function discretenewtons($func, $xmin, $xmax, $guess = null)
{
$func = makepretty($func);
$func = mathphp($func, "x");
$func = str_replace("(x)", '($x)', $func);
if ($guess == null) {
$guess = ($xmin + $xmax) / 2;
}
$cnt = 0;
$eps = 1.0E-7;
$x = $guess;
$curx = $guess;
$dx = min(($xmax - $xmin) / 100, 0.001);
$y = eval("return ({$func});");
while (abs($y) > $eps && $cnt < 20) {
$x = $curx + $dx;
$ny = eval("return ({$func});");
$m = ($ny - $y) / $dx;
$curx = $curx - $y / $m;
$x = $curx;
$y = eval("return ({$func});");
$cnt++;
}
//echo "N cnt: $cnt. ";
if ($cnt == 20) {
if ($x > $xmax || $x < $xmin) {
echo "Newton's did not converge within interval";
} else {
echo "Newton's did not acheive good accuracy";
}
return null;
} else {
if ($x > $xmax || $x < $xmin) {
echo "Newton's did not converge within interval";
return null;
} else {
return $curx;
}
}
}
function ASplot($function)
{
$funcstr = implode(',', $function);
preg_match_all('/[a-zA-Z]+/', $funcstr, $matches, PREG_PATTERN_ORDER);
$okfunc = array('sin', 'cos', 'tan', 'sec', 'csc', 'cot', 'arcsin', 'arccos', 'arctan', 'x', 't', 'log', 'ln', 'e', 'pi', 'abs', 'sqrt', 'safepow');
foreach ($matches[0] as $m) {
if (!in_array($m, $okfunc)) {
echo "{$m}";
return;
}
}
//do safety check, as this will be eval'ed
//$function = explode(',',str_replace(array('"','\'',';'),'',$function));
$function = str_replace(array('"', '\'', ';'), '', $function);
if (strpos($function[0], '[') === 0) {
$funcp = explode(',', $function[0]);
$isparametric = true;
$xfunc = str_replace("[", "", $funcp[0]);
$xfunc = mathphp($xfunc, "t");
$xfunc = str_replace("(t)", '($t)', $xfunc);
$exfunc = create_function('$t', 'return (' . $xfunc . ');');
$yfunc = str_replace("]", "", $funcp[1]);
$yfunc = mathphp($yfunc, "t");
$yfunc = str_replace("(t)", '($t)', $yfunc);
$eyfunc = create_function('$t', 'return (' . $yfunc . ');');
} else {
$isparametric = false;
$func = mathphp($function[0], "x");
$func = str_replace("(x)", '($x)', $func);
$efunc = create_function('$x', 'return (' . $func . ');');
}
$avoid = array();
if (isset($function[1]) && $function[1] != '' && $function[1] != 'null') {
$xmin = $function[1];
} else {
$xmin = $this->xmin - min($this->border[0], 5) / $this->xunitlength;
}
if (isset($function[2]) && $function[2] != '' && $function[2] != 'null') {
$xmaxarr = explode('!', $function[2]);
$xmax = $xmaxarr[0];
$avoid = array_slice($xmaxarr, 1);
} else {
$xmax = $this->xmax + min($this->border[2], 5) / $this->xunitlength;
}
$xmin += ($xmax - $xmin) / 100000;
//avoid divide by zero errors
if (isset($function[3]) && $function[3] != '' && $function[3] != 'null') {
$dx = ($xmax - $xmin) / ($function[3] - 1);
$stopat = $function[3];
} else {
$dx = ($xmax - $xmin) / 100;
$stopat = 101;
}
$px = null;
$py = null;
$lasty = 0;
$lastl = 0;
for ($i = 0; $i < $stopat; $i++) {
if ($isparametric) {
$t = $xmin + $dx * $i;
if (in_array($t, $avoid)) {
continue;
}
$x = $exfunc($t);
$y = $eyfunc($t);
if (is_nan($x) || is_nan($y)) {
continue;
