Started doing 207

16 files changed, 297 insertions, 14 deletions

diff --git a/207/Makefile b/207/Makefile
new file mode 100644
index 0000000..17aed33
--- /dev/null
+++ b/207/Makefile
@@ -0,0 +1,18 @@
+
+CFLAGS = -std=c++2c -mavx -Iinclude -ggdb
+
+.PHONY: all run_main clean gnuplot 
+
+run: gnuplot
+
+gnuplot: plots.gp run_main
+	gnuplot $< &>/dev/null
+
+run_main: main
+	./main
+
+main: main.cpp include/*
+	$(CXX) -o $@ $< $(CFLAGS)
+
+clean: 
+	rm -fr main *.png *.plot *.print
diff --git a/207/README.md b/207/README.md
new file mode 100644
index 0000000..96fd716
--- /dev/null
+++ b/207/README.md
@@ -0,0 +1,5 @@
+<!-- Шаблон для прака -->
+<!-- файлы, заканчивающиеся на .plot считаются генерируемыми и удаляются через make clean -->
+# Обработка <> прака
+
+
diff --git a/207/compile_flags.txt b/207/compile_flags.txt
new file mode 100644
index 0000000..34ae930
--- /dev/null
+++ b/207/compile_flags.txt
@@ -0,0 +1,4 @@
+-Iinclude
+-std=c++2c
+-mavx2
+
diff --git a/207/data1 b/207/data1
new file mode 100644
index 0000000..0675a6e
--- /dev/null
+++ b/207/data1
@@ -0,0 +1,11 @@
+n	P	T	V	x
+1	1110.3	289.9	35.5	?
+2	1091.8	289.9	36.0	?
+3	1089.9	289.9	36.5	?
+4	1074.4	289.9	37.0	?
+5	1062.4	289.9	37.5	?
+6	1050.0	289.9	38.0	?
+7	1038.8	289.9	38.5	?
+8	1024.0	289.9	39.0	?
+9	1012.2	289.9	39.5	?
+10	996.5	289.9	40.0	?
diff --git a/207/data2 b/207/data2
new file mode 100644
index 0000000..c5cabbf
--- /dev/null
+++ b/207/data2
@@ -0,0 +1,7 @@
+n	P	T	V	x
+1	991.0	298.33	40.0	?
+2	991.0	302.84	40.5	?
+3	991.7	305.34	41.0	?
+4	991.2	307.78	41.5	?
+5	991.0	310.46	42.0	?
+6	990.8	313.57	42.5	?
diff --git a/207/data3 b/207/data3
new file mode 100644
index 0000000..ca2ca40
--- /dev/null
+++ b/207/data3
@@ -0,0 +1,12 @@
+n	P	T	V	x
+1	990.8	315.40	43.5	?
+2	984.6	316.42	?	?
+3	986.8	317.22	?	?
+4	989.2	317.98	?	?
+5	993.0	319.17	?	?
+6	995.3	320.04	?	?
+7	997.1	321.03	44.0	?
+8	998.5	322.02	?	?
+9	1000.0	323.02	?	?
+10	1000.0	323.85	?	?
+11	998.0	323.91	44.5	?
diff --git a/207/data4 b/207/data4
new file mode 100644
index 0000000..4941d5c
--- /dev/null
+++ b/207/data4
@@ -0,0 +1,16 @@
+n	P	T	V	x
+1	997.1	323.61	44.5	?
+2	997.4	323.51	44.0	?
+3	999.0	323.51	43.5	?
+4	1014.2	323.48	43.0	?
+5	1023.3	323.48	42.5	?
+6	1037.3	323.38	42.0	?
+7	1048.0	323.38	41.5	?
+8	1060.0	323.35	41.0	?
+9	1070.7	323.35	40.5	?
+10	1083.8	323.35	40.0	?
+11	1098.5	323.35	39.5	?
+12	1108.8	323.35	39.0	?
+13	1122.9	323.35	38.5	?
+14	1139.0	323.35	38.0	?
+15	1148.1	323.28	37.5	?
diff --git a/207/ex1_1.print b/207/ex1_1.print
new file mode 100644
index 0000000..ec5efe0
--- /dev/null
+++ b/207/ex1_1.print
@@ -0,0 +1,24 @@
+Данные упражнения 1columns: 6, rows: 10
+_______________________________________________________________________________
+|n           |P           |T           |V           |x           |nu          |
+|____________|____________|____________|____________|____________|____________|
+|1           |1110.3      |289.9       |35.5        |39415.7     |16.3526     |
+|____________|____________|____________|____________|____________|____________|
+|2           |1091.8      |289.9       |36          |39304.8     |16.3066     |
+|____________|____________|____________|____________|____________|____________|
+|3           |1089.9      |289.9       |36.5        |39781.4     |16.5043     |
+|____________|____________|____________|____________|____________|____________|
+|4           |1074.4      |289.9       |37          |39752.8     |16.4925     |
+|____________|____________|____________|____________|____________|____________|
+|5           |1062.4      |289.9       |37.5        |39840       |16.5286     |
+|____________|____________|____________|____________|____________|____________|
+|6           |1050        |289.9       |38          |39900       |16.5535     |
+|____________|____________|____________|____________|____________|____________|
+|7           |1038.8      |289.9       |38.5        |39993.8     |16.5924     |
+|____________|____________|____________|____________|____________|____________|
+|8           |1024        |289.9       |39          |39936       |16.5685     |
+|____________|____________|____________|____________|____________|____________|
+|9           |1012.2      |289.9       |39.5        |39981.9     |16.5875     |
