Developer Reference for Intel® oneAPI Math Kernel Library for C
?unmtr
Multiplies a complex matrix by the complex unitary matrix Q determined by ?hetrd .
Syntax
lapack_intLAPACKE_cunmtr ( intmatrix_layout , charside , charuplo , chartrans , lapack_intm , lapack_intn , constlapack_complex_float*a , lapack_intlda , constlapack_complex_float*tau , lapack_complex_float*c , lapack_intldc );
lapack_intLAPACKE_zunmtr ( intmatrix_layout , charside , charuplo , chartrans , lapack_intm , lapack_intn , constlapack_complex_double*a , lapack_intlda , constlapack_complex_double*tau , lapack_complex_double*c , lapack_intldc );
Include Files
mkl.h
Description
cunmtr zunmtr unmtr
The routine multiplies a complex matrix C by Q or Q:code:`H` , where Q is the unitary matrix Q formed by ?hetrd when reducing a complex Hermitian matrix A to tridiagonal form: A = Q*T*Q^{H} . Use this routine after a call to ?hetrd .
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 on C ).
Input Parameters
In the descriptions below, r denotes the order of Q :
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 ).
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.
uplo
Must be ‘U’ or ‘L’ .
Use the same uplo as supplied to ?hetrd .
trans
Must be either ‘N’ or ‘T’ .
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 ).
- a , c , tau , work
-
COMPLEX for cunmtr DOUBLE COMPLEX for zunmtr .
a (size max(1, lda * r )) and tau are the arrays returned by ?hetrd .
The second dimension of a must be at least max(1, r ). The dimension of tau must be at least max(1, r -1).
c (size max(1, ldc * n ) for column major layout and max(1, ldc * m ) for row major layout) contains the 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, r) .
ldc
The leading dimension of c ; ldc≥ max(1, n) for column major layout and ldc ≥ max(1, m ) 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 computed product differs from the exact product by a matrix \(E\) such that \(||E||_{2} = O(\varepsilon) ||C||_{2}\) , where \(\varepsilon\) is the machine precision.
The total number of floating-point operations is approximately \(8 m^{2} n\) if side = 'L' or \(8 n^{2} m\) if side = 'R' .
The real counterpart of this routine is ormtr .