function countUpHords(array $param)
{
foreach ($param as $key => $value) {
${$key} = $value;
}
unset($param);
if (empty($end)) {
//$end = 0 => A ; $end = 1 => B
$forDiff = 1;
$x = $b;
} else {
$forDiff = -1;
$x = $a;
$a = $b;
}
$f_a = $coef1 * pow($a, 3) + $coef2 * pow($a, 2) + $coef3 * $a + $coef4;
//count f(a) or f(b)
$n = 0;
$tabCalc = "<tr><th></th><th>{$coef1}</th><th>{$coef2}</th><th>{$coef3}</th><th>{$coef4}</th></tr>";
//table for calcs
$listOfH = '';
//this var have list of calcs h
do {
$param = ['id' => $n, 'x[n]' => $x];
$calc = getCalc($coef1, $coef2, $coef3, $coef4, $x);
$tabCalc .= "<tr style='border-top: 2px solid black;'><td rowspan='2'>x[{$n}] = {$x}</td><td>:</td><td>{$calc['0']}</td><td>{$calc['2']}</td><td>{$calc['4']}</td></tr>\n <tr><td>{$coef1}</td><td>{$calc['1']}</td><td>{$calc['3']}</td><td>{$calc['5']}</td></tr>";
$param['f(x[n])'] = $calc[5];
$param['a/b'] = correctNum(($x - $a) * $forDiff);
$param['f(a/b)'] = correctNum(($param['f(x[n])'] - $f_a) * $forDiff);
if (empty($param['f(a/b)'])) {
//early exit (division by zero)
return false;
}
$param['h'] = correctNum($param['f(x[n])'] * $param['a/b'] / $param['f(a/b)']);
$listOfH .= "h[{$n}] = {$param['f(x[n])']} * {$param['a/b']} / {$param['f(a/b)']} = {$param['h']}<br/>";
$params[$n] = $param;
$x = correctNum($x - $param['h']);
$n++;
} while (!empty($param['h']) && $n < 56);
//if there is closing, 56 step will be last
$lastX =& $params[count($params) - 1]['x[n]'];
$lastX = "<span class='colGreen'>{$lastX}</span>";
unset($lastX);
return [$params, $tabCalc, $listOfH];
}
function countUpKos(array $param)
{
foreach ($param as $key => $value) {
${$key} = $value;
}
unset($param);
/*count coefs f'(x[n])*/
$coef1_L = $coef1 * 3;
$coef2_L = $coef2 * 2;
$coef3_L = $coef3;
/*//count coefs f'(x[n])*/
$n = 0;
$tabCalc = "<tr><th></th><th>{$coef1}</th><th>{$coef2}</th><th>{$coef3}</th><th>{$coef4}</th></tr>";
// table for calcs f(x)
$tabCalc_L = "<tr><th></th><th>{$coef1_L}</th><th>{$coef2_L}</th><th>{$coef3_L}</th></tr>";
// table for calcs f'(x)
do {
$param = array('id' => $n, 'x[n]' => $x);
$calc = getCalc($coef1, $coef2, $coef3, $coef4, $x);
$calc_L = getCalc_L($coef1_L, $coef2_L, $coef3_L, $x);
$tabCalc .= "<tr style='border-top: 2px solid black;'><td rowspan='2'>x[{$n}] = {$x}</td><td>:</td><td>{$calc['0']}</td><td>{$calc['2']}</td><td>{$calc['4']}</td></tr>\n <tr><td>{$coef1}</td><td>{$calc['1']}</td><td>{$calc['3']}</td><td>{$calc['5']}</td></tr>";
$tabCalc_L .= "<tr style='border-top: 2px solid black;'><td rowspan='2'>x[{$n}] = {$x}</td><td>:</td><td>{$calc_L['0']}</td><td>{$calc_L['2']}</td></tr>\n <tr><td>{$coef1_L}</td><td>{$calc_L['1']}</td><td>{$calc_L['3']}</td></tr>";
$param['f(x[n])'] = $calc[5];
$param['f\'(x[n])'] = $calc_L[3];
if (empty($param['f\'(x[n])'])) {
//early exit (division by zero)
return false;
}
$param['h'] = correctNum($param['f(x[n])'] / $param['f\'(x[n])']);
$params[$n] = $param;
if (empty($param['h'])) {
// keeping coefs square equation for counting two other solutions
$coef2 = $calc[1];
$coef3 = $calc[3];
}
$x = correctNum($x - $param['h']);
$n++;
} while (!empty($param['h']) && $n < 56);
//if there is closing, 56 step will be last
$lastX =& $params[count($params) - 1]['x[n]'];
$lastX = "<span class='colGreen'>{$lastX}</span>";
unset($lastX);
