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<!DOCTYPE html>
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<title>arrayfire.lapack — ArrayFire Python documentation</title>
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<h1>Source code for arrayfire.lapack</h1><div class="highlight"><pre>
<span></span><span class="c1">#######################################################</span>
<span class="c1"># Copyright (c) 2015, ArrayFire</span>
<span class="c1"># All rights reserved.</span>
<span class="c1">#</span>
<span class="c1"># This file is distributed under 3-clause BSD license.</span>
<span class="c1"># The complete license agreement can be obtained at:</span>
<span class="c1"># http://arrayfire.com/licenses/BSD-3-Clause</span>
<span class="c1">########################################################</span>
<span class="sd">"""</span>
<span class="sd">Dense Linear Algebra functions (solve, inverse, etc).</span>
<span class="sd">"""</span>
<span class="kn">from</span> <span class="nn">.library</span> <span class="kn">import</span> <span class="o">*</span>
<span class="kn">from</span> <span class="nn">.array</span> <span class="kn">import</span> <span class="o">*</span>
<div class="viewcode-block" id="lu"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.lu">[docs]</a><span class="k">def</span> <span class="nf">lu</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> LU decomposition.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> A 2 dimensional arrayfire array.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (L,U,P): tuple of af.Arrays</span>
<span class="sd"> - L - Lower triangular matrix.</span>
<span class="sd"> - U - Upper triangular matrix.</span>
<span class="sd"> - P - Permutation array.</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> The original matrix `A` can be reconstructed using the outputs in the following manner.</span>
<span class="sd"> >>> A[P, :] = af.matmul(L, U)</span>
<span class="sd"> """</span>
<span class="n">L</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">P</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_lu</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">L</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">U</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">))</span>
<span class="k">return</span> <span class="n">L</span><span class="p">,</span><span class="n">U</span><span class="p">,</span><span class="n">P</span></div>
<div class="viewcode-block" id="lu_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.lu_inplace">[docs]</a><span class="k">def</span> <span class="nf">lu_inplace</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">pivot</span><span class="o">=</span><span class="s2">"lapack"</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> In place LU decomposition.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - a 2 dimensional arrayfire array on entry.</span>
<span class="sd"> - Contains L in the lower triangle on exit.</span>
<span class="sd"> - Contains U in the upper triangle on exit.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> P: af.Array</span>
<span class="sd"> - Permutation array.</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> This function is primarily used with `af.solve_lu` to reduce computations.</span>
<span class="sd"> """</span>
<span class="n">P</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">is_pivot_lapack</span> <span class="o">=</span> <span class="kc">False</span> <span class="k">if</span> <span class="p">(</span><span class="n">pivot</span> <span class="o">==</span> <span class="s2">"full"</span><span class="p">)</span> <span class="k">else</span> <span class="kc">True</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_lu_inplace</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">is_pivot_lapack</span><span class="p">))</span>
<span class="k">return</span> <span class="n">P</span></div>
<div class="viewcode-block" id="qr"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.qr">[docs]</a><span class="k">def</span> <span class="nf">qr</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> QR decomposition.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> A 2 dimensional arrayfire array.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (Q,R,T): tuple of af.Arrays</span>
<span class="sd"> - Q - Orthogonal matrix.</span>
<span class="sd"> - R - Upper triangular matrix.</span>
<span class="sd"> - T - Vector containing additional information to solve a least squares problem.</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> The outputs of this funciton have the following properties.</span>
<span class="sd"> >>> A = af.matmul(Q, R)</span>
<span class="sd"> >>> I = af.matmulNT(Q, Q) # Identity matrix</span>
<span class="sd"> """</span>
<span class="n">Q</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">R</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">T</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_qr</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">Q</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">R</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">T</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">))</span>
<span class="k">return</span> <span class="n">Q</span><span class="p">,</span><span class="n">R</span><span class="p">,</span><span class="n">T</span></div>
<div class="viewcode-block" id="qr_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.qr_inplace">[docs]</a><span class="k">def</span> <span class="nf">qr_inplace</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> In place QR decomposition.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - a 2 dimensional arrayfire array on entry.</span>
<span class="sd"> - Packed Q and R matrices on exit.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> T: af.Array</span>
<span class="sd"> - Vector containing additional information to solve a least squares problem.</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> This function is used to save space only when `R` is required.</span>
<span class="sd"> """</span>