+|____________|____________|____________|____________|____________|____________|
+|10          |996.5       |289.9       |40          |39860       |16.5369     |
+|____________|____________|____________|____________|____________|____________|
diff --git a/207/ex1_4.print b/207/ex1_4.print
new file mode 100644
index 0000000..9863903
--- /dev/null
+++ b/207/ex1_4.print
@@ -0,0 +1,34 @@
+Данные упражнения 1columns: 6, rows: 15
+_______________________________________________________________________________
+|n           |P           |T           |V           |x           |nu          |
+|____________|____________|____________|____________|____________|____________|
+|1           |997.1       |323.61      |44.5        |44371       |16.4908     |
+|____________|____________|____________|____________|____________|____________|
+|2           |997.4       |323.51      |44          |43885.6     |16.3155     |
+|____________|____________|____________|____________|____________|____________|
+|3           |999         |323.51      |43.5        |43456.5     |16.156      |
+|____________|____________|____________|____________|____________|____________|
+|4           |1014.2      |323.48      |43          |43610.6     |16.2148     |
+|____________|____________|____________|____________|____________|____________|
+|5           |1023.3      |323.48      |42.5        |43490.2     |16.17       |
+|____________|____________|____________|____________|____________|____________|
+|6           |1037.3      |323.38      |42          |43566.6     |16.2034     |
+|____________|____________|____________|____________|____________|____________|
+|7           |1048        |323.38      |41.5        |43492       |16.1757     |
+|____________|____________|____________|____________|____________|____________|
+|8           |1060        |323.35      |41          |43460       |16.1653     |
+|____________|____________|____________|____________|____________|____________|
+|9           |1070.7      |323.35      |40.5        |43363.3     |16.1293     |
+|____________|____________|____________|____________|____________|____________|
+|10          |1083.8      |323.35      |40          |43352       |16.1251     |
+|____________|____________|____________|____________|____________|____________|
+|11          |1098.5      |323.35      |39.5        |43390.8     |16.1395     |
+|____________|____________|____________|____________|____________|____________|
+|12          |1108.8      |323.35      |39          |43243.2     |16.0846     |
+|____________|____________|____________|____________|____________|____________|
+|13          |1122.9      |323.35      |38.5        |43231.7     |16.0803     |
+|____________|____________|____________|____________|____________|____________|
+|14          |1139        |323.35      |38          |43282       |16.0991     |
+|____________|____________|____________|____________|____________|____________|
+|15          |1148.1      |323.28      |37.5        |43053.8     |16.0176     |
+|____________|____________|____________|____________|____________|____________|
diff --git a/207/include b/207/include
new file mode 120000
index 0000000..2225752
--- /dev/null
+++ b/207/include
@@ -0,0 +1 @@
+../libprakpp/include/
\ No newline at end of file
diff --git a/207/main.cpp b/207/main.cpp
new file mode 100644
index 0000000..6f606bd
--- /dev/null
+++ b/207/main.cpp
@@ -0,0 +1,86 @@
+#include <cmath>
+#include <iostream>
+#include <ranges>
+
+#include "include/praktable.hpp"
+#include "include/prakphys.hpp"
+
+using table = prak::table<f64>;
+using f64p = prak::pvalue<f64>;
+using f64v = std::vector<f64>;
+using vecarg = const std::vector<f64> &;
+using argvec = const std::vector<f64> &;
+
+f64p add_nu(table& t) {
+	t.add_column("nu").apply([](vecarg a) { return a[0] * a[1] / (prak::R<f64> * a[2]); }, {"P", "V", "T"}, "nu");
+	return {t.col_avg("nu"), t.col_stddev("nu")};
+}
+
+void ex1(table &t1, const char *name) {
+	f64 DA = prak::discrete_integral_trapezoid(t1.cbegin("V"), t1.cend("V"), t1.cbegin("P"), t1.cend("P"));
+	f64 DS = DA / t1.col_avg("T");
+	f64p nu = add_nu(t1);
+	f64p DS_teor = nu * prak::R<f64> * std::abs(std::log(*(t1.end("V")-1) / *t1.begin("V")));
+	std::cout << "Упражнение 1\n" var(DA) var(DS) var(nu) var(DS_teor) << std::endl;
