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<div class="highlight"><pre><div class='line' id='LC1'><span class="c">#cython: cdivison=True boundscheck=False</span></div><div class='line' id='LC2'><br/></div><div class='line' id='LC3'><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">'homography'</span><span class="p">]</span></div><div class='line' id='LC4'><br/></div><div class='line' id='LC5'><span class="k">cimport</span> <span class="nn">cython</span></div><div class='line' id='LC6'><span class="k">cimport</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></div><div class='line' id='LC7'><br/></div><div class='line' id='LC8'><span class="k">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span></div><div class='line' id='LC9'><span class="k">import</span> <span class="nn">cython</span></div><div class='line' id='LC10'><br/></div><div class='line' id='LC11'><span class="k">from</span> <span class="nn">cython.operator</span> <span class="k">import</span> <span class="n">dereference</span></div><div class='line' id='LC12'><br/></div><div class='line' id='LC13'><span class="n">np</span><span class="o">.</span><span class="n">import_array</span><span class="p">()</span></div><div class='line' id='LC14'><br/></div><div class='line' id='LC15'><span class="k">cdef</span> <span class="kr">extern</span> <span class="k">from</span> <span class="s">"math.h"</span><span class="p">:</span></div><div class='line' id='LC16'> <span class="n">double</span> <span class="n">floor</span><span class="p">(</span><span class="n">double</span><span class="p">)</span></div><div class='line' id='LC17'> <span class="n">double</span> <span class="n">fmod</span><span class="p">(</span><span class="n">double</span><span class="p">,</span> <span class="n">double</span><span class="p">)</span></div><div class='line' id='LC18'><br/></div><div class='line' id='LC19'><span class="k">cdef</span> <span class="kt">double</span> <span class="nf">get_pixel</span><span class="p">(</span><span class="n">double</span> <span class="o">*</span><span class="n">image</span><span class="p">,</span> <span class="nb">int</span> <span class="n">rows</span><span class="p">,</span> <span class="nb">int</span> <span class="n">cols</span><span class="p">,</span></div><div class='line' id='LC20'> <span class="nb">int</span> <span class="n">r</span><span class="p">,</span> <span class="nb">int</span> <span class="n">c</span><span class="p">,</span> <span class="n">char</span> <span class="n">mode</span><span class="p">,</span> <span class="n">double</span> <span class="n">cval</span><span class="o">=</span><span class="mf">0</span><span class="p">):</span></div><div class='line' id='LC21'> <span class="sd">"""Get a pixel from the image, taking wrapping mode into consideration.</span></div><div class='line' id='LC22'><br/></div><div class='line' id='LC23'><span class="sd"> Parameters</span></div><div class='line' id='LC24'><span class="sd"> ----------</span></div><div class='line' id='LC25'><span class="sd"> image : *double</span></div><div class='line' id='LC26'><span class="sd"> Input image.</span></div><div class='line' id='LC27'><span class="sd"> rows, cols : int</span></div><div class='line' id='LC28'><span class="sd"> Dimensions of image.</span></div><div class='line' id='LC29'><span class="sd"> r, c : int</span></div><div class='line' id='LC30'><span class="sd"> Position at which to get the pixel.</span></div><div class='line' id='LC31'><span class="sd"> mode : {'C', 'W', 'M'}</span></div><div class='line' id='LC32'><span class="sd"> Wrapping mode. Constant, Wrap or Mirror.</span></div><div class='line' id='LC33'><span class="sd"> cval : double</span></div><div class='line' id='LC34'><span class="sd"> Constant value to use for mode constant.</span></div><div class='line' id='LC35'><span class="sd"> </span></div><div class='line' id='LC36'><span class="sd"> """</span></div><div class='line' id='LC37'> <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s">'C'</span><span class="p">:</span></div><div class='line' id='LC38'> <span class="k">if</span> <span class="p">(</span><span class="n">r</span> <span class="o"><</span> <span class="mf">0</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">r</span> <span class="o">></span> <span class="n">rows</span> <span class="o">-</span> <span class="mf">1</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">c</span> <span class="o"><</span> <span class="mf">0</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">c</span> <span