return [$params, $tabCalc, $tabCalc_L, countUpSquare($coef1, $coef2, $coef3, $param['x[n]'])];
}
function countUpSquare($coef1, $coef2, $coef3, $firstSolution)
{
$calcSquare = "<br />Урав. 2-го порядка: ({$coef1} * x<sup>2</sup>) + ({$coef2} * x) + ({$coef3}) = 0<br />";
$d = correctNum(pow($coef2, 2) - 4 * $coef1 * $coef3);
$calcSquare .= "<br />D = {$coef2}<sup>2</sup> - 4*{$coef1}*{$coef3} = {$d}<br /><br />";
if ($d < 0) {
$d = abs($d);
$pow12 = correctNum(pow($d, 1 / 2));
$part1 = correctNum(-$coef2 / (2 * $coef1));
$part2 = correctNum($pow12 / (2 * $coef1));
$calcSquare .= "x<sub>2, 3</sub> = ( -({$coef2}) ± √<span class='radical'>-{$d}</span> ) / (2*{$coef1}) = ( -({$coef2}) ± {$pow12}i ) / (2*{$coef1}) = <span class='colorBlue''>{$part1} ± {$part2}i</span>";
} elseif ($d > 0) {
$pow12 = correctNum(pow($d, 1 / 2));
$secondSolution = correctNum((-$coef2 + $pow12) / (2 * $coef1));
$thirdSolution = correctNum((-$coef2 - $pow12) / (2 * $coef1));
$calcSquare .= "x<sub>2</sub> = ( -({$coef2}) + √<span class='radical'>{$d}</span> ) / (2*{$coef1}) = ( -({$coef2}) + {$pow12} ) / (2*{$coef1}) = <span class='colorBlue''>{$secondSolution}</span><br /><br />\n x<sub>3</sub> = ( -({$coef2}) - √<span class='radical'>{$d}</span> ) / (2*{$coef1}) = ( -({$coef2}) - {$pow12} ) / (2*{$coef1}) = <span class='colorBlue''>{$thirdSolution}</span>";
} else {
$secondSolution = -$coef2 / (2 * $coef1);
$calcSquare .= "x<sub>2</sub> = -({$coef2}) / (2 * {$coef1}) = {$secondSolution}<br /><br />\n <span style='color: red;'>По идее такого быть не должно!<br />Лучше перепроверить введённые данные</span>";
}
$calcSquare .= "<br /><br />x<sub>1</sub> = <span class='colorBlue'>{$firstSolution}</span><br />";
return $calcSquare;
}
function countUpKombo(array $param)
{
$pattern = '<span>x<sub class=\'index\' >n</sub></span>';
$pattern_line = '<span>x<sub class=\'index\' >n</sub><sup class=\'line\' >—</sup></span>';
$patOnlyLine = '<sup class=\'line\' >—</sup>';
//transformation array's items on single vars | begin
foreach ($param as $key => $value) {
${$key} = $value;
}
unset($param);
//transformation array's items on single vars | end
if (empty($end)) {
//$end = 0 => fixed A ; $end = 1 => fixed B
$forDiff = 1;
$x = $b;
$x_line = $a;
$forTable = "{$pattern} - {$pattern_line}";
$forTableF = "f({$pattern}) - f({$pattern_line})";
} else {
$forDiff = -1;
$x = $a;
$x_line = $b;
$forTable = "{$pattern_line} - {$pattern}";
$forTableF = "f({$pattern_line}) - f({$pattern})";
}
/*count coefs f'(x[n])*/
$coef1_L = $coef1 * 3;
$coef2_L = $coef2 * 2;
$coef3_L = $coef3;
/*//count coefs f'(x[n])*/
$n = 0;
$mainTable = "<tr><th rowspan='2'>n</th><th>{$pattern}</th><th rowspan='2'>{$forTable}</th><th>f({$pattern})</th><th rowspan='2'>{$forTableF}</th><th rowspan='2'>f '({$pattern_line})</th><th>h</th></tr>\n <tr><th>{$pattern_line}</th><th>f({$pattern_line})</th><th>h<sup class='lineH' >—</sup></th></tr>";
//table for calcs f(x)
$tabCalc = "<tr><th class='fontNorm' ><span class='colorBlack'>result:</span> f({$pattern})</th><th>{$coef1}</th><th>{$coef2}</th><th>{$coef3}</th><th>{$coef4}</th></tr>\n";
//table for calcs f(x_line)
$tabCalc_line = "<tr><th class='fontNorm'><span class='colorBlack'>result:</span> f({$pattern_line})</th><th>{$coef1}</th><th>{$coef2}</th><th>{$coef3}</th><th>{$coef4}</th></tr>\n";
//table for calcs f'(x_line)