+	t1.write_plot(std::string("P(V)") + name + ".plot", "V", "P", std::nullopt);
+	t1.write_plot(std::string("PV(V)") + name + ".plot", "V", "x", std::nullopt);
+	std::ofstream f(std::string("ex1_") + name + ".print");
+	f << "Данные упражнения 1";
+	t1.print(f);
+	f.close();
+}
+
+void ex2(const table &t) {
+	
+}
+
+void ex3(const table &t) {
+
+}
+
+void ex4(void) {
+
+}
+
+void ex(void) {
+	table tables[] = {table("data1"), table("data2"), table("data3"), table("data4")};
+
+	// approximate how the volume should have changed in ex3 using parabola
+	std::vector<f64> mrxdata; mrxdata.reserve(9);
+	std::vector<f64> mrydata; mrydata.reserve(3);
+	for (size_t i = 0; i < tables[2].rows; ++i) {
+		if (f64 v; !std::isnan(v = tables[2]["V", i])) {
+			f64 n = tables[2]["n", i];
+			mrxdata.push_back(n*n);
+			mrxdata.push_back(n);
+			mrxdata.push_back(1);
+			mrydata.push_back(v);
+		}
+	}
+	prak::matrix<f64> xs(3, 3, std::move(mrxdata)), ys(3, 1, std::move(mrydata));
+	prak::matrix<f64> poly = xs.inv().value() * ys;
+	for (size_t i = 0; i < tables[2].rows; ++i)
+		tables[2]["V", i] = (poly.tr() * prak::matrix<f64>(3, 1, {(double)(i+1)*(i+1), (double)(i+1), 1}))[0, 0];
+
+	std::function<f64(vecarg)> fs[] = {
+		[](vecarg a) { return a[0] * a[1]; },
+		[](vecarg a) { return a[0] / a[1]; },
+		[](vecarg a) { return a[0] / a[1]; },
+		[](vecarg a) { return a[0] * a[1]; },
+	};
+	std::vector<std::string> vs[] = {
+		{"P", "V"}, {"V", "T"}, {"P", "T"}, {"P", "V"},
+	};
+	for (auto elem : std::views::zip(tables, fs, vs))
+		std::get<0>(elem).apply(std::get<1>(elem), std::get<2>(elem), "x");
+	ex1(tables[0], "1");
+	ex1(tables[3], "4");
+	ex2(tables[1]);
+	ex3(tables[2]);
+	ex4();
+}
+
+int main() {
+	ex();	
+	return 0;
+}
diff --git a/207/plots.gp b/207/plots.gp
new file mode 100644
index 0000000..f197258
--- /dev/null
+++ b/207/plots.gp
@@ -0,0 +1,16 @@
+set term pngcairo size 1000, 800
+set grid
+
+#f1(x) = a1*x+b1
+#fit f1(x) '.plot' using 1:2:3 yerr via a1, b1
+
+set output ''
+set title ""
+set xlabel ""
+set ylabel ""
+set key top left
+
+#set label sprintf("A = %.4g\n B = %.4g", a1, b1) at graph 0.2, 0.9 front boxed
+#plot 	'.plot' using 1:2:3 with yerrorbars notitle lc 0 pt 1 lw 2,	\
+#	f1(x) title "" lc rgb "red"
+
diff --git a/207/print.txt b/207/print.txt
new file mode 100644
index 0000000..85be337
--- /dev/null
+++ b/207/print.txt
@@ -0,0 +1,25 @@
+columns: 5, rows: 10
+__________________________________________________________________
+|n           |P           |T           |V           |x           |
+|____________|____________|____________|____________|____________|
+|1           |1110.3      |289.9       |35.5        |39415.7     |
+|____________|____________|____________|____________|____________|
+|2           |1091.8      |289.9       |36          |39304.8     |
+|____________|____________|____________|____________|____________|
+|3           |1089.9      |289.9       |36.5        |39781.4     |
+|____________|____________|____________|____________|____________|
+|4           |1074.4      |289.9       |37          |39752.8     |
+|____________|____________|____________|____________|____________|
+|5           |1062.4      |289.9       |37.5        |39840       |
+|____________|____________|____________|____________|____________|
+|6           |1050        |289.9       |38          |39900       |
+|____________|____________|____________|____________|____________|
+|7           |1038.8      |289.9       |38.5        |39993.8     |
+|____________|____________|____________|____________|____________|
+|8           |1024        |289.9       |39          |39936       |
+|____________|____________|____________|____________|____________|
+|9           |1012.2      |289.9       |39.5        |39981.9     |
+|____________|____________|____________|____________|____________|
+|10          |996.5       |289.9       |40          |39860       |
+|____________|____________|____________|____________|____________|
+
diff --git a/libprakpp/include/prakmath.hpp b/libprakpp/include/prakmath.hpp
index ebd02bf..bb09e74 100644
--- a/libprakpp/include/prakmath.hpp
+++ b/libprakpp/include/prakmath.hpp
@@ -289,6 +289,22 @@ pvalue<T> function(function_t<T> func, const std::vector<pvalue<T>> &args) {
 	return ret;
 }
 
