Developer Reference for Intel® oneAPI Math Kernel Library for C
?orgbr
Generates the real orthogonal matrix Q or P:code:`T` determined by ?gebrd .
Syntax
lapack_intLAPACKE_sorgbr ( intmatrix_layout , charvect , lapack_intm , lapack_intn , lapack_intk , float*a , lapack_intlda , constfloat*tau );
lapack_intLAPACKE_dorgbr ( intmatrix_layout , charvect , lapack_intm , lapack_intn , lapack_intk , double*a , lapack_intlda , constdouble*tau );
Include Files
mkl.h
Description
sorgbr dorgbr orgbr
The routine generates the whole or part of the orthogonal matrices Q and P:code:`T` formed by the routines gebrd (Reduces a general matrix to bidiagonal form.) . Use this routine after a call to sgebrd / dgebrd . All valid combinations of arguments are described in Input parameters . In most cases you need the following:
To compute the whole m -by- m matrix Q :
call ?orgbr(‘Q’, m, m, n, a … ) LAPACKE_?orgbr(matrix_layout, ‘Q’, m, m, n, a, lda, tau )
(note that the array a must have at least m columns).
To form the n leading columns of Q if m > n :
call ?orgbr(‘Q’, m, n, n, a … ) LAPACKE_?orgbr(matrix_layout, ‘Q’, m, n, n, a, lda, tau )
To compute the whole n -by- n matrix P:code:`T` :
call ?orgbr(‘P’, n, n, m, a … ) LAPACKE_?orgbr(matrix_layout, ‘P’, n, n, m, a, lda, tau )
(note that the array a must have at least n rows).
To form the m leading rows of P:code:`T` if m < n :
call ?orgbr(‘P’, m, n, m, a … ) LAPACKE_?orgbr(matrix_layout, ‘P’, m, n, m, a, lda, tau )
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
vect
Must be ‘Q’ or ‘P’ .
If vect = 'Q' , the routine generates the matrix Q . If vect = 'P' , the routine generates the matrix P:code:`T` .
m, n
The number of rows ( m ) and columns ( n ) in the matrix Q or P:code:`T` to be returned ( m≥ 0 , n≥ 0 ).
If vect = 'Q' , m ≥ n ≥ min(m, k) . If vect = 'P' , n ≥ m ≥ min(n, k) .
- k
-
If vect = 'Q' , the number of columns in the original m -by- k matrix reduced by gebrd . If vect = 'P' , the number of rows in the original k -by- n matrix reduced by gebrd .
- a
-
REAL for sorgbr DOUBLE PRECISION for dorgbr
Array, size at least lda * n for column major layout and lda * m for row major layout. The vectors which define the elementary reflectors, as returned by gebrd .
lda
The leading dimension of the array a . lda ≥ max(1, m) for column major layout and at least max(1, n ) for row major layout .
- tau
-
REAL for sorgbr DOUBLE PRECISION for dorgbr Array, size min (m,k) if vect = 'Q' , min (n,k) if vect = 'P' . Scalar factor of the elementary reflector H ( i ) or G ( i ), which determines Q and P:code:`T` as returned by gebrd (Reduces a general matrix to bidiagonal form.) in the array tauq or taup .
- work
-
REAL for sorgbr DOUBLE PRECISION for dorgbr Workspace array, size max(1, lwork) .
lwork
Dimension of the array work . See Application Notes for the suggested value of lwork .
If lwork = -1 then the routine performs a workspace query and 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 .
Output Parameters
- a
-
Overwritten by the orthogonal matrix Q or P:code:`T` (or the leading rows or columns thereof) as specified by vect , m , and n .
- 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 \(||E||_{2} = O(\varepsilon)\) .
The approximate numbers of floating-point operations for the cases listed in Description are as follows:
To form the whole of \(Q\) : * \((4/3) n (3m^{2} - 3m n + n^{2})\) if m > n ; * \((4/3) m^{3}\) if m≤n .
To form the n leading columns of \(Q\) when m > n : * \((2/3) n^{2} (3m - n)\) if m > n .
To form the whole of \(P^{T}\) : * \((4/3) n^{3}\) if m≥n ; * \((4/3) m (3n^{2} - 3m n + m^{2})\) if m < n .
To form the m leading columns of \(P^{T}\) when m < n : * \((2/3) n^{2} (3m - n)\) if m > n .
The complex counterpart of this routine is ungbr .