class="o">></span> <span class="n">cols</span> <span class="o">-</span> <span class="mf">1</span><span class="p">):</span></div><div class='line' id='LC39'> <span class="k">return</span> <span class="n">cval</span></div><div class='line' id='LC40'> <span class="k">else</span><span class="p">:</span></div><div class='line' id='LC41'> <span class="k">return</span> <span class="n">image</span><span class="p">[</span><span class="n">r</span> <span class="o">*</span> <span class="n">cols</span> <span class="o">+</span> <span class="n">c</span><span class="p">]</span></div><div class='line' id='LC42'> <span class="k">else</span><span class="p">:</span></div><div class='line' id='LC43'> <span class="k">return</span> <span class="n">image</span><span class="p">[</span><span class="n">coord_map</span><span class="p">(</span><span class="n">rows</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">mode</span><span class="p">)</span> <span class="o">*</span> <span class="n">cols</span> <span class="o">+</span></div><div class='line' id='LC44'> <span class="n">coord_map</span><span class="p">(</span><span class="n">cols</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">mode</span><span class="p">)]</span></div><div class='line' id='LC45'><br/></div><div class='line' id='LC46'><span class="k">cdef</span> <span class="kt">int</span> <span class="nf">coord_map</span><span class="p">(</span><span class="nb">int</span> <span class="n">dim</span><span class="p">,</span> <span class="nb">int</span> <span class="n">coord</span><span class="p">,</span> <span class="n">char</span> <span class="n">mode</span><span class="p">):</span></div><div class='line' id='LC47'> <span class="sd">"""</span></div><div class='line' id='LC48'><span class="sd"> Wrap a coordinate, according to a given dimension and mode.</span></div><div class='line' id='LC49'><span class="sd"> </span></div><div class='line' id='LC50'><span class="sd"> Parameters</span></div><div class='line' id='LC51'><span class="sd"> ----------</span></div><div class='line' id='LC52'><span class="sd"> dim : int</span></div><div class='line' id='LC53'><span class="sd"> Maximum coordinate.</span></div><div class='line' id='LC54'><span class="sd"> coord : int</span></div><div class='line' id='LC55'><span class="sd"> Coord provided by user. May be < 0 or > dim.</span></div><div class='line' id='LC56'><span class="sd"> mode : {'W', 'M'}</span></div><div class='line' id='LC57'><span class="sd"> Whether to wrap or mirror the coordinate if it</span></div><div class='line' id='LC58'><span class="sd"> falls outside [0, dim).</span></div><div class='line' id='LC59'><span class="sd"> </span></div><div class='line' id='LC60'><span class="sd"> """</span></div><div class='line' id='LC61'> <span class="n">dim</span> <span class="o">=</span> <span class="n">dim</span> <span class="o">-</span> <span class="mf">1</span></div><div class='line' id='LC62'> <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s">'M'</span><span class="p">:</span> <span class="c"># mirror</span></div><div class='line' id='LC63'> <span class="k">if</span> <span class="p">(</span><span class="n">coord</span> <span class="o"><</span> <span class="mf">0</span><span class="p">):</span></div><div class='line' id='LC64'> <span class="c"># How many times times does the coordinate wrap?</span></div><div class='line' id='LC65'> <span class="k">if</span> <span class="p">(<</span><span class="kt">int</span><span class="p">>(</span><span class="o">-</span><span class="n">coord</span> <span class="o">/</span> <span class="n">dim</span><span class="p">)</span> <span class="o">%</span> <span class="mf">2</span> <span class="o">!=</span> <span class="mf">0</span><span class="p">):</span></div><div class='line' id='LC66'> <span class="k">return</span> <span class="n">dim</span> <span class="o">-</span> <span class="p"><</span><span class="kt">int</span><span class="p">>(</span><span class="o">-</span><span class="n">coord</span> <span class="o">%</span> <span class="n">dim</span><span class="p">)</span></div><div class='line' id='LC67'> <span class="k">else</span><span class="p">:</span></div><div class='line' id='LC68'> <span class="k">return</span> <span class="p"><</span><span class="kt">int</span><span class="p">>(</span><span class="o">-</span><span class="n">coord</span> <span class="o">%</span> <span class="n">dim</span><span class="p">)</span></div><div class='line' id='LC69'> <span class="k">elif</span> <span class="p">(</span><span class="n">coord</span> <span class="o">></span> <span class="n">dim</span><span class="p">):</span></div><div class='line' id='LC70'> <span class="k">if</span> <span class="p">(<</span><span class="kt">int</span><span class="p">>(</span><span class="n">coord</span> <span class="o">/</span> <span class="n">dim</span><span class="p">)</span> <span class="o">%</span> <span class="mf">2</span> <span class="o">!