+template <typename iterator, typename T = iterator::value_type>
+requires requires(iterator a){ ++a; *a; } && (std::integral<T> || std::floating_point<T>)
+T discrete_integral_trapezoid(iterator X_start, iterator X_end, iterator Y_start, iterator Y_end)
+{
+	T ret = 0;
+	for (T Xl = *X_start, Yl = *Y_start; 
+	     X_start != X_end && Y_start != Y_end; 
+	     ++X_start, ++Y_start) 
+	{
+		ret += std::abs(*X_start - Xl) * (*Y_start + Yl) / 2; // first iteration will add 0
+		Xl = *X_start;
+		Yl = *Y_start;
+	}
+	return ret;
+}
+
 /// calculate least-squares linear approximation to fit data
 /// ax+b = y (ss is an error of Y value)
 template <std::floating_point T>
diff --git a/libprakpp/include/prakmatrix.hpp b/libprakpp/include/prakmatrix.hpp
index 53d3b4b..f1ccddc 100644
--- a/libprakpp/include/prakmatrix.hpp
+++ b/libprakpp/include/prakmatrix.hpp
@@ -14,7 +14,7 @@ struct dimension_error : public std::logic_error {
 };
 
 /// A class to represent a matrix. Works as an extension to std::vector, so all methods of std::vector are available on this class
-/// BIG TODO: replave `throw` with `std::optional` return type
+/// BIG TODO: replace `throw` with `std::optional` return type
 template <typename T>
 struct matrix : public std::vector<T> {
 	size_t rows, cols;
@@ -75,7 +75,7 @@ struct matrix : public std::vector<T> {
 	}
 	/// multiply matrix by a scalar
 	template <typename Arg>
-	std::enable_if_t<std::is_arithmetic_v<Arg>, struct matrix<T>> 
+	std::enable_if_t<std::is_arithmetic_v<Arg>, struct matrix<T>>::type
 	operator*(const Arg other) const {
 		struct matrix<T> ret(rows, cols);
 		for (size_t i = 0; i < this->size(); ++i)
diff --git a/libprakpp/include/praktable.hpp b/libprakpp/include/praktable.hpp
index f00e7b9..1870ec6 100644
--- a/libprakpp/include/praktable.hpp
+++ b/libprakpp/include/praktable.hpp
@@ -222,6 +222,14 @@ public:
 		return data.at(names.size() * row + column);
 	}
 