$tabCalc_deriv_line = "<tr><th class='fontNorm'><span class='colorBlack'>result:</span> f '({$pattern_line})</th><th>{$coef1_L}</th><th>{$coef2_L}</th><th>{$coef3_L}</th></tr>\n";
//this var have list of calcs h
$listOfH = '';
do {
$param = ['id' => $n, 'x[n]' => $x, 'x[n]line' => $x_line, 'x[n]-x[n]line' => correctNum(($x - $x_line) * $forDiff)];
$patChanging = "<sub class=\\'index\\' >{$n}</sub>";
$calc = getCalc($coef1, $coef2, $coef3, $coef4, $x);
$calc_line = getCalc($coef1, $coef2, $coef3, $coef4, $x_line);
$calc_deriv_line = getCalc_L($coef1_L, $coef2_L, $coef3_L, $x_line);
$tabCalc .= "<tr class='separate' ><td rowspan='2'>x{$patChanging} = {$x}</td><td>:</td><td>{$calc[0]}</td><td>{$calc[2]}</td><td>{$calc[4]}</td></tr>\n <tr><td>{$coef1}</td><td>{$calc[1]}</td><td>{$calc[3]}</td><td class='colGreen'>{$calc[5]}</td></tr>";
$tabCalc_line .= "<tr class='separate' ><td rowspan='2'>x{$patChanging}{$patOnlyLine} = {$x_line}</td><td>:</td><td>{$calc_line[0]}</td><td>{$calc_line[2]}</td><td>{$calc_line[4]}</td></tr>\n <tr><td>{$coef1}</td><td>{$calc_line[1]}</td><td>{$calc_line[3]}</td><td class='colGreen'>{$calc_line[5]}</td></tr>";
$tabCalc_deriv_line .= "<tr class='separate' ><td rowspan='2'>x{$patChanging}{$patOnlyLine} = {$x_line}</td><td>:</td><td>{$calc_deriv_line[0]}</td><td>{$calc_deriv_line[2]}</td></tr>\n <tr><td>{$coef1_L}</td><td>{$calc_deriv_line[1]}</td><td class='colGreen'>{$calc_deriv_line[3]}</td></tr>";
if (abs($param['x[n]-x[n]line']) <= 0.0001) {
$mainTable .= "<tr class='separate'><td rowspan='2'>{$n}</td><td>{$param['x[n]']}</td><td rowspan='2'>{$param['x[n]-x[n]line']}</td></tr>\n <tr><td>{$param['x[n]line']}</td></tr>";
break 1;
}
$param['f(x[n])'] = $calc[5];
$param['f(x[n])line'] = $calc_line[5];
$param['f\'(x[n])line'] = $calc_deriv_line[3];
$param['f(x[n])-f(x[n])line'] = ($param['f(x[n])'] - $param['f(x[n])line']) * $forDiff;
//early exit (division by zero)
if (empty($param['f(x[n])-f(x[n])line']) || empty($param['f\'(x[n])line'])) {
return false;
}
$param['h'] = correctNum($param['f(x[n])'] * $param['x[n]-x[n]line'] / $param['f(x[n])-f(x[n])line']);
$param['h_line'] = correctNum($param['f(x[n])line'] / $param['f\'(x[n])line']);
$listOfH .= "h{$patChanging} = {$param['f(x[n])']} * {$param['x[n]-x[n]line']} / {$param['f(x[n])-f(x[n])line']} = {$param['h']}<br/>\n h{$patChanging}<sup class='lineH' style='right: 19px;' >—</sup> = {$param['f(x[n])line']} / {$param['f\'(x[n])line']} = {$param['h_line']}";
$mainTable .= "<tr class='separate'><td rowspan='2'>{$n}</td><td>{$param['x[n]']}</td><td rowspan='2'>{$param['x[n]-x[n]line']}</td>\n <td>{$param['f(x[n])']}</td><td rowspan='2'>{$param['f(x[n])-f(x[n])line']}</td>\n <td rowspan='2'>{$param['f\'(x[n])line']}</td><td>{$param['h']}</td></tr>\n <tr><td>{$param['x[n]line']}</td><td>{$param['f(x[n])line']}</td><td>{$param['h_line']}</td></tr>";
if (empty($param['h']) && empty($param['h_line'])) {
$listOfH .= '<hr />';
break 1;
}
$x = correctNum($x - $param['h']);
$x_line = correctNum($x_line - $param['h_line']);
$n++;
$listOfH .= "<br />x<sub class=\\'index\\' >{$n}</sub> = {$param['x[n]']} - ({$param['h']}) = {$x}<br />\n x<sub class=\\'index\\' >{$n}</sub>{$patOnlyLine} = {$param['x[n]line']} - ({$param['h_line']}) = {$x_line}<hr />";
} while ($n < 30);
//if there is closing, 30 step will be last
//keeping coefs square equation for counting two other solutions |begin
