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                <?php  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                namespace Np\core;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * OpenBlas  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * php interface for OpenBLAS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * @package Np  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                 * @category Scientific Computing  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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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 blas { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    const CblasLeft = 141, CblasRight = 142;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    const CblasUpper = 121, CblasLower = 122;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    const CblasNonUnit = 131, CblasUnit = 132;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    const CblasRowMajor = 101, CblasColMajor = 102;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    const CblasNoTrans = 111, CblasTrans = 112, CblasConjTrans = 113;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static $ffi_blas = null;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function init() { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        if (is_null(self::$ffi_blas)) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            self::$ffi_blas = \FFI::scope('blas'); | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas;  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function setNumThreads(int $num_threads) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::$ffi_blas->openblas_set_num_threads($num_threads);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function getNumThreads(): int { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->openblas_get_num_threads();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function getNumPorcs(): int { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->openblas_get_num_procs();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function getConfig() { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->openblas_get_config();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function getCoreName() { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->openblas_get_corename();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function getNumParallel(): int { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->openblas_get_parallel();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * Product of general matrix and general matrix  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *    C := alpha * AB + beta * C  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @dtype Float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $mr  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @return \FFI\CData  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function gemm(\Np\matrix $m1, \Np\matrix $m2, \Np\matrix $mr, int $trans1 = self::CblasNoTrans, int $trans2 = self::CblasNoTrans) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->cblas_dgemm(self::CblasRowMajor, $trans1, $trans2, $m1->row, $m2->col, $m1->col, 1.0, $m1->data, $m1->col, $m2->data, $m2->col, 0.0, $mr->data, $mr->col);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *  Product of symmetric matrix and general matrix  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *    C := alpha * AB + beta * C  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *            or  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *    C := alpha * BA + beta * C  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $mr  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function symm(\Np\matrix $m1, \Np\matrix $m2, \Np\matrix $mr) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->cblas_dsymm(self::CblasRowMajor, self::CblasLeft, self::CblasUpper, $m1->row,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                        $m2->col, 1.0, $m1->data, $m1->row, $m2->data, $m2->row, 0.0, $mr->data, $mr->row);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * Update rank n of symmetric matrix  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *    C := alpha * A A^T + beta * C  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *            or  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *    C := alpha * A^T A + beta * C  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function syrk(\Np\matrix $m1, \Np\matrix $m2) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->cblas_dsyrk(self::CblasRowMajor, self::CblasUpper,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                        self::CblasNoTrans, $m1->row, $m2->col, 1.0, $m1->data, $m1->row, 0.0, $m2->data, $m2->row);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * Update rank 2k of symmetric matrix  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *    C := alpha * A B^T + alpha B A^T + beta * C  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *            or  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *    C := alpha * B^T A + alpha A^T B + beta * C  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $mr  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    public static function syr2k(\Np\matrix $m1, \Np\matrix $m2, \Np\matrix $mr) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return self::$ffi_blas->cblas_dsyr2k(self::CblasRowMajor, self::CblasLower, self::CblasNoTrans,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                                        $m1->col, $m2->row, 1.0, $m1->data, $m1->row, $m2->data, $m2->row, 0.0, $mr->data, $mr->row);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @static  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @dtype Double  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\matrix $m  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     * @param \Np\vector $v  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    129
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                                                     | 
                
                 | 
                     * @param \Np\vector $mvr  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    130
                 | 
                                    
                                                     | 
                
                 | 
                     * @return \FFI\CData  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    131
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    132
                 | 
                                    
                                                     | 
                
                 | 
                    public static function gemv(\Np\matrix $m, \Np\vector $v, \Np\vector $mvr) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    133
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    134
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dgemv(self::CblasRowMajor, self::CblasNoTrans, $m->row, $m->col,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    135
                 | 
                                    
                                                     | 
                
                 | 
                                        1.0, $m->data, $m->row, $v->data, 1, 1.0, $mvr->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    136
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    137
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    138
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    139
                 | 
                                    
