/**
* Solves a linear system
*
* @param NumArray $squareMatrix matrix of size n*n
* @param NumArray $numArray vector of size n or matrix of size n*m
*
* @throws \NumPHP\LinAlg\Exception\SingularMatrixException will be thrown, if
* `$squareMatrix` is singular
* @throws \NumPHP\LinAlg\Exception\InvalidArgumentException will be thrown, if
* linear system of `$squareMatrix` and `$numArray` can not be solved
*
* @return NumArray
*
* @since 1.0.0
*/
public static function solve(NumArray $squareMatrix, NumArray $numArray)
{
if (!Helper::isNotSingularMatrix($squareMatrix)) {
throw new SingularMatrixException(sprintf("First Argument has to be a not singular square matrix"));
}
if (!Helper::isVector($numArray) && !Helper::isMatrix($numArray)) {
throw new InvalidArgumentException(sprintf("Second argument has to be a vector or a matrix, NumArray with dimension %d given", $numArray->getNDim()));
}
$shape1 = $squareMatrix->getShape();
$shape2 = $numArray->getShape();
if ($shape1[0] !== $shape2[0]) {
throw new InvalidArgumentException(sprintf("Can not solve a linear system with matrix (%s) and matrix (%s)", implode(', ', $shape1), implode(', ', $shape2)));
}
/**
* The result of LinAlg::lud is a array with three NumArrays
*
* @var NumArray $pMatrix
* @var NumArray $lMatrix
* @var NumArray $uMatrix
*/
list($pMatrix, $lMatrix, $uMatrix) = LinAlg::lud($squareMatrix);
$yNumArray = self::forwardSubstitution($lMatrix, $pMatrix->getTranspose()->dot($numArray));
$zNumArray = self::backSubstitution($uMatrix, $yNumArray);
return $zNumArray;
}
/**
* @param InputInterface $input
* @param OutputInterface $output
*
* @SuppressWarnings(PHPMD.UnusedFormalParameter)
*/
protected function execute(InputInterface $input, OutputInterface $output)
{
$matrixA = new NumArray([[49, -525, 7, -315], [-525, 6921, -3279, 3483], [7, -3279, 8178, -328], [-315, 3483, -328, 624556]]);
$output->writeln('<comment>Matrix A:</comment>');
$output->writeln($matrixA->__toString());
$output->writeln('<info>Cholesky:</info>');
$time = microtime(true);
$matrixL = LinAlg::cholesky($matrixA);
$timeDiff = microtime(true) - $time;
$output->writeln($matrixL->__toString());
$output->writeln('<info>Time for calculation: ' . $timeDiff . ' sec</info>');
}
/**
* @param InputInterface $input
* @param OutputInterface $output
*
* @SuppressWarnings(PHPMD.UnusedFormalParameter)
*/
protected function execute(InputInterface $input, OutputInterface $output)
{
$matrix = new NumArray([[-3, 4, 7 / 6], [2, 0.1, 0], [23, -5, 8]]);
$output->writeln('<comment>Matrix:</comment>');
$output->writeln($matrix->__toString());
$output->writeln('<info>Inverse:</info>');
$time = microtime(true);
$inv = LinAlg::inv($matrix);
$timeDiff = microtime(true) - $time;
$output->writeln($inv->__toString());
$output->writeln('<info>Time for calculation: ' . $timeDiff . ' sec</info>');
}
/**
* @param InputInterface $input
* @param OutputInterface $output
*
* @SuppressWarnings(PHPMD.UnusedFormalParameter)
*/
protected function execute(InputInterface $input, OutputInterface $output)
