Developer Reference for Intel® oneAPI Math Kernel Library for C
?gerqf
Computes the RQ factorization of a general m-by-n matrix.
Syntax
lapack_intLAPACKE_sgerqf ( intmatrix_layout , lapack_intm , lapack_intn , float*a , lapack_intlda , float*tau );
lapack_intLAPACKE_dgerqf ( intmatrix_layout , lapack_intm , lapack_intn , double*a , lapack_intlda , double*tau );
lapack_intLAPACKE_cgerqf ( intmatrix_layout , lapack_intm , lapack_intn , lapack_complex_float*a , lapack_intlda , lapack_complex_float*tau );
lapack_intLAPACKE_zgerqf ( intmatrix_layout , lapack_intm , lapack_intn , lapack_complex_double*a , lapack_intlda , lapack_complex_double*tau );
Include Files
mkl.h
Description
sgerqf dgerqf cgerqf zgerqf gerqf
The routine forms the RQ factorization of a general m -by- n matrix A (see Orthogonal Factorizations ). No pivoting is performed.
The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min( m , n ) elementary reflectors . Routines are provided to work with Q in this representation.
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
m
The number of rows in the matrix A ( m≥ 0 ).
n
The number of columns in A ( n≥ 0 ).
- a , work
-
REAL for sgerqf DOUBLE PRECISION for dgerqf COMPLEX for cgerqf DOUBLE COMPLEX for zgerqf . Arrays:
Array a of size max(1, lda * n ) for column major layout and max(1, lda * m ) for row major layout contains the m -by- n matrix A .
The second dimension of a must be at least max(1, n ). 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≥ max(1, m) . 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 on exit by the factorization data as follows: if m≤n , the upper triangle of the subarray a (1: m , n - m +1: n ) contains the m -by- m upper triangular matrix R ; if m≥n , the elements on and above the ( m - n )th subdiagonal contain the m -by- n upper trapezoidal matrix R ; in both cases, the remaining elements, with the array tau , represent the orthogonal/unitary matrix Q as a product of min( m , n ) elementary reflectors.
- tau
-
REAL for sgerqf DOUBLE PRECISION for dgerqf COMPLEX for cgerqf DOUBLE COMPLEX for zgerqf . Array, size at least max (1, min( m , n )). (See Orthogonal Factorizations .) Contains scalar factors of the elementary reflectors for the matrix Q .
- work(1)
-
If info = 0 , on exit work(1) contains the minimum value of lwork required for optimum performance.
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
Related routines include:
to generate matrix Q (for real matrices);
to generate matrix Q (for complex matrices);
to apply matrix Q (for real matrices);
to apply matrix Q (for complex matrices).