                                                     | 
                
                 | 
                     * Compute the product of a general matrix and a vector stored in band format.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    140
                 | 
                                    
                                                     | 
                
                 | 
                     *    y := alpha * Ax + beta * y  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                     * @param int $KL   Number of elements in the lower left part  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
                     * @param int $KU   Number of elements in the upper right part  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    143
                 | 
                                    
                                                     | 
                
                 | 
                     * @param double $alpha  Coefficient of scalar multiple of vector  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                     * @param double $beta   Coefficient of scalar multiple of  mvr  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    145
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\matrix $matrix  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $vector  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $mvr  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                    public static function gbmv(int $KL, int $KU, float $alpha, float $beta, \Np\matrix $matrix, \Np\vector $vector, \Np\vector $mvr) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dgbmv(self::CblasRowMajor,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    152
                 | 
                                    
                                                     | 
                
                 | 
                                        self::CblasNoTrans, $matrix->row, $matrix->col,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                                        $KL, $KU, $alpha,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
                                                     | 
                
                 | 
                                        $matrix->data, $matrix->row, $vector->data,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                                        1, $beta, $mvr->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                     * Compute the product of a column vector and a row vector. (Real number)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                     *    A := alpha * x y^t + A  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\matrix $m  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                     * @return void  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                    public static function ger(\Np\vector $v1, \Np\vector $v2, \Np\matrix $m) { | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dger(self::CblasRowMajor, $v1->col, $v2->col,  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                                        1.0, $v1->data, 1, $v2->data, 1, $m->data, $m->row);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                     * @static  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                     * @dtype Double  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    177
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    178
                 | 
                                    
                                                     | 
                
                 | 
                    public static function dot(\Np\vector $v1, \Np\vector $v2) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    180
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_ddot($v1->col, $v1->data, 1, $v2->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    181
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    182
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    183
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    184
                 | 
                                    
                                                     | 
                
                 | 
                     * Calculates the index of the element with the largest absolute value in the vector.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    185
                 | 
                                    
                                                     | 
                
                 | 
                     *  Note that this subscript starts from 1. If 0 is returned, n is invalid.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    186
                 | 
                                    
                                                     | 
                
                 | 
                     *    ret := arg max |X(i)|  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    187
                 | 
                                    
                                                     | 
                
                 | 
                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    188
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param \Np\vector $v  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    189
                 | 
                                    
                                                     | 
                
                 | 
                     * @return int index of the element(Note that start from 0 according to cblas)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    190
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    191
                 | 
                                    
                                                     | 
                
                 | 
                    public static function max(\Np\vector $v) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    192
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    193
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_idamax($v->col, $v->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    194
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    195
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    196
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    197
                 | 
                                    
                                                     | 
                
                 | 
                     *  Calculates the index of the element with the smallest absolute value in the vector.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    198
                 | 
                                    
                                                     | 
                
                 | 
                     *  Note that this subscript starts from 1. If 0 is returned, n is invalid.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    199
                 | 
                                    
                                                     | 
                
                 | 
                     *   ret := arg min |X(i)|  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    200
                 | 
                                    
                                                     | 
                
                 | 
                     *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    201
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    202
                 | 
                                    
                                                     | 
                
                 | 
                     * @return int  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    203
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    204
                 | 
                                    
                                                     | 
                
                 | 
                    public static function min(\Np\vector $v) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    205
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    206
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_idamin($v->col, $v->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    207
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    208
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    209
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    210
                 | 
                                    
                                                     | 
                
                 | 
                     * Exchange the contents of the vector.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    211
                 | 
                                    
                                                     | 
                
                 | 
                     *    X := Y  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    212
                 | 
                                    
                                                     | 
                
                 | 
                     *    Y := X  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    213
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    214
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    215
                 | 
                                    
                                                     | 
                
                 | 
                     * @param int $inv1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    216
                 | 
                                    
                                                     | 
                
                 | 
                     * @param int $inv2  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    217
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    218
                 | 
                                    