<span class="n">T</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_qr_inplace</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">T</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">))</span>
<span class="k">return</span> <span class="n">T</span></div>
<div class="viewcode-block" id="cholesky"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.cholesky">[docs]</a><span class="k">def</span> <span class="nf">cholesky</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">is_upper</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Cholesky decomposition</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> A 2 dimensional, symmetric, positive definite matrix.</span>
<span class="sd"> is_upper: optional: bool. default: True</span>
<span class="sd"> Specifies if output `R` is upper triangular (if True) or lower triangular (if False).</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (R,info): tuple of af.Array, int.</span>
<span class="sd"> - R - triangular matrix.</span>
<span class="sd"> - info - 0 if decomposition sucessful.</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> The original matrix `A` can be reconstructed using the outputs in the following manner.</span>
<span class="sd"> >>> A = af.matmulNT(R, R) #if R is upper triangular</span>
<span class="sd"> """</span>
<span class="n">R</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">info</span> <span class="o">=</span> <span class="n">c_int_t</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_cholesky</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">R</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">info</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">is_upper</span><span class="p">))</span>
<span class="k">return</span> <span class="n">R</span><span class="p">,</span> <span class="n">info</span><span class="o">.</span><span class="n">value</span></div>
<div class="viewcode-block" id="cholesky_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.cholesky_inplace">[docs]</a><span class="k">def</span> <span class="nf">cholesky_inplace</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">is_upper</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> In place Cholesky decomposition.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - a 2 dimensional, symmetric, positive definite matrix.</span>
<span class="sd"> - Trinangular matrix on exit.</span>
<span class="sd"> is_upper: optional: bool. default: True.</span>
<span class="sd"> Specifies if output `R` is upper triangular (if True) or lower triangular (if False).</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> info : int.</span>
<span class="sd"> 0 if decomposition sucessful.</span>
<span class="sd"> """</span>
<span class="n">info</span> <span class="o">=</span> <span class="n">c_int_t</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_cholesky_inplace</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">info</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">is_upper</span><span class="p">))</span>
<span class="k">return</span> <span class="n">info</span><span class="o">.</span><span class="n">value</span></div>
<div class="viewcode-block" id="solve"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.solve">[docs]</a><span class="k">def</span> <span class="nf">solve</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">options</span><span class="o">=</span><span class="n">MATPROP</span><span class="o">.</span><span class="n">NONE</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Solve a system of linear equations.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> A 2 dimensional arrayfire array representing the coefficients of the system.</span>
<span class="sd"> B: af.Array</span>
<span class="sd"> A 1 or 2 dimensional arrayfire array representing the constants of the system.</span>
<span class="sd"> options: optional: af.MATPROP. default: af.MATPROP.NONE.</span>
<span class="sd"> - Additional options to speed up computations.</span>
<span class="sd"> - Currently needs to be one of `af.MATPROP.NONE`, `af.MATPROP.LOWER`, `af.MATPROP.UPPER`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> X: af.Array</span>
<span class="sd"> A 1 or 2 dimensional arrayfire array representing the unknowns in the system.</span>
<span class="sd"> """</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_solve</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">B</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">options</span><span class="o">.</span><span class="n">value</span><span class="p">))</span>
<span class="k">return</span> <span class="n">X</span></div>
<div class="viewcode-block" id="solve_lu"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.solve_lu">[docs]</a><span class="k">def</span> <span class="nf">solve_lu</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">options</span><span class="o">=</span><span class="n">MATPROP</span><span class="o">.</span><span class="n">NONE</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Solve a system of linear equations, using LU decomposition.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - A 2 dimensional arrayfire array representing the coefficients of the system.</span>
<span class="sd"> - This matrix should be decomposed previously using `lu_inplace(A)`.</span>
<span class="sd"> P: af.Array</span>
<span class="sd"> - Permutation array.</span>
<span class="sd"> - This array is the output of an earlier call to `lu_inplace(A)`</span>
<span class="sd"> B: af.Array</span>
<span class="sd"> A 1 or 2 dimensional arrayfire array representing the constants of the system.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> X: af.Array</span>
<span class="sd"> A 1 or 2 dimensional arrayfire array representing the unknowns in the system.</span>
<span class="sd"> """</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_solve_lu</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">P</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">B</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">options</span><span class="o">.</span><span class="n">value</span><span class="p">))</span>