=</span> <span class="mf">0</span><span class="p">):</span></div><div class='line' id='LC71'> <span class="k">return</span> <span class="p"><</span><span class="kt">int</span><span class="p">>(</span><span class="n">dim</span> <span class="o">-</span> <span class="p">(</span><span class="n">coord</span> <span class="o">%</span> <span class="n">dim</span><span class="p">))</span></div><div class='line' id='LC72'> <span class="k">else</span><span class="p">:</span></div><div class='line' id='LC73'> <span class="k">return</span> <span class="p"><</span><span class="kt">int</span><span class="p">>(</span><span class="n">coord</span> <span class="o">%</span> <span class="n">dim</span><span class="p">)</span></div><div class='line' id='LC74'> <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s">'W'</span><span class="p">:</span> <span class="c"># wrap</span></div><div class='line' id='LC75'> <span class="k">if</span> <span class="p">(</span><span class="n">coord</span> <span class="o"><</span> <span class="mf">0</span><span class="p">):</span></div><div class='line' id='LC76'> <span class="k">return</span> <span class="p"><</span><span class="kt">int</span><span class="p">>(</span><span class="n">dim</span> <span class="o">-</span> <span class="p">(</span><span class="o">-</span><span class="n">coord</span> <span class="o">%</span> <span class="n">dim</span><span class="p">))</span></div><div class='line' id='LC77'> <span class="k">elif</span> <span class="p">(</span><span class="n">coord</span> <span class="o">></span> <span class="n">dim</span><span class="p">):</span></div><div class='line' id='LC78'> <span class="k">return</span> <span class="p"><</span><span class="kt">int</span><span class="p">>(</span><span class="n">coord</span> <span class="o">%</span> <span class="n">dim</span><span class="p">)</span></div><div class='line' id='LC79'><br/></div><div class='line' id='LC80'> <span class="k">return</span> <span class="n">coord</span></div><div class='line' id='LC81'><br/></div><div class='line' id='LC82'><span class="k">cdef</span> <span class="nf">tf</span><span class="p">(</span><span class="n">double</span> <span class="n">x</span><span class="p">,</span> <span class="n">double</span> <span class="n">y</span><span class="p">,</span> <span class="n">double</span><span class="o">*</span> <span class="n">H</span><span class="p">,</span> <span class="n">double</span> <span class="o">*</span><span class="n">x_</span><span class="p">,</span> <span class="n">double</span> <span class="o">*</span><span class="n">y_</span><span class="p">):</span></div><div class='line' id='LC83'> <span class="sd">"""Apply a homography to a coordinate.</span></div><div class='line' id='LC84'><br/></div><div class='line' id='LC85'><span class="sd"> Parameters</span></div><div class='line' id='LC86'><span class="sd"> ----------</span></div><div class='line' id='LC87'><span class="sd"> x, y : double</span></div><div class='line' id='LC88'><span class="sd"> Input coordinate.</span></div><div class='line' id='LC89'><span class="sd"> H : (3,3) *double</span></div><div class='line' id='LC90'><span class="sd"> Transformation matrix.</span></div><div class='line' id='LC91'><span class="sd"> x_, y_ : *double</span></div><div class='line' id='LC92'><span class="sd"> Output coordinate.</span></div><div class='line' id='LC93'><br/></div><div class='line' id='LC94'><span class="sd"> """</span></div><div class='line' id='LC95'> <span class="k">cdef</span> <span class="kt">double</span> <span class="nf">xx</span><span class="p">,</span> <span class="nf">yy</span><span class="p">,</span> <span class="nf">zz</span></div><div class='line' id='LC96'><br/></div><div class='line' id='LC97'> <span class="n">xx</span> <span class="o">=</span> <span class="n">H</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">H</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">y</span> <span class="o">+</span> <span class="n">H</span><span class="p">[</span><span class="mf">2</span><span class="p">]</span></div><div class='line' id='LC98'> <span class="n">yy</span> <span