}
} else {
$x = $xmin + $dx * $i;
if (in_array($x, $avoid)) {
continue;
}
$y = $efunc($x);
if (is_nan($y)) {
continue;
}
}
if ($i < 2 || $i == $stopat - 2) {
$fx[$i] = $x;
$fy[$i] = $y;
}
$lastx = $x;
/*if (abs($y-$lasty) > ($this->ymax-$this->ymin)) {
if ($lastl > 1) { $lastl = 0; }//break path
$lasty = $y;
} else {
$lasty = $y;
if ($lastl > 0) {
$this->ASline(array("[$px,$py]","[$x,$y]"));
}
$px = $x;
$py = $y;
$lastl++;
}*/
if ($py == null) {
//starting line
} else {
if ($y > $this->ymax || $y < $this->ymin) {
//going or still out of bounds
if ($py <= $this->ymax && $py >= $this->ymin) {
//going out
if ($y > $this->ymax) {
//going up
$iy = $this->ymax + min($this->border[3], 5) / $this->yunitlength;
} else {
//going down
$iy = $this->ymin - min($this->border[1], 5) / $this->yunitlength;
}
$ix = ($x - $px) * ($iy - $py) / ($y - $py) + $px;
$this->ASline(array("[{$px},{$py}]", "[{$ix},{$iy}]"));
} else {
//still out
}
} else {
if ($py > $this->ymax || $py < $this->ymin) {
//coming or staying in bounds
if ($y <= $this->ymax && $y >= $this->ymin) {
//comin in
if ($py > $this->ymax) {
//comin from top
$iy = $this->ymax + min($this->border[3], 5) / $this->yunitlength;
} else {
//coming from bottom
$iy = $this->ymin - min($this->border[1], 5) / $this->yunitlength;
}
$ix = ($x - $px) * ($iy - $py) / ($y - $py) + $px;
$this->ASline(array("[{$ix},{$iy}]", "[{$x},{$y}]"));
} else {
//still out
}
} else {
//all in
$this->ASline(array("[{$px},{$py}]", "[{$x},{$y}]"));
}
}
}
$px = $x;
$py = $y;
}
if (isset($function[5]) && $function[5] != '' && $function[5] != 'null') {
if ($function[5] == 1) {
//need pt2arr for xunit adjust
$this->ASarrowhead($this->pt2arr("{$fx[1]},{$fy[1]}"), $this->pt2arr("{$fx[0]},{$fy[0]}"));
} else {
if ($function[5] == 2) {
$this->ASdot2(array("[{$fx[0]},{$fy[0]}]", "open"));
} else {
if ($function[5] == 3) {
$this->ASdot2(array("[{$fx[0]},{$fy[0]}]", "closed"));
}
}
}
}
if (isset($function[6]) && $function[6] != '' && $function[6] != 'null') {
if ($function[6] == 1) {
$this->ASarrowhead($this->pt2arr("{$fx[$stopat - 2]},{$fy[$stopat - 2]}"), $this->pt2arr("{$x},{$y}"));
} else {
if ($function[6] == 2) {
$this->ASdot2(array("[{$x},{$y}]", "open"));
} else {
if ($function[6] == 3) {
$this->ASdot2(array("[{$x},{$y}]", "closed"));
}
}
}
}
}
function spacecurve($func, $tmin, $tmax)
{
global $imasroot;
if ($GLOBALS['inquestiondisplay'] == false) {
return '';
}
if (func_num_args() > 3) {
$disc = func_get_arg(3);
if (!is_numeric($disc)) {
$disc = 50;
}
} else {
$disc = 50;
}
if (func_num_args() > 5) {
$width = func_get_arg(4);
$height = func_get_arg(5);
} else {
$width = 300;
$height = 300;
}
if (func_num_args() > 6) {
$axes = func_get_arg(6);
} else {
$axes = 1;
}
if (func_num_args() > 12) {
$bounds = array_slice(func_get_args(), 7, 6);
}
$useragent = $_SERVER['HTTP_USER_AGENT'];
$oldschool = false;
if (isset($GLOBALS['sessiondata']['useflash'])) {
$oldschool = true;
} else {
if (preg_match('/MSIE\\s*(\\d+)/i', $useragent, $matches)) {