<span class="k">return</span> <span class="n">X</span></div>
<div class="viewcode-block" id="inverse"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.inverse">[docs]</a><span class="k">def</span> <span class="nf">inverse</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">options</span><span class="o">=</span><span class="n">MATPROP</span><span class="o">.</span><span class="n">NONE</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Invert a matrix.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - A 2 dimensional arrayfire array</span>
<span class="sd"> options: optional: af.MATPROP. default: af.MATPROP.NONE.</span>
<span class="sd"> - Additional options to speed up computations.</span>
<span class="sd"> - Currently needs to be one of `af.MATPROP.NONE`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> AI: af.Array</span>
<span class="sd"> - A 2 dimensional array that is the inverse of `A`</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> `A` needs to be a square matrix.</span>
<span class="sd"> """</span>
<span class="n">AI</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_inverse</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">AI</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">options</span><span class="o">.</span><span class="n">value</span><span class="p">))</span>
<span class="k">return</span> <span class="n">AI</span></div>
<div class="viewcode-block" id="pinverse"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.pinverse">[docs]</a><span class="k">def</span> <span class="nf">pinverse</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1E-6</span><span class="p">,</span> <span class="n">options</span><span class="o">=</span><span class="n">MATPROP</span><span class="o">.</span><span class="n">NONE</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Find pseudo-inverse(Moore-Penrose) of a matrix.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - A 2 dimensional arrayfire input matrix array</span>
<span class="sd"> tol: optional: scalar. default: 1E-6.</span>
<span class="sd"> - Tolerance for calculating rank</span>
<span class="sd"> options: optional: af.MATPROP. default: af.MATPROP.NONE.</span>
<span class="sd"> - Currently needs to be `af.MATPROP.NONE`.</span>
<span class="sd"> - Additional options may speed up computation in the future</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> AI: af.Array</span>
<span class="sd"> - A 2 dimensional array that is the pseudo-inverse of `A`</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> This function is not supported in GFOR</span>
<span class="sd"> """</span>
<span class="n">AI</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_pinverse</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">AI</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">c_double_t</span><span class="p">(</span><span class="n">tol</span><span class="p">),</span> <span class="n">options</span><span class="o">.</span><span class="n">value</span><span class="p">))</span>
<span class="k">return</span> <span class="n">AI</span></div>
<div class="viewcode-block" id="rank"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.rank">[docs]</a><span class="k">def</span> <span class="nf">rank</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1E-5</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Rank of a matrix.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - A 2 dimensional arrayfire array</span>
<span class="sd"> tol: optional: scalar. default: 1E-5.</span>
<span class="sd"> - Tolerance for calculating rank</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> r: int</span>
<span class="sd"> - Rank of `A` within the given tolerance</span>
<span class="sd"> """</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">c_uint_t</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_rank</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">r</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">c_double_t</span><span class="p">(</span><span class="n">tol</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">r</span><span class="o">.</span><span class="n">value</span></div>
<div class="viewcode-block" id="det"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.det">[docs]</a><span class="k">def</span> <span class="nf">det</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Determinant of a matrix.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - A 2 dimensional arrayfire array</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> res: scalar</span>
<span class="sd"> - Determinant of the matrix.</span>
<span class="sd"> """</span>
<span class="n">re</span> <span class="o">=</span> <span class="n">c_double_t</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">im</span> <span class="o">=</span> <span class="n">c_double_t</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_det</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">re</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">im</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">))</span>
<span class="n">re</span> <span class="o">=</span> <span class="n">re</span><span class="o">.</span><span class="n">value</span>
<span class="n">im</span> <span class="o">=</span> <span class="n">im</span><span class="o">.</span><span class="n">value</span>
<span class="k">return</span> <span class="n">re</span> <span class="k">if</span> <span class="p">(</span><span class="n">im</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span> <span class="k">else</span> <span class="n">re</span> <span class="o">+</span> <span class="n">im</span> <span class="o">*</span> <span class="mi">1</span><span class="n">j</span></div>
<div class="viewcode-block" id="norm"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.norm">[docs]</a><span class="k">def</span> <span class="nf">norm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">norm_type</span><span class="o">=</span><span class="n">NORM</span><span class="o">.</span><span class="n">EUCLID</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">q</span><span class="o">=</span><span class="mf">1.0</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Norm of an array or a matrix.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> - A 1 or 2 dimensional arrayfire array</span>