class="o">=</span> <span class="n">H</span><span class="p">[</span><span class="mf">3</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">H</span><span class="p">[</span><span class="mf">4</span><span class="p">]</span> <span class="o">*</span> <span class="n">y</span> <span class="o">+</span> <span class="n">H</span><span class="p">[</span><span class="mf">5</span><span class="p">]</span></div><div class='line' id='LC99'> <span class="n">zz</span> <span class="o">=</span> <span class="n">H</span><span class="p">[</span><span class="mf">6</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">H</span><span class="p">[</span><span class="mf">7</span><span class="p">]</span> <span class="o">*</span> <span class="n">y</span> <span class="o">+</span> <span class="n">H</span><span class="p">[</span><span class="mf">8</span><span class="p">]</span></div><div class='line' id='LC100'><br/></div><div class='line' id='LC101'> <span class="n">xx</span> <span class="o">=</span> <span class="n">xx</span> <span class="o">/</span> <span class="n">zz</span></div><div class='line' id='LC102'> <span class="n">yy</span> <span class="o">=</span> <span class="n">yy</span> <span class="o">/</span> <span class="n">zz</span></div><div class='line' id='LC103'><br/></div><div class='line' id='LC104'> <span class="n">x_</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">xx</span></div><div class='line' id='LC105'> <span class="n">y_</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">yy</span></div><div class='line' id='LC106'><br/></div><div class='line' id='LC107'><span class="nd">@cython</span><span class="o">.</span><span class="n">boundscheck</span><span class="p">(</span><span class="bp">False</span><span class="p">)</span></div><div class='line' id='LC108'><span class="k">def</span> <span class="nf">homography</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ndarray</span> <span class="n">image</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span> <span class="n">H</span><span class="p">,</span> <span class="n">output_shape</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span></div><div class='line' id='LC109'> <span class="n">mode</span><span class="o">=</span><span class="s">'constant'</span><span class="p">,</span> <span class="n">double</span> <span class="n">cval</span><span class="o">=</span><span class="mf">0</span><span class="p">):</span></div><div class='line' id='LC110'> <span class="sd">"""</span></div><div class='line' id='LC111'><span class="sd"> Projective transformation (homography).</span></div><div class='line' id='LC112'><span class="sd"> </span></div><div class='line' id='LC113'><span class="sd"> Perform a projective transformation (homography) of a</span></div><div class='line' id='LC114'><span class="sd"> floating point image, using bi-linear interpolation.</span></div><div class='line' id='LC115'><br/></div><div class='line' id='LC116'><span class="sd"> For each pixel, given its homogeneous coordinate :math:`\mathbf{x}</span></div><div class='line' id='LC117'><span class="sd"> = [x, y, 1]^T`, its target position is calculated by multiplying</span></div><div class='line' id='LC118'><span class="sd"> with the given matrix, :math:`H`, to give :math:`H \mathbf{x}`.</span></div><div class='line' id='LC119'><span class="sd"> E.g., to rotate by theta degrees clockwise, the matrix should be</span></div><div class='line' id='LC120'><br/></div><div class='line' id='LC121'><span class="sd"> ::</span></div><div class='line' id='LC122'><br/></div><div class='line' id='LC123'><span class="sd"> [[cos(theta) -sin(theta) 0]</span></div><div class='line' id='LC124'><span class="sd"> [sin(theta) cos(theta) 0]</span></div><div class='line' id='LC125'><span class="sd"> [0 0 1]]</span></div><div class='line' id='LC126'><br/></div><div class='line' id='LC127'><span class="sd"> or, to translate x by 10 and y by 20,</span></div><div class='line' id='LC128'><br/></div><div class='line' id='LC129'><span class="sd"> ::</span></div><div class='line' id='LC130'><br/></div><div class='line' id='LC131'><span class="sd"> [[1 0 10]</span></div><div class='line' id='LC132'><span class="sd"> [0 1 20]</span></div><div class='line' id='LC133'><span class="sd"> [0 0 1 ]].</span></div><div class='line' id='LC134'><br/></div><div class='line' id='LC135'><span class="sd"> Parameters</span></div><div class='line' id='LC136'><span class="sd"> ----------</span></div><div class='line' id='LC137'><span class="sd"> image : 2-D array</span></div><div class='line' id='LC138'><span class="sd"> Input image.