//redefine vars $coef2 and $coef3
if (abs($calc[5]) <= abs($calc_line[5])) {
$coef2 = $calc[1];
$coef3 = $calc[3];
$firstSolution = $param['x[n]'];
} else {
$coef2 = $calc_line[1];
$coef3 = $calc_line[3];
$firstSolution = $param['x[n]line'];
}
//keeping coefs square equation for counting two other solutions |end
return [$mainTable, $tabCalc, $tabCalc_line, $tabCalc_deriv_line, $listOfH, countUpSquare($coef1, $coef2, $coef3, $firstSolution)];
}
function countUpKos(array $param)
{
foreach ($param as $key => $value) {
${$key} = $value;
}
unset($param);
/*count coefs f'()*/
$coef1_L = $coef1 * 3;
$coef2_L = $coef2 * 2;
$coef3_L = $coef3;
/*//count coefs f'()*/
$n = 0;
$tabCalc = "<tr><th></th><th>{$coef1}</th><th>{$coef2}</th><th>{$coef3}</th><th>{$coef4}</th></tr>";
// table for calcs f(x)
$tabCalc_L = "<tr><th></th><th>{$coef1_L}</th><th>{$coef2_L}</th><th>{$coef3_L}</th></tr>";
// table for calcs f'(x)
do {
$param = array('id' => $n, 'x[n]' => $x);
$calc[0] = correctNum($coef1 * $x);
//2 row, 3 col
$calc[1] = correctNum($calc[0] + $coef2);
//3 row, 3 col
$calc[2] = correctNum($calc[1] * $x);
//2 row, 4 col
$calc[3] = correctNum($calc[2] + $coef3);
//3 row, 4 col
$calc[4] = correctNum($calc[3] * $x);
//2 row, 5 col
$calc[5] = correctNum($calc[4] + $coef4);
//3 row, 5 col
$calc_L[0] = correctNum($coef1_L * $x);
$calc_L[1] = correctNum($calc_L[0] + $coef2_L);
$calc_L[2] = correctNum($calc_L[1] * $x);
$calc_L[3] = correctNum($calc_L[2] + $coef3_L);
$tabCalc .= "<tr style='border-top: 2px solid black;'><td rowspan='2'>x[{$n}] = {$x}</td><td>:</td><td>{$calc['0']}</td><td>{$calc['2']}</td><td>{$calc['4']}</td></tr>\n <tr><td>{$coef1}</td><td>{$calc['1']}</td><td>{$calc['3']}</td><td>{$calc['5']}</td></tr>";
$tabCalc_L .= "<tr style='border-top: 2px solid black;'><td rowspan='2'>x[{$n}] = {$x}</td><td>:</td><td>{$calc_L['0']}</td><td>{$calc_L['2']}</td></tr>\n <tr><td>{$coef1_L}</td><td>{$calc_L['1']}</td><td>{$calc_L['3']}</td></tr>";
$param['f(x[n])'] = $calc[5];
$param['f\'(x[n])'] = $calc_L[3];
if (empty($param['f\'(x[n])'])) {
//early exit (division by zero)
return false;
}
$param['h'] = correctNum($param['f(x[n])'] / $param['f\'(x[n])']);
$params[$n] = $param;
if (empty($param['h'])) {
// keeping coefs square equation for counting two other solutions
$resX[0] = $x;
$coef2 = $calc[1];
$coef3 = $calc[3] + $calc[5] * -1;
}
$x = correctNum($x - $param['h']);
$n++;
} while (!empty($param['h']) && $n < 56);
//if there is closing, 56 step will be last
$lastX = $params[count($params) - 1]['x[n]'];
$params[count($params) - 1]['x[n]'] = "<span style='color: green;'>{$lastX}</span>";
$d = correctNum(pow($coef2, 2) - 4 * $coef1 * $coef3);
$calcSquare = "<br />D = {$coef2}^2 - 4*{$coef1}*{$coef3} = {$d}";
$i = $d < 0 ? 'i' : '';
$calcSquare .= "{$i}<br /><br />";
$d = abs($d);
if ($d == 1) {
$resX[1] = -$coef2 / (2 * $coef1);
$calcSquare .= "x2 = -({$coef2}) / (2 * {$coef1}) = {$resX['1']}<br /><br />x1 = {$resX['0']}";
}
$resX[1] = correctNum((-$coef2 + pow($d, 1 / 2)) / (2 * $coef1));
$resX[2] = correctNum((-$coef2 - pow($d, 1 / 2)) / (2 * $coef1));
$calcSquare .= "x2 = (-({$coef2}) + {$d}{$i}^(1/2)) / (2*{$coef1}) = {$resX['1']}<br />x3 = (-({$coef2}) - {$d}{$i}^(1/2)) / (2*{$coef1}) = {$resX['2']}<br /><br />x1 = {$resX['0']}";
return [$params, $tabCalc, $tabCalc_L, $calcSquare];
}