Developer Reference for Intel® oneAPI Math Kernel Library for C
?ormqr
Multiplies a real matrix by the orthogonal matrix Q of the QR factorization formed by ?geqrf or ?geqpf .
Syntax
lapack_intLAPACKE_sormqr ( intmatrix_layout , charside , chartrans , lapack_intm , lapack_intn , lapack_intk , constfloat*a , lapack_intlda , constfloat*tau , float*c , lapack_intldc );
lapack_intLAPACKE_dormqr ( intmatrix_layout , charside , chartrans , lapack_intm , lapack_intn , lapack_intk , constdouble*a , lapack_intlda , constdouble*tau , double*c , lapack_intldc );
Include Files
mkl.h
Description
sormqr dormqr ormqr
The routine multiplies a real matrix C by Q or Q:code:`T` , where Q is the orthogonal matrix Q of the QR factorization formed by the routine ?geqrf or ?geqpf .
Depending on the parameters sideleft_right and trans , the routine can form one of the matrix products Q*C , Q^{T}*C , C*Q , or C*Q^{T} (overwriting the result on C ).
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
side
Must be either ‘L’ or ‘R’ .
If side='L' , Q or Q:code:`T` is applied to C from the left. If side='R' , Q or Q:code:`T` is applied to C from the right.
trans
Must be either ‘N’ or ‘T’ .
If trans='N' , the routine multiplies C by Q . If trans='T' , the routine multiplies C by Q:code:`T` .
m
The number of rows in the matrix C ( m≥ 0 ).
n
The number of columns in C ( n≥ 0 ).
k
The number of elementary reflectors whose product defines the matrix Q . Constraints:
0 ≤k≤m if side='L' ; 0 ≤k≤n if side='R' .
- a , tau , c , work
-
REAL for sgeqrf DOUBLE PRECISION for dgeqrf . Arrays:
a and tau are the arrays returned by sgeqrf / dgeqrf or sgeqpf / dgeqpf .
The size of a is max(1, lda * k ) for column major layout, max(1, lda * m ) for row major layout and side = ‘L’, and max(1, lda * n ) for row major layout and side = ‘R’. The second dimension of a must be at least max(1, k ). The size of tau must be at least max(1, k ). c ( ldc ,*) contains the matrix C . Array c of size max(1, ldc * n ) for column major layout and max(1, ldc * m ) for row major layout contains the m -by- n matrix C . The second dimension of c must be at least max(1, n ) work is a workspace array, its dimension max(1, lwork) .
lda
The leading dimension of a . Constraints:
if side = 'L' , lda≥ max(1, m) for column major layout and max(1, k ) for row major layout ;
if side = 'R' , lda≥ max(1, n) for column major layout and max(1, k ) for row major layout .
ldc
The leading dimension of c . Constraint:
ldc ≥ max(1, m ) for column major layout and max(1, n ) for row major layout .
lwork
The size of the work array. Constraints:
lwork≥ max(1, n) if side = 'L' ; lwork≥ max(1, m) if side = 'R' . 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
- c
-
Overwritten by the product Q*C , Q^{T}*C , C*Q , or C*Q^{T} (as specified by side and trans ).
- 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 complex counterpart of this routine is unmqr .