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                <?php  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                declare (strict_types=1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                namespace Np\linAlgb\decompositions;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                use Np\matrix;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                use Np\vector;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                use Np\core\lapack;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * SVD  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * Compute the singular value decomposition of a matrix and   | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * return an object of the singular values and unitary matrices  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * @package Np  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * @category Scientific Library for Php  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * @author ghost (Shubham Chaudhary)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * @email [email protected]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * @copyright (c) 2020-2021, Shubham Chaudhary  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
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                 */  | 
            
            
                                                                        
                            
            
                                    
            
            
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                class svd { | 
            
            
                                                                        
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @param matrix $m  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @return self  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    public static function factory(\Np\matrix $m): self { | 
            
            
                                                                        
                            
            
                                    
            
            
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                        $k = min($m->row, $m->col);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        $ar = $m->copy();  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        $s = vector::factory($k);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        $u = matrix::factory($m->row, $m->row);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        $v = matrix::factory($m->col, $m->col);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        $lp = lapack::gesdd($ar, $s, $u, $v);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        if ($lp != 0) { | 
            
            
                                                                        
                            
            
                                    
            
            
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                            return null;  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        }  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        unset($ar);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        unset($k);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        unset($lp);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return new self($u, $v, $s);  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @param \Np\matrix $u  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @param \Np\matrix $v  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @param \Np\vector $s  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    protected function __construct(protected \Np\matrix $u, protected \Np\matrix $v, protected \Np\vector $s) { | 
            
            
                                                                        
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * Return the U matrix.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @return matrix  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    public function u(): matrix { | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return $this->u;  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * Return the singular values of matrix.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @return vector  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    public function s(): vector { | 
            
            
                                                                        
                            
            
                                    
            
            
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                        return $this->s;  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * Return the V matrix.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @return matrix  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public function v(): matrix { | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
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                        return $this->v;  | 
            
            
                                                                        
                                                                
            
                                    
            
            
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                    }  | 
            
            
                                                                        
                                                                
            
                                    
            
            
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                    /**  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * Return the V transposed matrix.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     *  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     * @return matrix  | 
            
            
                                                                        
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public function vt(): matrix { | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
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                        return $this->v->transpose();  | 
            
            
                                                                        
                                                                
            
                                    
            
            
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                    }  | 
            
            
                                                                        
                                                                
            
                                    
            
            
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                }  | 
            
            
                                                        
            
                                    
            
            
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