Developer Reference for Intel® oneAPI Math Kernel Library for C
?unmrz
Multiplies a complex matrix by the unitary matrix defined from the factorization formed by ?tzrzf .
Syntax
lapack_intLAPACKE_cunmrz ( intmatrix_layout , charside , chartrans , lapack_intm , lapack_intn , lapack_intk , lapack_intl , constlapack_complex_float*a , lapack_intlda , constlapack_complex_float*tau , lapack_complex_float*c , lapack_intldc );
lapack_intLAPACKE_zunmrz ( intmatrix_layout , charside , chartrans , lapack_intm , lapack_intn , lapack_intk , lapack_intl , constlapack_complex_double*a , lapack_intlda , constlapack_complex_double*tau , lapack_complex_double*c , lapack_intldc );
Include Files
mkl.h
Description
cunmrz zunmrz unmrz
The routine multiplies a complex m -by- n matrix C by Q or Q:code:`H` , where Q is the unitary matrix defined as a product of k elementary reflectors H(i) :
Q = H(1)^{H}* H(2)^{H}*...*H(k)^{H} as returned by the factorization routine tzrzf .
Depending on the parameters side and trans , the routine can form one of the matrix products Q*C , Q:code:`H`*C , C*Q , or C*Q:code:`H` (overwriting the result over C ).
The matrix Q is of order m if side = 'L' and of order n if side = 'R' .
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:`H` is applied to C from the left. If side = 'R' , Q or Q:code:`H` is applied to C from the right.
trans
Must be either ‘N’ or ‘C’ .
If trans = 'N' , the routine multiplies C by Q . If trans = 'C' , the routine multiplies C by Q:code:`H` .
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' .
- l
-
INTEGER . The number of columns of the matrix A containing the meaningful part of the Householder reflectors. Constraints: 0 ≤l≤m , if side = 'L' ; 0 ≤l≤n , if side = 'R' .
- a , tau , c , work
-
COMPLEX for cunmrz DOUBLE COMPLEX for zunmrz . Arrays: a ( lda ,*), tau (*), c ( ldc ,*), work ( lwork ). Arrays: a (size for side = ‘L’: max(1, lda * m ) for column major layout and max(1, lda * k ) for row major layout; for side = ‘R’: max(1, lda * b ) for column major layout and max(1, lda * k ) for row major layout), tau , c (size max(1, ldc * n ) for column major layout and max(1, ldc * m ) for row major layout). On entry, the i th row of a must contain the vector which defines the elementary reflector H(i) , for i = 1,2,…, k , as returned by ctzrzf / ztzrzf in the last k rows of its array argument a . The second dimension of a must be at least max(1, m ) if side = 'L' , and at least max(1, n ) if side = 'R' .
tau [ i - 1] must contain the scalar factor of the elementary reflector H(i) , as returned by ctzrzf / ztzrzf .
The size of tau must be at least max(1, k ).
c 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 ; lda≥ max(1, k) for column major layout. For row major layout, lda≥ max(1, m) if side = ‘L’, and lda≥ max(1, n) if side = ‘R’ .
ldc
The leading dimension of c ; 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:code:`H`*C , C*Q , or C*Q:code:`H` (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 real counterpart of this routine is ormrz .