{
$matrixA = new NumArray([[1, 6, 1], [2, 3, 2], [4, 2, 1]]);
$output->writeln('<comment>Matrix A:</comment>');
$output->writeln($matrixA->__toString());
$output->writeln('<info>LU decomposition</info>');
$time = microtime(true);
list($matrixP, $matrixL, $matrixU) = LinAlg::lud($matrixA);
$timeDiff = microtime(true) - $time;
$output->writeln('<comment>Matrix P:</comment>');
$output->writeln($matrixP->__toString());
$output->writeln('<comment>Matrix L:</comment>');
$output->writeln($matrixL->__toString());
$output->writeln('<comment>Matrix U:</comment>');
$output->writeln($matrixU->__toString());
$output->writeln('<info>Time for calculation: ' . $timeDiff . ' sec</info>');
}
public function testCholeskyCache()
{
$numArray = new NumArray(5);
$numArray->setCache(LinAlg\CholeskyDecomposition::CACHE_KEY_CHOLESKY, 8);
$this->assertSame(8, LinAlg::cholesky($numArray));
}
/**
* Tests if a matrix is not singular
*
* @param NumArray $numArray given NumArray
*
* @todo better use matrix_rank to check if a matrix is singular
*
* @return bool
*
* @since 1.0.0
*/
public static function isNotSingularMatrix(NumArray $numArray)
{
return self::isSquareMatrix($numArray) && LinAlg::det($numArray) != 0;
}
/**
* Tests if InvalidArgumentException will be thrown, when using LinAlg::solve with not align matrix and vector
*
* @expectedException \NumPHP\LinAlg\Exception\InvalidArgumentException
* @expectedExceptionMessage Can not solve a linear system with matrix (4, 4) and matrix (3)
*/
public function testSolveNotAlign()
{
$matrix = NumPHP::identity(4);
$vector = NumPHP::ones(3);
LinAlg::solve($matrix, $vector);
}
private function receiveText($object)
{
$keyword_raw = trim($object->Content);
$str_key = mb_substr($keyword_raw, 0, 2, "UTF-8");
$keyword = mb_substr($keyword_raw, 2, mb_strlen($keyword_raw) - 2, "UTF-8");
if ($keyword_raw == "博主真帅") {
$result = $this->transmitText($object, "谢谢夸奖。。不过我好像记错了。。。回复“帮助”查看帮助。。");
return $result;
}
if ($keyword_raw == "主页君照片") {
$result = $this->transmitText($object, '<a href="http://pic4.nipic.com/20091206/3688710_225859078487_2.jpg">点此查看主页君照片</a>');
return $result;
}
if ($keyword_raw == "关于平台") {
$content = json_decode('[{
"Title": "关于平台",
"Description": "关于本平台的一切",
"PicUrl": "http://mmbiz.qpic.cn/mmbiz/9p8h2H28HOmAbjeSichfxCpLZt5Y4icvaicuwwf6JCXkVKvhVhVveuad1q4WD2FMOALOrCJNHQ2wA7unGvFpZufRw/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1",
"Url": "http://mp.weixin.qq.com/s?__biz=MzA3NDY5MDQ0OQ==&mid=401351136&idx=1&sn=2dbcbde7a50df32f5af8917c703d5d48&scene=4#wechat_redirect"
}]', true);
$result = $this->transmitNews($object, $content);
return $result;
}
if ($keyword_raw == "帮助") {
$result = $this->transmitText($object, "回复天气+城市名（如“天气北京”）查看本地天气预报\n回复翻译+词汇（如“翻译你好”）查看中译英\n回复英文单词（如“hello”）查看英译中（注：若有标点，请在前加翻译二字。）\n回复“关于平台”查看本平台详细信息\n回复“新闻”查看新闻\n回复菜名，如“鱼香肉丝”查看菜谱\n普通回复，将会召唤出图灵机器人与您聊天。\n回复邮件+内容（如“邮件主页君你好帅”）为主页君发送邮件，最好在邮件内容中附上你的邮箱方便主页君尽快联系您。");
return $result;
}
if ($str_key == '计算') {
if (strstr($keyword, "[")) {
$input = explode("#", $keyword);
