vsip_cmprodh_p - Complex Matrix Product with Hermitian Transpose

Core

6.1.12 vsip_cmprodh_p - Complex Matrix Product with Hermitian Transpose

void vsip_cmprodh_f(const vsip_cmview_f *a, const vsip_cmview_f *b, const vsip_cmview_f *r);

Description

This function computes the product of a complex matrix $A$ with the Hermitian transpose of a complex matrix $B$ , storing the result in complex matrix $R$ . The operation performed is:

r = ∑︁n a ·b--- i,j k=1 i,k j,k

for all $i$ and $j$ , where $A$ is an $m × n$ complex matrix, $B$ is a $p ×n$ complex matrix, and $R$ is the resulting $m ×p$ complex matrix. $---- bj,k$ denotes the complex conjugate of $bj,k$ .

Parameters

const vsip_cmview_p* a: First input matrix of size $m × n$ (complex).
const vsip_cmview_p* b: Second input matrix of size $p× n$ (complex), which will be Hermitian transposed in the operation.
const vsip_cmview_p* r: Output matrix of size $m × p$ (complex) that will store the result.

Example

vsip_cmview_f *A, *B, *R; 
vsip_length m = 2, n = 3, p = 2; 
 
// Create complex matrices 
A = vsip_cmcreate_f(m, n, VSIP_ROW, VSIP_MEM_NONE); 
B = vsip_cmcreate_f(p, n, VSIP_ROW, VSIP_MEM_NONE); 
R = vsip_cmcreate_f(m, p, VSIP_ROW, VSIP_MEM_NONE); 
 
// Initialize matrices A and B with complex values 
for (vsip_index i = 0; i < m; i++) { 
    for (vsip_index j = 0; j < n; j++) { 
        vsip_cscalar_f val = VSIP_CMPLX_F(i*n + j + 1, -(i*n + j + 1)); 
        vsip_cmput_f(A, i, j, val); 
    } 
} 
 
for (vsip_index i = 0; i < p; i++) { 
    for (vsip_index j = 0; j < n; j++) { 
        vsip_cscalar_f val = VSIP_CMPLX_F(i*n + j + 1, i*n + j + 2); 
        vsip_cmput_f(B, i, j, val); 
    } 
} 
 
// Compute matrix product with Hermitian transpose: R = A * B^H 
vsip_cmprodh_f(A, B, R); 
 
// Print the result 
printf("Result matrix R = A * B^H (%lux%lu):\n", m, p); 
for (vsip_index i = 0; i < m; i++) { 
    for (vsip_index j = 0; j < p; j++) { 
        vsip_cscalar_f val = vsip_cmget_f(R, i, j); 
        printf("(%.2f%+.2fi) ", val.r, val.i); 
    } 
    printf("\n"); 
} 
 
// Clean up 
vsip_cmalldestroy_f(A); 
vsip_cmalldestroy_f(B); 
vsip_cmalldestroy_f(R);

Notes

The input matrices must have compatible dimensions: Both matrices $A$ and $B$ must have the same number of columns ( $n$ ).
The output matrix $R$ must have dimensions $m ×p$ , where $m$ is the number of rows in $A$ and $p$ is the number of rows in $B$ .
If you need more flexibility in choosing which matrix to transpose, consider using vsip_cgemp_p instead.

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