if ($matches[1] < 9) {
$oldschool = true;
}
}
}
if ($oldschool) {
$func = str_replace('[', '', $func);
$func = str_replace(']', '', $func);
$func = explode(',', $func);
$func[0] = "(1+.01*cos(u))*({$func[0]})";
$func[1] = "(1+.01*cos(u))*({$func[1]})";
$func[2] = "(1+.01*sin(u))*({$func[2]})";
foreach ($func as $k => $v) {
$func[$k] = mathphp($v, 'u|t');
$func[$k] = str_replace('(u)', '($u)', $func[$k]);
$func[$k] = str_replace('(t)', '($t)', $func[$k]);
$usefunc[$k] = create_function('$u,$t', 'return(' . $func[$k] . ');');
}
$count = 0;
$dt = ($tmax - $tmin) / ($disc - 1);
for ($i = 0; $i < 4; $i++) {
for ($j = 0; $j < $disc; $j++) {
if ($count > 0) {
$verts .= '~';
}
$u = 1.571 * $i;
$t = $vmin + $dt * $j;
$x = $usefunc[0]($u, $t);
$y = $usefunc[1]($u, $t);
$z = $usefunc[2]($u, $t);
$verts .= "{$x},{$y},{$z}";
$count++;
}
}
$count = 0;
for ($i = 0; $i < 3; $i++) {
for ($j = 0; $j < $disc - 1; $j++) {
if ($count > 0) {
$faces .= '~';
}
$faces .= $i * $disc + $j . ',';
$faces .= ($i + 1) * $disc + $j . ',';
$faces .= ($i + 1) * $disc + $j + 1 . ',';
$faces .= $i * $disc + $j + 1;
$count++;
}
}
if (!isset($GLOBALS['3dplotcnt'])) {
$r = 1;
} else {
$r = $GLOBALS['3dplotcnt'] + 1;
}
$GLOBALS['3dplotcnt'] = $r;
$html .= "<div id=\"plot3d{$r}\">";
$html .= '<p><a href="http://www.adobe.com/go/getflashplayer"><img src="http://www.adobe.com/images/shared/download_buttons/get_flash_player.gif" alt="Get Adobe Flash player" /></a></p>';
$html .= '</div>';
$html .= '<script type="text/javascript">';
$html .= 'var FlashVars = {';
$html .= ' verts: "' . $verts . '",';
$html .= ' faces: "' . $faces . '",';
$html .= " width: {$width}, height: {$height} };";
$html .= " swfobject.embedSWF(\"{$imasroot}/assessment/libs/viewer3d.swf\", \"plot3d{$r}\", \"{$width}\", \"{$height}\", \"9.0.0\", \"{$imasroot}/assessment/libs/expressInstall.swf\",FlashVars);";
$html .= '</script>';
/*if (isset($GLOBALS['sessiondata']['useflash'])) {
} else {
$html = "<applet codebase=\"{$GLOBALS['imasroot']}/assessment/libs\" code=\"Viewer.class\" width=$width height=$height>\n";
$html .= "<param name=\"verts\" value=\"$verts\">\n";
$html .= "<param name=\"faces\" value=\"$faces\">\n";
if ($axes==1) {
$html .= "<param name=\"axes\" value=\"show\">\n";
} else {
$html .= "<param name=\"axes\" value=\"hide\">\n";
}
$html .= "<param name=\"edges\" value=\"hide\">\n";
if (isset($bounds)) {
$html .= "<param name=\"bounds\" value=\"" . implode(',',$bounds) . "\">\n";
}
$url = $GLOBALS['urlmode'] . $_SERVER['HTTP_HOST'] . $_SERVER['PHP_SELF'] . (isset($_SERVER['QUERY_STRING'])?'?'.$_SERVER['QUERY_STRING'].'&useflash=true':'?useflash=true');
$html .= "Not seeing the 3D graph? <a href=\"$url\">Try Alternate</a></applet>\n";
} */
} else {
//new approach
$func = str_replace('[', '', $func);
$func = str_replace(']', '', $func);
$func = explode(',', $func);
foreach ($func as $k => $v) {
$func[$k] = mathphp($v, 't');
$func[$k] = str_replace('(t)', '($t)', $func[$k]);
