vsip_dvouter_p - Outer Product of Two Vectors

Core

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While our Core implementation implements all functions given in the standard we are still working on completing this documentation.

Please refer to the VSIPL standard for a complete function reference of the Core profile until we have completed work on this documentation.

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6.1.3 vsip_dvouter_p - Outer Product of Two Vectors

void vsip_vouter_f(vsip_scalar_f alpha, const vsip_vview_f *x, const vsip_vview_f *y, const vsip_mview_f *r); 
void vsip_cvouter_f(vsip_cscalar_f alpha, const vsip_cvview_f *x, const vsip_cvview_f *y, const vsip_cmview_f *r);

Description

This function computes the outer product of two vectors $x$ and $y$ , scaled by $α$ , and stores the result in matrix $r$ . The outer product is defined as:

ri,j= α·xi·yj

for all $i$ and $j$ , where $xi$ is the $i$ -th element of vector $x$ and $yj$ is the $j$ -th element of vector $y$ .

Parameters

vsip_dscalar_p alpha: Scalar multiplier for the outer product.
const vsip_dvview_p* x: Pointer to the first input vector of length $m$ .
const vsip_dvview_p* y: Pointer to the second input vector of length $n$ .
const vsip_dmview_p* r: Pointer to the output matrix of size $m ×n$ that will store the result.

Example

vsip_vview_f *x, *y; 
vsip_mview_f *r; 
vsip_length m = 5, n = 4; 
 
// Create vectors and matrix 
x = vsip_vcreate_f(m, VSIP_MEM_NONE); 
y = vsip_vcreate_f(n, VSIP_MEM_NONE); 
r = vsip_mcreate_f(m, n, VSIP_ROW, VSIP_MEM_NONE); 
 
// Initialize vectors 
vsip_vramp_f(1.0f, 1.0f, x);  // x = [1, 2, 3, 4, 5] 
vsip_vramp_f(0.5f, 0.5f, y);  // y = [0.5, 1.0, 1.5, 2.0] 
 
// Compute outer product: r = x * y^T 
vsip_vouter_f(1.0f, x, y, r); 
 
// Print the resulting matrix 
printf("Outer product result:\n"); 
for (vsip_index i = 0; i < m; i++) { 
    for (vsip_index j = 0; j < n; j++) { 
        printf("%8.2f ", vsip_mget_f(r, i, j)); 
    } 
    printf("\n"); 
} 
 
// Compute scaled outer product: r = 2.0 * x * y^T 
vsip_vouter_f(2.0f, x, y, r); 
 
// Clean up 
vsip_valldestroy_f(x); 
vsip_valldestroy_f(y); 
vsip_malldestroy_f(r);

Notes

The output matrix $r$ must have dimensions $m ×n$ where $m$ is the length of vector $x$ and $n$ is the length of vector $y$ .
The outer product is not commutative: $x⊗ y̸= y⊗x$ .
If $α= 0$ , the result will be a zero matrix regardless of the input vectors.

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