Developer Reference for Intel® oneAPI Math Kernel Library for C
?ungqr
Generates the complex unitary matrix Q of the QR factorization formed by ?geqrf .
Syntax
lapack_intLAPACKE_cungqr ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intk , lapack_complex_float*a , lapack_intlda , constlapack_complex_float*tau );
lapack_intLAPACKE_zungqr ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intk , lapack_complex_double*a , lapack_intlda , constlapack_complex_double*tau );
Include Files
mkl.h
Description
cungqr zungqr ungqr
The routine generates the whole or part of m -by- m unitary matrix Q of the QR factorization formed by the routines ?geqrf or geqpf . Use this routine after a call to cgeqrf / zgeqrf or cgeqpf / zgeqpf .
Usually Q is determined from the QR factorization of an m by p matrix A with m≥p . To compute the whole matrix Q , use:
call LAPACKE_?ungqr ( matrix_layout,m , m , p , a , lda , tau, work, lwork, info )
To compute the leading p columns of Q (which form an orthonormal basis in the space spanned by the columns of A ):
call LAPACKE_?ungqr ( matrix_layout,m , p , p , a , lda , tau, work, lwork, info )
To compute the matrix Q:code:`k` of the QR factorization of the leading k columns of the matrix A :
call LAPACKE_?ungqr ( matrix_layout,m , m , k , a , lda , tau, work, lwork, info )
To compute the leading k columns of Q:code:`k` (which form an orthonormal basis in the space spanned by the leading k columns of the matrix A ):
call LAPACKE_?ungqr ( matrix_layout,m , k , k , a , lda , tau, work, lwork, info )
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
m
The order of the unitary matrix Q ( m≥ 0 ).
n
The number of columns of Q to be computed
(0 ≤ n≤m ).
k
The number of elementary reflectors whose product defines the matrix Q (0 ≤ k ≤ n ).
- a , tau , work
-
COMPLEX for cungqr DOUBLE COMPLEX for zungqr
Arrays: a and tau are the arrays returned by cgeqrf / zgeqrf or cgeqpf / zgeqpf .
The size of a is max(1, lda * n ) for column major layout and max(1, lda * m ) for row major layout . The second dimension of a must be at least max(1, n ). The size of tau must be at least max(1, k ). work is a workspace array, its dimension max(1, lwork) .
lda
The leading dimension of a ; at least max(1, m ) for column major layout and max(1, n ) for row major layout .
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
- 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 \(Q\) differs from an exactly unitary matrix by a matrix \(E\) such that \(||E||_{2} = O(\varepsilon) ||A||_{2}\) , where \(\varepsilon\) is the machine precision.
The total number of floating-point operations is approximately \(16 m n k - 8 (m + n) k2 + (16/3) k^{3}\) .
If n = k , the number is approximately \((8/3) n^{2} (3m - n)\) .
The real counterpart of this routine is orgqr .