+	const dtype & SUBSCR_OPRTR (const std::string &column, size_t row) const noexcept(false) {
+		size_t i = index(column);
+		return data.at(names.size() * row + index(column));
+	}
+
+	const dtype & SUBSCR_OPRTR (size_t column, size_t row) const {
+		return data.at(names.size() * row + column);
+	}
 	// prints a table. defaults to using std::cout, but any std::ostream can be passed in it.
 	void print(std::ostream &stream = std::cout) const {
 		stream << "columns: " << columns << ", rows: " << rows << std::endl;
@@ -493,7 +501,7 @@ public:
 
 	// returns an std::pair with coefficients A and B in that order
 	std::pair<prak::pvalue<dtype>, prak::pvalue<dtype>> 
-	least_squares_linear(std::string x, std::string y, std::optional<std::string> sigma, std::optional<dtype> sigma_fixed) 
+	least_squares_linear(std::string x, std::string y, std::optional<std::string> sigma, std::optional<dtype> sigma_fixed) const
 	noexcept(false) {
 		if (sigma.has_value() == sigma_fixed.has_value()) 
 			throw std::invalid_argument("sigma and sigma_fixed can't both have (no) value");
@@ -501,9 +509,9 @@ public:
 		prak::vector<dtype> _y(rows);
 		prak::vector<dtype> _s(rows);
 
-		std::copy(begin(x), end(x), _x.begin());
-		std::copy(begin(y), end(y), _y.begin());
-		if (sigma.has_value()) std::copy(begin(*sigma), end(*sigma), _s.begin());
+		std::copy(cbegin(x), cend(x), _x.begin());
+		std::copy(cbegin(y), cend(y), _y.begin());
+		if (sigma.has_value()) std::copy(cbegin(*sigma), cend(*sigma), _s.begin());
 		else _s = prak::vector<dtype>(rows, static_cast<dtype>(*sigma_fixed));
 
 		std::pair<prak::pvalue<dtype>, prak::pvalue<dtype>> ret;
@@ -512,31 +520,31 @@ public:
 	}
 
 	// calculate an average of the column 
-	dtype col_avg(const std::string &column) {
+	dtype col_avg(const std::string &column) const {
 		dtype accum = dtype{};
-		for (auto it = begin(column); it != end(column); ++it) 
+		for (auto it = cbegin(column); it != cend(column); ++it) 
 			accum += *it;
 		return accum / rows;
 	}
 
-	dtype col_max(const std::string &column) {
+	dtype col_max(const std::string &column) const {
 		dtype max = dtype{};
-		for (auto it = begin(column); it != end(column); ++it) 
+		for (auto it = cbegin(column); it != cend(column); ++it) 
 			max = max < *it ? *it : max;
 		return max;
 	}
-	dtype col_min(const std::string &column) {
+	dtype col_min(const std::string &column) const {
 		dtype min = dtype{};
-		for (auto it = begin(column); it != end(column); ++it) 
+		for (auto it = cbegin(column); it != cend(column); ++it) 
 			min = min > *it ? *it : min;
 		return min;
 	}
 
 	// calculate standard deviation of the column
-	dtype col_stddev(const std::string &column) {
+	dtype col_stddev(const std::string &column) const {
 		dtype accum = dtype{};
 		dtype avg = col_avg(column);
-		for (auto it = begin(column); it != end(column); ++it)
+		for (auto it = cbegin(column); it != cend(column); ++it)
 			accum += (*it - avg)*(*it - avg);
 		return std::sqrt(accum / rows);
 	}