                                                     | 
                
                 | 
                    public static function swap(\Np\vector $v1, \Np\vector $v2, int $inv1 = 1, int $inv2 = 1) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    219
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    220
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dswap($v1->col, $v1->data, $inv1, $v2->data, $inv2);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    221
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    222
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    223
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    224
                 | 
                                    
                                                     | 
                
                 | 
                     *  Copy the vector from X to Y.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    225
                 | 
                                    
                                                     | 
                
                 | 
                     *    Y := X  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    226
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param \Np\vector $vect_X        Vector X buffer  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    227
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param \Np\vector $vect_Y        Vector Y buffer  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    228
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param int $invX  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    229
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param int $invY   | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    230
                 | 
                                    
                                                     | 
                
                 | 
                     *  @return void  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    231
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    232
                 | 
                                    
                                                     | 
                
                 | 
                    public static function copy(\Np\vector $vect_X, \Np\vector $vect_Y, int $invX = 1, int $invY = 1) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    233
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    234
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dcopy($vect_X->col, $vect_X->data, $invX,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    235
                 | 
                                    
                                                     | 
                
                 | 
                                        $vect_Y->data, $invY);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    236
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    237
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    238
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    239
                 | 
                                    
                                                     | 
                
                 | 
                     * Compute the Euclidean norm of a vector.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    240
                 | 
                                    
                                                     | 
                
                 | 
                     *    ret := ||X||  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    241
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    242
                 | 
                                    
                                                     | 
                
                 | 
                     * @return float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    243
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    244
                 | 
                                    
                                                     | 
                
                 | 
                    public static function nrm2(\Np\vector $v): float { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    245
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    246
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dnrme($v->col, $v->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    247
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    248
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    249
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    250
                 | 
                                    
                                                     | 
                
                 | 
                     *  Add vectors  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    251
                 | 
                                    
                                                     | 
                
                 | 
                     *    Y := alpha * X + Y  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    252
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param float $alpha     Coefficient of scalar multiple of X vector  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    253
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param \Np\vector $vect_X        Vector X buffer  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    254
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param \Np\vector $vect_Y        Vector Y buffer  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    255
                 | 
                                    
                                                     | 
                
                 | 
                     *  @return void  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    256
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    257
                 | 
                                    
                                                     | 
                
                 | 
                    public static function axpy(float $alpha, \Np\vector $vect_X, \Np\vector $vect_Y) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    258
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    259
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_daxpy($vect_X->col, $alpha, $vect_X->data,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    260
                 | 
                                    
                                                     | 
                
                 | 
                                        1, $vect_Y->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    261
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    262
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    263
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    264
                 | 
                                    
                                                     | 
                
                 | 
                     *  Calculates the sum of the absolute values of each component of the vector.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    265
                 | 
                                    
                                                     | 
                
                 | 
                     *    ret := |x_1| + ... + |x_n|  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    266
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param \Np\vector $v        Vector X buffer  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    267
                 | 
                                    
                                                     | 
                
                 | 
                     *  @return float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    268
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    269
                 | 
                                    
                                                     | 
                
                 | 
                    public static function asum(\Np\vector $v): float { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    270
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    271
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dasum($v->col, $v->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    272
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    273
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    274
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    275
                 | 
                                    
                                                     | 
                
                 | 
                     * Rotate about a given point.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    276
                 | 
                                    
                                                     | 
                
                 | 
                     *    X(i) := c * X(i) + s * Y(i)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    277
                 | 
                                    
                                                     | 
                
                 | 
                     *    Y(i) :=-s * X(i) + c * Y(i)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    278
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v1 Vector X buffer  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    279
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector $v2 Vector Y buffer  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    280
                 | 
                                    
                                                     | 
                
                 | 
                     * @param float $c         value of cos A(Value obtained with rotg function.)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    281
                 | 
                                    
                                                     | 
                
                 | 
                     * @param float $s         value of sin A(Value obtained with rotg function.)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    282
                 | 
                                    