</span></div><div class='line' id='LC139'><span class="sd"> H : array of shape ``(3, 3)``</span></div><div class='line' id='LC140'><span class="sd"> Transformation matrix H that defines the homography.</span></div><div class='line' id='LC141'><span class="sd"> output_shape : tuple (rows, cols)</span></div><div class='line' id='LC142'><span class="sd"> Shape of the output image generated.</span></div><div class='line' id='LC143'><span class="sd"> order : int</span></div><div class='line' id='LC144'><span class="sd"> Order of splines used in interpolation.</span></div><div class='line' id='LC145'><span class="sd"> mode : {'constant', 'mirror', 'wrap'}</span></div><div class='line' id='LC146'><span class="sd"> How to handle values outside the image borders.</span></div><div class='line' id='LC147'><span class="sd"> cval : string</span></div><div class='line' id='LC148'><span class="sd"> Used in conjunction with mode 'C' (constant), the value</span></div><div class='line' id='LC149'><span class="sd"> outside the image boundaries.</span></div><div class='line' id='LC150'><br/></div><div class='line' id='LC151'><span class="sd"> """</span></div><div class='line' id='LC152'><br/></div><div class='line' id='LC153'> <span class="k">cdef</span> <span class="kt">np</span>.<span class="kt">ndarray</span>[<span class="nf">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double_t</span><span class="p">,</span> <span class="n">ndim</span><span class="o">=</span><span class="mf">2</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">"c"</span><span class="p">]</span> <span class="n">img</span> <span class="o">=</span> \</div><div class='line' id='LC154'> <span class="n">np</span><span class="o">.</span><span class="n">ascontiguousarray</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">)</span></div><div class='line' id='LC155'> <span class="k">cdef</span> <span class="kt">np</span>.<span class="kt">ndarray</span>[<span class="nf">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double_t</span><span class="p">,</span> <span class="n">ndim</span><span class="o">=</span><span class="mf">2</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">"c"</span><span class="p">]</span> <span class="n">M</span> <span class="o">=</span> \</div><div class='line' id='LC156'> <span class="n">np</span><span class="o">.</span><span class="n">ascontiguousarray</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">H</span><span class="p">))</span></div><div class='line' id='LC157'><br/></div><div class='line' id='LC158'> <span class="k">if</span> <span class="n">mode</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="s">'constant'</span><span class="p">,</span> <span class="s">'wrap'</span><span class="p">,</span> <span class="s">'mirror'</span><span class="p">):</span></div><div class='line' id='LC159'> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"Invalid mode specified. Please use "</span></div><div class='line' id='LC160'> <span class="s">"`constant`, `wrap` or `mirror`."</span><span class="p">)</span></div><div class='line' id='LC161'> <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s">'constant'</span><span class="p">:</span></div><div class='line' id='LC162'> <span class="n">mode_c</span> <span class="o">=</span> <span class="nb">ord</span><span class="p">(</span><span class="s">'C'</span><span class="p">)</span></div><div class='line' id='LC163'> <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s">'wrap'</span><span class="p">:</span></div><div class='line' id='LC164'> <span class="n">mode_c</span> <span class="o">=</span> <span class="nb">ord</span><span class="p">(</span><span class="s">'W'</span><span class="p">)</span></div><div class='line' id='LC165'> <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s">'mirror'</span><span class="p">:</span></div><div class='line' id='LC166'> <span class="n">mode_c</span> <span class="o">=</span> <span class="nb">ord</span><span class="p">(</span><span class="s">'M'</span><span class="p">)</span></div><div class='line' id='LC167'><br/></div><div class='line' id='LC168'> <span class="k">cdef</span> <span class="kt">int</span> <span class="nf">out_r</span><span class="p">,</span> <span class="nf">out_c</span><span class="p">,</span> <span class="nf">columns</span><span class="p">,</span> <span class="nf">rows</span></div><div class='line' id='LC169'> <span class="k">if</span> <span class="n">output_shape</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span></div><div