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<div class="section" id="computing-products">
<h1>Computing products<a class="headerlink" href="#computing-products" title="Permalink to this headline">ΒΆ</a></h1>
<div class="highlight-python"><div class="highlight"><pre><span class="c">#!python</span>
<span class="sd">"""</span>
<span class="sd">The overloading of the * operator in PyViennaCL is not directly compatible with</span>
<span class="sd">the usage in NumPy. In PyViennaCL, given the emphasis on linear algebra, we have</span>
<span class="sd">attempted to make the usage of * as natural as possible.</span>
<span class="sd">The semantics are as follows:</span>
<span class="sd">* Scalar * scalar -> scalar;</span>
<span class="sd">* scalar * vector -> scaled vector;</span>
<span class="sd">* scalar * matrix -> scaled matrix;</span>
<span class="sd">* vector * vector -> undefined;</span>
<span class="sd">* vector * matrix -> undefined;</span>
<span class="sd">* matrix * vector -> matrix-vector product;</span>
<span class="sd">* matrix * matrix -> matrix-matrix product.</span>
<span class="sd">Of course, there exist other products in some cases, which is why the * operator</span>
<span class="sd">is sometimes undefined. For instance, in the case of `vector * vector`, we</span>
<span class="sd">could have either a dot product, an outer product, a cross product, or an</span>
<span class="sd">elementwise product. The cross product is not currently implemented in</span>
<span class="sd">PyViennaCL, but this still leaves three cases from which to choose.</span>
<span class="sd">Here, we demonstrate the different notation for these products.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">pyviennacl</span> <span class="kn">as</span> <span class="nn">p</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="c"># Let's construct some random 1-D and 2-D arrays</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="n">w</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">g</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="c"># Now transfer them to the compute device</span>
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">Vector</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="n">p</span><span class="o">.</span><span class="n">Vector</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
<span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">f</span><span class="p">),</span> <span class="n">p</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"a is</span><span class="se">\n</span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">a</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"b is</span><span class="se">\n</span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">b</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"x is </span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">x</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s">"y is </span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">y</span><span class="p">)</span>
<span class="c">#</span>
<span class="c"># Scaling</span>
<span class="c">#</span>
<span class="c"># Represent the scaling of x by 2.0</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">x</span> <span class="o">*</span> <span class="mf">2.0</span>
<span class="c"># Compute and print the result</span>
<span class="k">print</span><span class="p">(</span><span class="s">"x * 2.0 = </span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">z</span><span class="p">)</span>
<span class="c"># Represent the scaling of a by 2.0</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mf">2.0</span>
<span class="c"># Compute and print the result</span>
<span class="k">print</span><span class="p">(</span><span class="s">"a * 2.0 =</span><span class="se">\n</span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">c</span><span class="p">)</span>
<span class="c">#</span>
<span class="c"># Vector products</span>
<span class="c">#</span>
<span class="c"># Represent the dot product of x and y</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="c"># or p.dot(x, y)</span>
<span class="c"># Compute the dot product and print it</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Dot product of x and y is </span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">d</span><span class="p">)</span>
<span class="c"># Represent the elementwise product of x and y</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">element_prod</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="c"># or x.element_mul(y)</span>
<span class="c"># Compute and print the result</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Elementwise product of x and y is </span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">z</span><span class="p">)</span>
<span class="c"># Represent the outer product of x and y</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="c"># Compute and print the result</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Outer product of x and y:</span><span class="se">\n</span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">c</span><span class="p">)</span>
<span class="c">#</span>
<span class="c"># Matrix and matrix-vector products</span>
<span class="c">#</span>
<span class="c"># Represent the elementwise product of a and b</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">element_prod</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="c"># or a.elementwise_mul(b)</span>
<span class="c"># Compute and print the result</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Elementwise product of a and b:</span><span class="se">\n</span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">c</span><span class="p">)</span>
<span class="c"># Represent the matrix product of a and b</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span>
<span class="c"># Compute and print the result</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Matrix product of a and b:</span><span class="se">\n</span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">c</span><span class="p">)</span>
<span class="c"># Represent the matrix-vector product of a and x</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="n">x</span>
<span class="c"># Compute and print the result</span>
<span class="k">print</span><span class="p">(</span><span class="s">"Matrix-vector product of a and x:</span><span class="se">\n</span><span class="si">%s</span><span class="s">"</span> <span class="o">%</span> <span class="n">c</span><span class="p">)</span>
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