if (sizeof($input) == 2) {
eval('$array1 = ' . $input[0] . ';');
$matrix1 = new NumArray($array1);
if (trim($input[1]) == "inv") {
$matrix1 = LinAlg::inv($matrix1);
}
if (trim($input[1]) == "det") {
$matrix1 = LinAlg::det($matrix1);
}
} elseif (sizeof($input) == 3) {
eval('$array1 = ' . $input[0] . ';');
eval('$array2 = ' . $input[2] . ';');
$matrix1 = new NumArray($array1);
$matrix2 = new NumArray($array2);
if (trim($input[1]) == "+") {
$matrix1->add($matrix2);
}
if (trim($input[1]) == "-") {
$matrix1->sub($matrix2);
}
if (trim($input[1]) == "*") {
$matrix1->dot($matrix2);
}
}
} else {
eval('$matrix1 = ' . $keyword . ';');
}
$output = (string) $matrix1;
if ($matrix1 == 0) {
$output == "0.000000000001";
}
$result = $this->transmitText($object, $output);
return $result;
}
if ($str_key == "天气") {
$url = "http://apix.sinaapp.com/weather/?appkey=" . $object->ToUserName . "&city=" . urlencode($keyword);
$output = file_get_contents($url);
$content = json_decode($output, true);
$result = $this->transmitNews($object, $content);
return $result;
}
if ($str_key == "邮件") {
//引入发送邮件类
require "smtp.php";
//使用163邮箱服务器
$smtpserver = "smtp.163.com";
//163邮箱服务器端口
$smtpserverport = 25;
//你的163服务器邮箱账号
$smtpusermail = "*****@*****.**";
//收件人邮箱
$smtpemailto = "*****@*****.**";
//你的邮箱账号(去掉@163.com)
$smtpuser = "******";
//SMTP服务器的用户帐号
//你的邮箱密码
$smtppass = "";
//SMTP服务器的用户密码
//邮件主题
$mailsubject = date("m-d") . "意见反馈";
//邮件内容
$mailbody = $keyword;
//邮件格式（HTML/TXT）,TXT为文本邮件
$mailtype = "TXT";
//这里面的一个true是表示使用身份验证,否则不使用身份验证.
$smtp = new smtp($smtpserver, $smtpserverport, true, $smtpuser, $smtppass);
//是否显示发送的调试信息
$smtp->debug = TRUE;
//发送邮件
$smtp->sendmail($smtpemailto, $smtpusermail, $mailsubject, $mailbody, $mailtype);
$result = $this->transmitText($object, "成功发送邮件！");
return $result;
}
if ($str_key == "翻译") {
$content = $this->baiduDic($keyword);
$result = $this->transmitText($object, $content);
return $result;
}
if (preg_match("/^[a-zA-Z\\s]+\$/", $keyword_raw)) {
$content = $this->baiduDic($keyword_raw);
$result = $this->transmitText($object, $content);
return $result;
}
$content = $this->tulingRobot($keyword_raw);
if (!($content == "")) {
$result = $this->transmitText($object, $content);
} else {
$output = $this->tulingRobotNews($keyword_raw);
$temp = json_encode(array_slice($output, 0, 4));
$final = json_decode($temp, true);
$subtemp = mb_substr($temp, 0, 1022, "utf-8");
$result = $this->transmitNews($object, $final);
}
return $result;
}
/**
* Tests if SingularMatrixException will be thrown, when using LinAlg::inv with singular matrix
*
* @expectedException \NumPHP\LinAlg\Exception\SingularMatrixException
* @expectedExceptionMessage Matrix is singular
*/
public function testInvSingular()
{
$matrix = new NumArray([[0]]);
LinAlg::inv($matrix);
}
/**
* Tests cache of LinAlg::lud
*/
public function testLUDecompositionCache()
{
$numArray = new NumArray(5);
$numArray->setCache(LUDecomposition::CACHE_KEY_LU_DECOMPOSITION, 8);
$this->assertSame(8, LinAlg::lud($numArray));
}