                                                     | 
                
                 | 
                     *   | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    283
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    284
                 | 
                                    
                                                     | 
                
                 | 
                    public static function rotate(\Np\vector $v1, \Np\vector $v2, float $c, float $s) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    285
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    286
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_drot($v1->col, $v1->data, 1, $v2->data, 1, $c, $s);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    287
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    288
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    289
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    290
                 | 
                                    
                                                     | 
                
                 | 
                     *  Give the point P (a, b).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    291
                 | 
                                    
                                                     | 
                
                 | 
                     *  Rotate this point to givens and calculate the parameters a, b, c,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    292
                 | 
                                    
                                                     | 
                
                 | 
                     *  and s to make the y coordinate zero.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    293
                 | 
                                    
                                                     | 
                
                 | 
                     *    Conditions description:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    294
                 | 
                                    
                                                     | 
                
                 | 
                     *       c * a + s * b = r  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    295
                 | 
                                    
                                                     | 
                
                 | 
                     *       -s * a + c * b = 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    296
                 | 
                                    
                                                     | 
                
                 | 
                     *       r = ||(a,b)||  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    297
                 | 
                                    
                                                     | 
                
                 | 
                     *       c^2 + s^2 = 1  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    298
                 | 
                                    
                                                     | 
                
                 | 
                     *       z=s if |a| > |b|  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    299
                 | 
                                    
                                                     | 
                
                 | 
                     *       z=1/c if |a| <= |b| and c != 0 and r != 0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    300
                 | 
                                    
                                                     | 
                
                 | 
                     *    Find r, z, c, s that satisfies the above description.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    301
                 | 
                                    
                                                     | 
                
                 | 
                     *    However, when r = 0, z = 0, c = 1, and s = 0 are returned.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    302
                 | 
                                    
                                                     | 
                
                 | 
                     *    Also, if c = 0, | a | <= | b | and c! = 0 and r! = 0, z = 1 is returned.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    303
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param float $a     X-coordinate of P: The calculated r value is stored and returned  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    304
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param float $b     Y-coordinate of P: The calculated z value is stored and returned  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    305
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param float $c     Stores the calculated value of c  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    306
                 | 
                                    
                                                     | 
                
                 | 
                     *  @param float $s     Stores the calculated value of s  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    307
                 | 
                                    
                                                     | 
                
                 | 
                     *  @return void  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    308
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    309
                 | 
                                    
                                                     | 
                
                 | 
                    public static function rotg(float $a, float $b, float $c, float $s) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    310
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    311
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_drotg($a, $b, $c, $s);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    312
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    313
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    314
                 | 
                                    
                                                     | 
                
                 | 
                    /**  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    315
                 | 
                                    
                                                     | 
                
                 | 
                     * Multiply vector by scalar.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    316
                 | 
                                    
                                                     | 
                
                 | 
                     *  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    317
                 | 
                                    
                                                     | 
                
                 | 
                     * @param float $alpha Coefficient of scalar multiple of V vector  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    318
                 | 
                                    
                                                     | 
                
                 | 
                     * @param \Np\vector|\Np\matrix $v  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    319
                 | 
                                    
                                                     | 
                
                 | 
                     * @return \FFI\CData  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    320
                 | 
                                    
                                                     | 
                
                 | 
                     */  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    321
                 | 
                                    
                                                     | 
                
                 | 
                    public static function scale(float $alpha, \Np\vector|\Np\matrix $v) { | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    322
                 | 
                                    
                                                     | 
                
                 | 
                        self::init();  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    323
                 | 
                                    
                                                     | 
                
                 | 
                        return self::$ffi_blas->cblas_dscal($v->ndim, $alpha, $v->data, 1);  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    324
                 | 
                                    
                                                     | 
                
                 | 
                    }  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    325
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    326
                 | 
                                    
                                                     | 
                
                 | 
                }  | 
            
            
                                                        
            
                                    
            
            
                | 
                    327
                 | 
                                    
                                                     | 
                
                 | 
                 |