class='line' id='LC170'> <span class="n">out_r</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span></div><div class='line' id='LC171'> <span class="n">out_c</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span></div><div class='line' id='LC172'> <span class="k">else</span><span class="p">:</span></div><div class='line' id='LC173'> <span class="n">out_r</span> <span class="o">=</span> <span class="n">output_shape</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span></div><div class='line' id='LC174'> <span class="n">out_c</span> <span class="o">=</span> <span class="n">output_shape</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span></div><div class='line' id='LC175'><br/></div><div class='line' id='LC176'> <span class="n">rows</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span></div><div class='line' id='LC177'> <span class="n">columns</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span></div><div class='line' id='LC178'><br/></div><div class='line' id='LC179'> <span class="k">cdef</span> <span class="kt">np</span>.<span class="kt">ndarray</span>[<span class="nf">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double_t</span><span class="p">,</span> <span class="n">ndim</span><span class="o">=</span><span class="mf">2</span><span class="p">]</span> <span class="n">out</span> <span class="o">=</span> \</div><div class='line' id='LC180'> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">out_r</span><span class="p">,</span> <span class="n">out_c</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">)</span></div><div class='line' id='LC181'> </div><div class='line' id='LC182'> <span class="k">cdef</span> <span class="kt">int</span> <span class="nf">tfr</span><span class="p">,</span> <span class="nf">tfc</span><span class="p">,</span> <span class="nf">r_int</span><span class="p">,</span> <span class="nf">c_int</span></div><div class='line' id='LC183'> <span class="k">cdef</span> <span class="kt">double</span> <span class="nf">y0</span><span class="p">,</span> <span class="nf">y1</span><span class="p">,</span> <span class="nf">y2</span><span class="p">,</span> <span class="nf">y3</span></div><div class='line' id='LC184'> <span class="k">cdef</span> <span class="kt">double</span> <span class="nf">r</span><span class="p">,</span> <span class="nf">c</span><span class="p">,</span> <span class="nf">z</span><span class="p">,</span> <span class="nf">t</span><span class="p">,</span> <span class="nf">u</span></div><div class='line' id='LC185'><br/></div><div class='line' id='LC186'> <span class="k">for</span> <span class="n">tfr</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">out_r</span><span class="p">):</span></div><div class='line' id='LC187'> <span class="k">for</span> <span class="n">tfc</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">out_c</span><span class="p">):</span></div><div class='line' id='LC188'> <span class="n">tf</span><span class="p">(</span><span class="n">tfc</span><span class="p">,</span> <span class="n">tfr</span><span class="p">,</span> <span class="o"><</span><span class="n">double</span><span class="o">*></span><span class="n">M</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="o">&</span><span class="n">c</span><span class="p">,</span> <span class="o">&</span><span class="n">r</span><span class="p">)</span></div><div class='line' id='LC189'> <span class="n">r_int</span> <span class="o">=</span> <span class="p"><</span><span class="kt">int</span><span class="p">></span><span class="n">floor</span><span class="p">(</span><span class="n">r</span><span class="p">)</span></div><div class='line' id='LC190'> <span class="n">c_int</span> <span class="o">=</span> <span class="p"><</span><span class="kt">int</span><span class="p">></span><span class="n">floor</span><span class="p">(</span><span class="n">c</span><span class="p">)</span></div><div class='line' id='LC191'><br/></div><div class='line' id='LC192'> <span class="n">t</span> <span class="o">=</span> <span class="n">r</span> <span class="o">-</span> <span class="n">r_int</span></div><div class='line' id='LC193'> <span class="n">u</span> <span class="o">=</span> <span class="n">c</span> <span class="o">-</span> <span class="n">c_int</span></div><div class='line' id='LC194'><br/></div><div class='line' id='LC195'> <span class="n">y0</span> <span class="o">=</span> <span class="n">get_pixel</span><span class="p">(</span><span class="o"><</span><span class="n">double</span><span