サムネイルを作成するときに画像の比率を維持するにはどうすればよいですか?

/**
 * 
 * Generate Thumbnail using Imagick class
 *  
 * @param string $img
 * @param string $width
 * @param string $height
 * @param int $quality
 * @return boolean on true
 * @throws Exception
 * @throws ImagickException
 */
function generateThumbnail($img, $width, $height, $quality = 90)
{
    if (is_file($img)) {
        $imagick = new Imagick(realpath($img));
        $imagick->setImageFormat('jpeg');
        $imagick->setImageCompression(Imagick::COMPRESSION_JPEG);
        $imagick->setImageCompressionQuality($quality);
        $imagick->thumbnailImage($width, $height, false, false);
        $filename_no_ext = reset(explode('.', $img));
        if (file_put_contents($filename_no_ext . '_thumb' . '.jpg', $imagick) === false) {
            throw new Exception("Could not put contents.");
        }
        return true;
    }
    else {
        throw new Exception("No valid image provided with {$img}.");
    }
}

function makeThumbnails($updir, $img, $id)
{
    $thumbnail_width = 134;
    $thumbnail_height = 189;
    $thumb_beforeword = "thumb";
    $arr_image_details = getimagesize("$updir" . $id . '_' . "$img"); // pass id to thumb name
    $original_width = $arr_image_details[0];
    $original_height = $arr_image_details[1];
    if ($original_width > $original_height) {
        $new_width = $thumbnail_width;
        $new_height = intval($original_height * $new_width / $original_width);
    } else {
        $new_height = $thumbnail_height;
        $new_width = intval($original_width * $new_height / $original_height);
    }
    $dest_x = intval(($thumbnail_width - $new_width) / 2);
    $dest_y = intval(($thumbnail_height - $new_height) / 2);
    if ($arr_image_details[2] == IMAGETYPE_GIF) {
        $imgt = "ImageGIF";
        $imgcreatefrom = "ImageCreateFromGIF";
    }
    if ($arr_image_details[2] == IMAGETYPE_JPEG) {
        $imgt = "ImageJPEG";
        $imgcreatefrom = "ImageCreateFromJPEG";
    }
    if ($arr_image_details[2] == IMAGETYPE_PNG) {
        $imgt = "ImagePNG";
        $imgcreatefrom = "ImageCreateFromPNG";
    }
    if ($imgt) {
        $old_image = $imgcreatefrom("$updir" . $id . '_' . "$img");
        $new_image = imagecreatetruecolor($thumbnail_width, $thumbnail_height);
        imagecopyresized($new_image, $old_image, $dest_x, $dest_y, 0, 0, $new_width, $new_height, $original_width, $original_height);
        $imgt($new_image, "$updir" . $id . '_' . "$thumb_beforeword" . "$img");
    }
}