<span class="sd"> norm_type: optional: af.NORM. default: af.NORM.EUCLID.</span>
<span class="sd"> - Type of norm to be calculated.</span>
<span class="sd"> p: scalar. default 1.0.</span>
<span class="sd"> - Used only if `norm_type` is one of `af.NORM.VECTOR_P`, `af.NORM_MATRIX_L_PQ`</span>
<span class="sd"> q: scalar. default 1.0.</span>
<span class="sd"> - Used only if `norm_type` is `af.NORM_MATRIX_L_PQ`</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> res: scalar</span>
<span class="sd"> - norm of the input</span>
<span class="sd"> """</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">c_double_t</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_norm</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">res</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">,</span> <span class="n">norm_type</span><span class="o">.</span><span class="n">value</span><span class="p">,</span>
<span class="n">c_double_t</span><span class="p">(</span><span class="n">p</span><span class="p">),</span> <span class="n">c_double_t</span><span class="p">(</span><span class="n">q</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">res</span><span class="o">.</span><span class="n">value</span></div>
<div class="viewcode-block" id="svd"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.svd">[docs]</a><span class="k">def</span> <span class="nf">svd</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Singular Value Decomposition</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> A 2 dimensional arrayfire array.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (U,S,Vt): tuple of af.Arrays</span>
<span class="sd"> - U - A unitary matrix</span>
<span class="sd"> - S - An array containing the elements of diagonal matrix</span>
<span class="sd"> - Vt - A unitary matrix</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> - The original matrix `A` is preserved and additional storage space is required for decomposition.</span>
<span class="sd"> - If the original matrix `A` need not be preserved, use `svd_inplace` instead.</span>
<span class="sd"> - The original matrix `A` can be reconstructed using the outputs in the following manner.</span>
<span class="sd"> >>> Smat = af.diag(S, 0, False)</span>
<span class="sd"> >>> A_recon = af.matmul(af.matmul(U, Smat), Vt)</span>
<span class="sd"> """</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">S</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">Vt</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_svd</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">U</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">S</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">Vt</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">))</span>
<span class="k">return</span> <span class="n">U</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">Vt</span></div>
<div class="viewcode-block" id="svd_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.svd_inplace">[docs]</a><span class="k">def</span> <span class="nf">svd_inplace</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Singular Value Decomposition</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> A: af.Array</span>
<span class="sd"> A 2 dimensional arrayfire array.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (U,S,Vt): tuple of af.Arrays</span>
<span class="sd"> - U - A unitary matrix</span>
<span class="sd"> - S - An array containing the elements of diagonal matrix</span>
<span class="sd"> - Vt - A unitary matrix</span>
<span class="sd"> Note</span>
<span class="sd"> ----</span>
<span class="sd"> - The original matrix `A` is not preserved.</span>
<span class="sd"> - If the original matrix `A` needs to be preserved, use `svd` instead.</span>
<span class="sd"> - The original matrix `A` can be reconstructed using the outputs in the following manner.</span>
<span class="sd"> >>> Smat = af.diag(S, 0, False)</span>
<span class="sd"> >>> A_recon = af.matmul(af.matmul(U, Smat), Vt)</span>
<span class="sd"> """</span>
<span class="n">U</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">S</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">Vt</span> <span class="o">=</span> <span class="n">Array</span><span class="p">()</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_svd_inplace</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">U</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">S</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span> <span class="n">c_pointer</span><span class="p">(</span><span class="n">Vt</span><span class="o">.</span><span class="n">arr</span><span class="p">),</span>
<span class="n">A</span><span class="o">.</span><span class="n">arr</span><span class="p">))</span>
<span class="k">return</span> <span class="n">U</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">Vt</span></div>
<div class="viewcode-block" id="is_lapack_available"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.is_lapack_available">[docs]</a><span class="k">def</span> <span class="nf">is_lapack_available</span><span class="p">():</span>
<span class="sd">"""</span>
<span class="sd"> Function to check if the arrayfire library was built with lapack support.</span>
<span class="sd"> """</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">c_bool_t</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">safe_call</span><span class="p">(</span><span class="n">backend</span><span class="o">.</span><span class="n">get</span><span class="p">()</span><span class="o">.</span><span class="n">af_is_lapack_available</span><span class="p">(</span><span class="n">c_pointer</span><span class="p">(</span><span class="n">res</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">res</span><span class="o">.</span><span class="n">value</span></div>
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