$usefunc[$k] = create_function('$t', 'return(' . $func[$k] . ');');
}
$count = 0;
$dt = ($tmax - $tmin) / ($disc - 1);
for ($j = 0; $j < $disc; $j++) {
if ($count > 0) {
$verts .= '~';
}
$t = $vmin + $dt * $j;
$x = $usefunc[0]($t);
$y = $usefunc[1]($t);
$z = $usefunc[2]($t);
$verts .= "{$x},{$y},{$z}";
$count++;
}
if (!isset($GLOBALS['3dplotcnt'])) {
$r = 1;
$html .= '<script type="text/javascript" src="' . $imasroot . '/javascript/3dviewer.js"></script>';
} else {
$r = $GLOBALS['3dplotcnt'] + 1;
}
$GLOBALS['3dplotcnt'] = $r;
$html .= "<canvas id=\"plot3d{$r}\" width=\"{$width}\" height=\"{$height}\">";
$url = $GLOBALS['urlmode'] . $_SERVER['HTTP_HOST'] . $_SERVER['PHP_SELF'] . (isset($_SERVER['QUERY_STRING']) ? '?' . $_SERVER['QUERY_STRING'] . '&useflash=true' : '?useflash=true');
$html .= "Not seeing the 3D graph? <a href=\"{$url}\">Try Alternate</a>";
$html .= "</canvas>";
$html .= "<script type=\"text/javascript\">\$(window).on('load',function() {var plot3d{$r} = new Viewer3D({verts: '{$verts}', curves: true, width: '{$width}', height:'{$height}'}, 'plot3d{$r}');});</script>";
}
return $html;
}
function checklineagainstdata($xarr, $yarr, $line, $var = "x", $alpha = 0.05)
{
if (!is_array($xarr)) {
$xarr = explode(',', $xarr);
}
if (!is_array($yarr)) {
$yarr = explode(',', $yarr);
}
if (count($xarr) != count($yarr)) {
echo "Error: linreg requires xarray length = yarray length";
return false;
}
if (count($xarr) < 3) {
echo "Requires 3 or more data values";
return false;
}
$sx = array_sum($xarr);
$sy = array_sum($yarr);
$sxx = 0;
$syy = 0;
$sxy = 0;
for ($i = 0; $i < count($xarr); $i++) {
$sxx += $xarr[$i] * $xarr[$i];
$syy += $yarr[$i] * $yarr[$i];
$sxy += $xarr[$i] * $yarr[$i];
}
$n = count($xarr);
$r = ($n * $sxy - $sx * $sy) / (sqrt($n * $sxx - $sx * $sx) * sqrt($n * $syy - $sy * $sy));
$m = ($n * $sxy - $sx * $sy) / ($n * $sxx - $sx * $sx);
$b = ($sy - $sx * $m) / $n;
if ($line == '') {
return array('', makepretty("`{$m} {$var} + {$b}`"));
}
foreach ($_POST as $k => $v) {
//try to catch junk answers
if ($v == $line) {
if (preg_match('/[^,\\d\\.\\-]/', $_POST['qn' . substr($k, 2) . '-vals'])) {
return array('', makepretty("`{$m} {$var} + {$b}`"));
}
}
}
$linec = mathphp(makepretty($line), $var);
$linec = str_replace("({$var})", '($t)', $linec);
$linefunc = create_function('$t', 'return(' . $linec . ');');
$xmin = min($xarr);
$xmax = max($xarr);
$dx = ($xmax - $xmin) / 5;
if ($dx <= 0) {
echo "error with xmin/xmax";
return false;
}
$isinbounds = true;
$sqres = 0;
for ($i = 0; $i < count($xarr); $i++) {
$sqres += ($yarr[$i] - ($m * $xarr[$i] + $b)) * ($yarr[$i] - ($m * $xarr[$i] + $b));
}
$sqres = sqrt($sqres / ($n - 2));
$sdiv = $sxx - $sx * $sx / $n;
$tcrit = abs(invtcdf($alpha / 2, $n - 2));
$xbar = $sx / $n;
for ($x = $xmin; $x < $xmax * 1.02; $x += $dx) {
$ypred = $m * $x + $b;
$yline = $linefunc($x);
$yconf = $tcrit * $sqres * sqrt(1 + 1 / $n + ($x - $xbar) * ($x - $xbar) / $sdiv);
if (abs($ypred - $yline) > $yconf) {
$isinbounds = false;
break;