class="o">*></span><span class="n">img</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">rows</span><span class="p">,</span> <span class="n">columns</span><span class="p">,</span></div><div class='line' id='LC196'> <span class="n">r_int</span><span class="p">,</span> <span class="n">c_int</span><span class="p">,</span> <span class="n">mode_c</span><span class="p">)</span></div><div class='line' id='LC197'> <span class="n">y1</span> <span class="o">=</span> <span class="n">get_pixel</span><span class="p">(</span><span class="o"><</span><span class="n">double</span><span class="o">*></span><span class="n">img</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">rows</span><span class="p">,</span> <span class="n">columns</span><span class="p">,</span></div><div class='line' id='LC198'> <span class="n">r_int</span> <span class="o">+</span> <span class="mf">1</span><span class="p">,</span> <span class="n">c_int</span><span class="p">,</span> <span class="n">mode_c</span><span class="p">)</span></div><div class='line' id='LC199'> <span class="n">y2</span> <span class="o">=</span> <span class="n">get_pixel</span><span class="p">(</span><span class="o"><</span><span class="n">double</span><span class="o">*></span><span class="n">img</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">rows</span><span class="p">,</span> <span class="n">columns</span><span class="p">,</span></div><div class='line' id='LC200'> <span class="n">r_int</span> <span class="o">+</span> <span class="mf">1</span><span class="p">,</span> <span class="n">c_int</span> <span class="o">+</span> <span class="mf">1</span><span class="p">,</span> <span class="n">mode_c</span><span class="p">)</span></div><div class='line' id='LC201'> <span class="n">y3</span> <span class="o">=</span> <span class="n">get_pixel</span><span class="p">(</span><span class="o"><</span><span class="n">double</span><span class="o">*></span><span class="n">img</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">rows</span><span class="p">,</span> <span class="n">columns</span><span class="p">,</span></div><div class='line' id='LC202'> <span class="n">r_int</span><span class="p">,</span> <span class="n">c_int</span> <span class="o">+</span> <span class="mf">1</span><span class="p">,</span> <span class="n">mode_c</span><span class="p">)</span></div><div class='line' id='LC203'><br/></div><div class='line' id='LC204'> <span class="n">out</span><span class="p">[</span><span class="n">tfr</span><span class="p">,</span> <span class="n">tfc</span><span class="p">]</span> <span class="o">=</span> \</div><div class='line' id='LC205'> <span class="p">(</span><span class="mf">1</span> <span class="o">-</span> <span class="n">t</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1</span> <span class="o">-</span> <span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">y0</span> <span class="o">+</span> \</div><div class='line' id='LC206'> <span class="n">t</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1</span> <span class="o">-</span> <span class="n">u</span><span class="p">)</span> <span class="o">*</span> <span class="n">y1</span> <span class="o">+</span> \</div><div class='line' id='LC207'> <span class="n">t</span> <span class="o">*</span> <span class="n">u</span> <span class="o">*</span> <span class="n">y2</span> <span class="o">+</span> <span class="p">(</span><span class="mf">1</span> <span class="o">-</span> <span class="n">t</span><span class="p">)</span> <span class="o">*</span> <span class="n">u</span> <span class="o">*</span> <span class="n">y3</span><span class="p">;</span></div><div class='line' id='LC208'><br/></div><div class='line' id='LC209'> <span class="k">return</span> <span class="n">out</span></div></pre></div>
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<div class="columns threecols">
<div class="column first">
<h3>Site wide shortcuts</h3>
<dl class="keyboard-mappings">
<dt>s</dt>
<dd>Focus site search</dd>
</dl>
<dl class="keyboard-mappings">
<dt>?</dt>
<dd>Bring up this help dialog</dd>
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<h3>Commit list</h3>
<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>c <em>or</em> o <em>or</em> enter</dt>
<dd>Open commit</dd>
</dl>
<dl class="keyboard-mappings">
<dt>y</dt>
<dd>Expand URL to its canonical form</dd>
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<h3>Pull request list</h3>
<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o <em>or</em> enter</dt>
<dd>Open issue</dd>
</dl>
