Developer Reference for Intel® oneAPI Math Kernel Library for C
?unmbr
Multiplies an arbitrary complex matrix by the unitary matrix Q or P determined by ?gebrd .
Syntax
lapack_intLAPACKE_cunmbr ( intmatrix_layout , charvect , charside , chartrans , lapack_intm , lapack_intn , lapack_intk , constlapack_complex_float*a , lapack_intlda , constlapack_complex_float*tau , lapack_complex_float*c , lapack_intldc );
lapack_intLAPACKE_zunmbr ( intmatrix_layout , charvect , charside , chartrans , lapack_intm , lapack_intn , lapack_intk , constlapack_complex_double*a , lapack_intlda , constlapack_complex_double*tau , lapack_complex_double*c , lapack_intldc );
Include Files
mkl.h
Description
cunmbr zunmbr unmbr
Given an arbitrary complex matrix C , this routine forms one of the matrix products Q*C , Q:code:`H`*C , C*Q , C*Q:code:`H` , P*C , P:code:`H`*C , C*P , or C*P:code:`H` , where Q and P are unitary matrices computed by a call to gebrd / gebrd . The routine overwrites the product on C .
Input Parameters
In the descriptions below, r denotes the order of Q or P:code:`H` :
If side = 'L' , r = m ; if side = 'R' , r = n .
- 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' , then Q or Q:code:`H` is applied to C . If vect = 'P' , then P or P:code:`H` is applied to C .
side
Must be ‘L’ or ‘R’ .
If side = 'L' , multipliers are applied to C from the left. If side = 'R' , they are applied to C from the right.
trans
Must be ‘N’ or ‘C’ .
If trans = 'N' , then Q or P is applied to C . If trans = 'C' , then Q:code:`H` or P:code:`H` is applied to C .
m
The number of rows in C .
n
The number of columns in C .
k
One of the dimensions of A in ?gebrd :
If vect = 'Q' , the number of columns in A ; If vect = 'P' , the number of rows in A . Constraints: m≥ 0 , n≥ 0 , k≥ 0 .
- a , c , work
-
COMPLEX for cunmbr DOUBLE COMPLEX for zunmbr . Arrays:
a is the array a as returned by ?gebrd .
The size of a depends on the value of the matrix_layout , vect , and side parameters: Its second dimension must be at least max(1, min( r , k )) for vect = 'Q' , or max(1, r )) for vect = 'P' .
c (size max(1, ldc * n ) for column major layout and max(1, ldc * m for row major layout) holds the matrix C .
Its second dimension must be at least max(1, n ). work is a workspace array, its dimension max(1, lwork) .
lda
The leading dimension of a . Constraints:
lda ≥ max(1, r ) for column major layout and at least max(1, k ) for row major layout if vect = 'Q' ;
lda ≥ max(1, min( r , k )) for column major layout and at least max(1, r ) for row major layout if vect = 'P' .
ldc
The leading dimension of c ; ldc≥ max(1, m) .
- tau
-
COMPLEX for cunmbr DOUBLE COMPLEX for zunmbr . Array, size at least max (1, min( r , k )). For vect = 'Q' , the array tauq as returned by ?gebrd . For vect = 'P' , the array taup as returned by ?gebrd .
lwork
The size of the work array.
lwork≥ max(1, n) if side = 'L' ; lwork≥ max(1, m) if side = 'R' . lwork≥ 1 if n=0 or m=0 . For optimum performance lwork ≥ max(1,n*nb) if side = 'L' , and lwork ≥ max(1,m*nb) if side = 'R' , where nb is the optimal blocksize. ( nb = 0 if m = 0 or n = 0 .) 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:code:`H`*C , C*Q , C*Q:code:`H` , P*C , P:code:`H`*C , C*P , or C*P:code:`H` , as specified by vect , 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 computed product differs from the exact product by a matrix \(E\) such that \(||E||_{2} = O(\varepsilon) ||C||_{2}\) .
The total number of floating-point operations is approximately
8*n*k(2*m - k) if side = 'L' and m≥k ;
8*m*k(2*n - k) if side = 'R' and n≥k ;
\(8 m^{2} n\) if side = 'L' and m < k ;
\(8 n^{2} m\) if side = 'R' and n < k .
The real counterpart of this routine is ormbr .