}
}
if ($isinbounds) {
return array($line, makepretty("{$m} {$var} + {$b}"));
} else {
return array("({$line}) + 200000", makepretty("`{$m} {$var} + {$b}`"));
}
}
function parsesloppycomplex($v)
{
$v = mathphp($v, 'i');
$v = str_replace('(i)', '($i)', $v);
$a = eval('$i=0;return (' . $v . ');');
$apb = eval('$i=1;return (' . $v . ');');
return array($a, $apb - $a);
}
function parseFloat($input)
{
if (preg_match("/-\\s*oo/i", $input)) {
return array(-INF, "-oo", false);
} elseif (preg_match("/\\+?oo/i", $input)) {
return array(INF, "oo", false);
}
$result = eval("return (" . mathphp($input, null) . ");");
$error = $result === false || is_string($result);
return array($result, $input, $error);
}
function ineqbetweenplot($funcs)
{
if (!is_array($funcs)) {
settype($funcs, "array");
}
$settings = array(-5, 5, -5, 5, 1, 1, 200, 200);
for ($i = 1; $i < func_num_args(); $i++) {
$settings[$i - 1] = func_get_arg($i);
}
$ymin = $settings[2];
$ymax = $settings[3];
$commands = "setBorder(5); initPicture({$settings[0]},{$settings[1]},{$settings[2]},{$settings[3]});";
$alt = "Graph, window x {$settings[0]} to {$settings[1]}, y {$settings[2]} to {$settings[3]}.";
if (strpos($settings[4], ':')) {
$lbl = explode(':', $settings[4]);
}
if (is_numeric($settings[4]) && $settings[4] > 0) {
$commands .= 'axes(' . $settings[4] . ',' . $settings[4] . ',1';
} else {
if (isset($lbl[0]) && is_numeric($lbl[0]) && $lbl[0] > 0 && $lbl[1] > 0) {
$commands .= 'axes(' . $lbl[0] . ',' . $lbl[1] . ',1';
} else {
$commands .= 'axes(1,1,null';
}
}
if (strpos($settings[5], ':')) {
$grid = explode(':', $settings[5]);
}
if (is_numeric($settings[5]) && $settings[5] > 0) {
$commands .= ',' . $settings[5] . ',' . $settings[5] . ');';
$dgrid = $settings[5];
} else {
if (isset($grid[0]) && is_numeric($grid[0]) && $grid[0] > 0 && $grid[1] > 0) {
$commands .= ',' . $grid[0] . ',' . $grid[1] . ');';
$dgrid = $grid[0];
} else {
$commands .= ');';
$dgrid = 1;
}
}
foreach ($funcs as $k => $function) {
$alt .= "Start Graph";
$function = explode(",", $function);
//correct for parametric
$func = makepretty($function[0]);
$func = mathphp($func, "x");
$func = str_replace("x", '$x', $func);
$xfunc = create_function('$x', 'return (' . $func . ');');
//even though ASCIIsvg has a plot function, we'll calculate it here to hide the function
// function of x,filltype,fillcolor,linecolor,dash,strokewidth
$path = '';
$shades = '';
$filltype = $function[1];
$shades .= "stroke=\"blue\";strokedasharray=\"none\";";
$alt .= "Shaded in blue " . substr($filltype, 0, 5);
if ($function[2] != '') {
$path .= "stroke=\"{$function[2]}\";";
$alt .= ", Color {$function[2]}";
} else {
$path .= "stroke=\"black\";";
$alt .= ", Color black";
}
if ($function[4] != '') {
$path .= "strokewidth=\"{$function[4]}\";";
} else {
$path .= "strokewidth=\"1\";";
}
if ($function[3] != '') {
if ($function[3] == "dash") {
$path .= "strokedasharray=\"5\";";
$alt .= ", Dashed";
} else {
$path .= "strokedasharray=\"none\";";
}
} else {
