorghr orghr
The routine explicitly generates the orthogonal matrix Q that has been determined by a preceding call to sgehrd / dgehrd . (The routine ?gehrd reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation, A = Q*H*Q^{T} , and represents the matrix Q as a product of ihi-ilo elementary reflectors . Here ilo and ihi are values determined by sgebal / dgebal when balancing the matrix; if the matrix has not been balanced, ilo = 1 and ihi = n .)
The matrix Q generated by ?orghr has the structure:
where Q22 occupies rows and columns ilo to ihi .
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
n
The order of the matrix Q ( n≥ 0 ).
ilo , ihi
These must be the same parameters ilo and ihi , respectively, as supplied to ?gehrd . (If n > 0 , then 1 ≤ilo≤ihi≤n ; if n = 0 , ilo = 1 and ihi = 0 .)
- a , tau , work
-
REAL for sorghr DOUBLE PRECISION for dorghr
Arrays: a (size max(1, lda * n )) contains details of the vectors which define the elementary reflectors, as returned by ?gehrd .
The second dimension of a must be at least max(1, n ).
tau contains further details of the elementary reflectors, as returned by ?gehrd .
The dimension 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≥ max(1, ihi-ilo) . 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 n -by- n 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 the exact result by a matrix \(E\) such that \(||E||_{2} = O(\varepsilon)\) , where \(\varepsilon\) is the machine precision.
The approximate number of floating-point operations is \((4/3)(ihi-ilo)^{3}\) .
The complex counterpart of this routine is unghr .