Add mean keyword to dpnp.std and dpnp.var (#2271)

The PR proposes to add `mean` keyword argument to `dpnp.std`,
`dpnp.var`, `dpnp.nanstd`, `dpnp.nanvar` functions and
`dpnp.ndarray.std`, `dpnp.ndarray.var` methods.

The keyword was introduced by NumPy 2.0 and intended to improve the
performance:

> Often when the standard deviation is needed the mean is also needed;
the same holds for the variance and the mean. With the current code the
mean is then calculated twice, this can be prevented if the functions
calculating the variance or the standard deviation can use a
precalculated mean

This PR implements similar improvement in dpnp code. b72f953

.buildinfo

@@ -1,4 +1,4 @@
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-config: b6c9da6510605204d4d666bc46eec2e7
+config: 82ae0d6989d5726c277b5be0c6a00600
 tags: 645f666f9bcd5a90fca523b33c5a78b7

_modules/dpnp/dpnp_array.html

@@ -14,14 +14,14 @@
     </script>
 
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>dpnp.dpnp_array &mdash; Data Parallel Extension for NumPy 0.17.0dev5+4.gd509d3f37ff documentation</title>
+  <title>dpnp.dpnp_array &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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@@ -1925,6 +1925,7 @@ <h1>Source code for dpnp.dpnp_array</h1><div class="highlight"><pre>
         <span class="n">keepdims</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
         <span class="o">*</span><span class="p">,</span>
         <span class="n">where</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="n">mean</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
     <span class="p">):</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Returns the standard deviation of the array elements, along given axis.</span>
@@ -1933,7 +1934,9 @@ <h1>Source code for dpnp.dpnp_array</h1><div class="highlight"><pre>
 
 <span class="sd">        &quot;&quot;&quot;</span>
 
-        <span class="k">return</span> <span class="n">dpnp</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="n">ddof</span><span class="p">,</span> <span class="n">keepdims</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="n">where</span><span class="p">)</span></div>
+        <span class="k">return</span> <span class="n">dpnp</span><span class="o">.</span><span class="n">std</span><span class="p">(</span>
+            <span class="bp">self</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="n">ddof</span><span class="p">,</span> <span class="n">keepdims</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="n">where</span><span class="p">,</span> <span class="n">mean</span><span class="o">=</span><span class="n">mean</span>
+        <span class="p">)</span></div>
 
 
     <span class="nd">@property</span>
@@ -2153,6 +2156,7 @@ <h1>Source code for dpnp.dpnp_array</h1><div class="highlight"><pre>
         <span class="n">keepdims</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
         <span class="o">*</span><span class="p">,</span>
         <span class="n">where</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="n">mean</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
     <span class="p">):</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Returns the variance of the array elements, along given axis.</span>
@@ -2161,7 +2165,9 @@ <h1>Source code for dpnp.dpnp_array</h1><div class="highlight"><pre>
 
 <span class="sd">        &quot;&quot;&quot;</span>
 
-        <span class="k">return</span> <span class="n">dpnp</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="n">ddof</span><span class="p">,</span> <span class="n">keepdims</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="n">where</span><span class="p">)</span></div>
+        <span class="k">return</span> <span class="n">dpnp</span><span class="o">.</span><span class="n">var</span><span class="p">(</span>
+            <span class="bp">self</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">out</span><span class="p">,</span> <span class="n">ddof</span><span class="p">,</span> <span class="n">keepdims</span><span class="p">,</span> <span class="n">where</span><span class="o">=</span><span class="n">where</span><span class="p">,</span> <span class="n">mean</span><span class="o">=</span><span class="n">mean</span>
+        <span class="p">)</span></div>
 </div>
 
 

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+  <title>dpnp.dpnp_flatiter &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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+  <title>dpnp.dpnp_iface &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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+  <title>dpnp.dpnp_iface_arraycreation &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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+  <title>dpnp.dpnp_iface_bitwise &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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+  <title>dpnp.dpnp_iface_functional &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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+  <title>dpnp.dpnp_iface_histograms &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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+  <title>dpnp.dpnp_iface_indexing &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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+  <title>dpnp.dpnp_iface_libmath &mdash; Data Parallel Extension for NumPy 0.17.0dev5+5.gb72f953b123 documentation</title>
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