$path .= "strokedasharray=\"none\";";
}
$xmin = $settings[0];
$xmax = $settings[1];
if ($GLOBALS['sessiondata']['graphdisp'] == 0) {
$dx = 1;
$alt .= "<table class=stats><thead><tr><th>x</th><th>y</th></thead></tr><tbody>";
$stopat = $xmax - $xmin + 1;
} else {
$dx = ($xmax - $xmin) / 100;
$stopat = 100;
}
$lasty = 0;
$lastl = 0;
for ($i = 0; $i < $stopat; $i++) {
$x = $xmin + $dx * $i;
$y = round($xfunc($x), 3);
$alt .= "<tr><td>{$x}</td><td>{$y}</td></tr>";
if (abs($y - $lasty) > $ymax - $ymin) {
if ($lastl > 1) {
$path .= ']);';
$lastl = 0;
}
$lasty = $y;
} else {
if ($lastl == 0) {
$path .= "path([";
} else {
$path .= ",";
}
$path .= "[{$x},{$y}]";
$lasty = $y;
$lastl++;
}
}
if ($lastl > 0) {
$path .= "]);";
}
$alt .= "</tbody></table>\n";
$commands .= $path;
//do shades
for ($i = 0; $i < ($xmax - $xmin) * 4 / $dgrid; $i++) {
$x = $xmin + $dgrid * (0.125 + 0.25 * $i);
$y = round($xfunc($x), 3);
if ($filltype == "above") {
$mins[$i][] = $y;
} else {
if ($filltype == "below") {
$maxs[$i][] = $y;
}
}
}
}
for ($i = 0; $i < ($xmax - $xmin) * 4 / $dgrid; $i++) {
$x = $xmin + $dgrid * (0.125 + 0.25 * $i);
if (count($mins) == 0) {
$miny = $ymin - 2;
} else {
$miny = max($mins[$i]);
}
if (count($maxs) == 0) {
$maxy = $ymax + 2;
} else {
$maxy = min($maxs[$i]);
}
if ($miny < $maxy) {
$shades .= "line([{$x},{$miny}],[{$x},{$maxy}]);";
}
}
$commands .= $shades;
if ($GLOBALS['sessiondata']['graphdisp'] == 0) {
return $alt;
} else {
return "<embed type='image/svg+xml' align='middle' width='{$settings['6']}' height='{$settings['7']}' src='{$GLOBALS['imasroot']}/javascript/d.svg' script='{$commands}' />\n";
}
}
function calculusnumint($func, $var, $a, $b, $n, $method)
{
if ($n <= 0 || $a >= $b) {
echo "invalid params to calculusnumint";
return false;
}
if ($method == 'simpsons' && $n % 2 != 0) {
echo "simpsons requires even n";
return false;
}
$func = makepretty($func);
$func = mathphp($func, $var);
if ($func == '0;') {
return 0;
}
$func = str_replace("({$var})", "(\${$var})", $func);
$evalfunc = create_function("\${$var}", 'return(' . $func . ');');
$dx = ($b - $a) / $n;
if ($method == 'right') {
$x = $a + $dx;
} else {
if ($method == 'midpoint') {
$x = $a + 0.5 * $dx;
} else {
$x = $a;
}
}
if ($method == 'left' || $method == 'right' || $method == 'midpoint') {
$ntodo = $n;
} else {
$ntodo = $n + 1;
}
$out = 0;
$mult = 1;
for ($i = 0; $i < $ntodo; $i++) {
if ($method == 'trapezoidal') {
if ($i == 0 || $i == $n) {
$mult = 1;
} else {
$mult = 2;
}
} else {
if ($method == 'simpsons') {
if ($i == 0 || $i == $n) {
$mult = 1;
} else {
if ($i % 2 == 0) {
$mult = 2;
} else {
$mult = 4;
}
}
}
}
$out += $mult * $evalfunc($x);
$x += $dx;
}
if ($method == 'trapezoidal') {
return $out * $dx / 2;
} else {
if ($method == 'simpsons') {
return $out * $dx / 3;
} else {
return $out * $dx;
}
}
}
function getnumbervalue($a)
{
$a = str_replace(',', '', $a);
if (is_numeric($a)) {
return $a * 1;
} else {
$a = @eval('return(' . mathphp($a, null) . ');');
return $a;
}
}