<dl class="keyboard-mappings">
<dt><span class="platform-mac">⌘</span><span class="platform-other">ctrl</span> <em>+</em> enter</dt>
<dd>Submit comment</dd>
</dl>
</div><!-- /.columns.last -->
</div><!-- /.columns.equacols -->
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<h3>Issues</h3>
<div class="columns threecols">
<div class="column first">
<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>x</dt>
<dd>Toggle selection</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o <em>or</em> enter</dt>
<dd>Open issue</dd>
</dl>
<dl class="keyboard-mappings">
<dt><span class="platform-mac">⌘</span><span class="platform-other">ctrl</span> <em>+</em> enter</dt>
<dd>Submit comment</dd>
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<dl class="keyboard-mappings">
<dt>c</dt>
<dd>Create issue</dd>
</dl>
<dl class="keyboard-mappings">
<dt>l</dt>
<dd>Create label</dd>
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<dl class="keyboard-mappings">
<dt>i</dt>
<dd>Back to inbox</dd>
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<dl class="keyboard-mappings">
<dt>u</dt>
<dd>Back to issues</dd>
</dl>
<dl class="keyboard-mappings">
<dt>/</dt>
<dd>Focus issues search</dd>
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<h3>Issues Dashboard</h3>
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<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
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<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o <em>or</em> enter</dt>
<dd>Open issue</dd>
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<h3>Network Graph</h3>
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<dt><span class="badmono">←</span> <em>or</em> h</dt>
<dd>Scroll left</dd>
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<dt><span class="badmono">→</span> <em>or</em> l</dt>
<dd>Scroll right</dd>
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<dt><span class="badmono">↑</span> <em>or</em> k</dt>
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<dt>t</dt>
<dd>Toggle visibility of head labels</dd>
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<dt>shift <span class="badmono">←</span> <em>or</em> shift h</dt>
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<h3>Source Code Browsing</h3>
<dl class="keyboard-mappings">
<dt>t</dt>
<dd>Activates the file finder</dd>
</dl>
<dl class="keyboard-mappings">
<dt>l</dt>
<dd>Jump to line</dd>
</dl>
<dl class="keyboard-mappings">
<dt>w</dt>
<dd>Switch branch/tag</dd>
</dl>
<dl class="keyboard-mappings">
<dt>y</dt>
<dd>Expand URL to its canonical form</dd>
</dl>
</div>
</div>
</div>
<div style='display:none'>
<div class="rule"></div>
<div class="columns threecols">
<div class="column first">
<h3>Browsing Commits</h3>
<dl class="keyboard-mappings">
<dt><span class="platform-mac">⌘</span><span class="platform-other">ctrl</span> <em>+</em> enter</dt>
<dd>Submit comment</dd>
</dl>
<dl class="keyboard-mappings">
<dt>escape</dt>
<dd>Close form</dd>
</dl>
<dl class="keyboard-mappings">
<dt>p</dt>
<dd>Parent commit</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o</dt>
<dd>Other parent commit</dd>
</dl>
</div>
</div>
</div>
</div>
<div id="markdown-help" class="instapaper_ignore readability-extra">
<h2>Markdown Cheat Sheet</h2>
<div class="cheatsheet-content">
<div class="mod">
<div class="col">
<h3>Format Text</h3>
<p>Headers</p>
<pre>
# This is an <h1> tag
## This is an <h2> tag
###### This is an <h6> tag</pre>
<p>Text styles</p>
<pre>
*This text will be italic*
_This will also be italic_
**This text will be bold**
__This will also be bold__
*You **can** combine them*
</pre>
</div>
<div class="col">
<h3>Lists</h3>
<p>Unordered</p>
<pre>
* Item 1
* Item 2
* Item 2a
* Item 2b</pre>
<p>Ordered</p>
<pre>
1. Item 1
2. Item 2
3. Item 3
* Item 3a
* Item 3b</pre>
</div>
<div class="col">
<h3>Miscellaneous</h3>
<p>Images</p>
<pre>
Format: 
</pre>
<p>Links</p>
<pre>
http://github.com - automatic!
[GitHub](http://github.com)</pre>
<p>Blockquotes</p>
<pre>
As Kanye West said:
> We're living the future so
> the present is our past.
</pre>
</div>
</div>
<div class="rule"></div>
<h3>Code Examples in Markdown</h3>
<div class="col">
<p>Syntax highlighting with <a href="http://github.github.com/github-flavored-markdown/" title="GitHub Flavored Markdown" target="_blank">GFM</a></p>
<pre>
```javascript
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
```</pre>
</div>
<div class="col">
<p>Or, indent your code 4 spaces</p>
<pre>
Here is a Python code example