22 files changed, 377 insertions, 114 deletions

diff --git a/.gitignore b/.gitignore
index 4b9dfd0..1bdd232 100644
--- a/.gitignore
+++ b/.gitignore
@@ -5,5 +5,6 @@ __pycache__/
 *.log
 *.out
 *.plot
+*.print
 vtek3/*.data
 */main
diff --git a/206/Makefile b/206/Makefile
new file mode 100644
index 0000000..224506f
--- /dev/null
+++ b/206/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
diff --git a/206/README.md b/206/README.md
new file mode 100644
index 0000000..96fd716
--- /dev/null
+++ b/206/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/206/compile_flags.txt b/206/compile_flags.txt
new file mode 100644
index 0000000..34ae930
--- /dev/null
+++ b/206/compile_flags.txt
@@ -0,0 +1,4 @@
+-Iinclude
+-std=c++2c
+-mavx2
+
diff --git a/206/data1 b/206/data1
new file mode 100644
index 0000000..c4b5435
--- /dev/null
+++ b/206/data1
@@ -0,0 +1,7 @@
+L	t1	t2	t3	t	St	st
+0.1	280	279	280	?	?	?
+0.2	568	569	567	?	?	?
+0.3	857	858	857	?	?	?
+0.4	1150	1150	1149	?	?	?
+0.5	1432	1431	1430	?	?	?
+0.6	1731	1730	1729	?	?	?
diff --git a/206/data2 b/206/data2
new file mode 100644
index 0000000..24cafe0
--- /dev/null
+++ b/206/data2
@@ -0,0 +1,27 @@
+t	T	sqrt(T)	tau	v
+51.0	?	?	1660	?
+50.0	?	?	1664	?
+48.8	?	?	1666	?
+47.9	?	?	1668	?
+47.0	?	?	1671	?
+46.0	?	?	1673	?
+45.0	?	?	1675	?
+44.0	?	?	1678	?
+43.0	?	?	1680	?
+42.0	?	?	1683	?
+41.0	?	?	1686	?
+40.0	?	?	1688	?
+39.0	?	?	1690	?
+38.0	?	?	1692	?
+37.0	?	?	1695	?
+36.0	?	?	1698	?
+35.0	?	?	1700	?
+34.0	?	?	1702	?
+33.0	?	?	1705	?
+32.0	?	?	1708	?
+31.0	?	?	1711	?
+30.0	?	?	1713	?
+28.8	?	?	1717	?
+28.0	?	?	1719	?
+27.2	?	?	1722	?
+26.0	?	?	1725	?
diff --git a/206/final.pdf b/206/final.pdf
new file mode 100644
index 0000000..f15f111
--- /dev/null
+++ b/206/final.pdf
diff --git a/206/include b/206/include
new file mode 120000
index 0000000..2225752
--- /dev/null
+++ b/206/include
@@ -0,0 +1 @@
+../libprakpp/include/
\ No newline at end of file
diff --git a/206/main.cpp b/206/main.cpp
new file mode 100644
index 0000000..8c94af3
--- /dev/null
+++ b/206/main.cpp
@@ -0,0 +1,51 @@
+#include <iostream>
+
+#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> &;
+
+void ex1(std::string file) {
+	table t(file);
+	f64 tmsgm = 1;
+	t	/*.multiply_column("t1", 1e-6)
+		.multiply_column("t2", 1e-6)
+		.multiply_column("t3", 1e-6)*/
+		.apply(prak::avg<f64>, {"t1", "t2", "t3"}, "t")
+		.apply(prak::stddev<f64>, {"t1", "t2", "t3"}, "St")
+		.apply([&](vecarg a) {return std::sqrt(a[0]*a[0] + tmsgm * tmsgm); }, "St", "st")
+		.write_plot("ex1.plot", "L", "t", "st")
+		.print();
+	auto [A, B] = t.least_squares_linear("L", "t", "st", std::nullopt);
+	A = A * 1e-6;
+	B = B * 1e-6;
+	f64p v = 1.0  / A;
+	std::cout  var(A) var(B) var(v);
+}
+
+void ex2(std::string file) {
+	table t(file);
+	f64 L0 = 0.6, mu = 29e-3;
+	t	.apply(prak::add<f64, conv::C_to_K<f64>>, "t", "T")
+		.apply([](vecarg a){ return std::sqrt(a[0]); }, "T", "sqrt(T)")
+		.multiply_column("tau", 1e-6)
+		.apply([&](vecarg a) { return L0 / a[0]; }, "tau", "v")
+		.write_plot("ex2.plot", "sqrt(T)", "v", std::nullopt)
+		.add_row({-273.15, 0, 0, 0, 0})
+		.print();
+	auto A = t.least_squares_prop("sqrt(T)", "v", std::nullopt, 0.01);
+	f64p gamma = A * A * mu / prak::R<f64>;
+	f64p Cv = prak::R<f64> / (gamma - 1.0), i = 2.0 / (gamma - 1.0);
+	f64p tau = 1.2041 * Cv * t.col_avg("v") * t.col_avg("v") / 4.0 / 1e6 / 0.0259;
+	std::cout var(L0) var(A) var(mu) var(gamma) var(Cv) var(i) var(tau);
+}
+
+int main() {
+	ex1("data1");
+	ex2("data2");
+	return 0;
+}
diff --git a/206/plots.gp b/206/plots.gp
new file mode 100644
index 0000000..5460021
--- /dev/null
+++ b/206/plots.gp
@@ -0,0 +1,38 @@
+set term pngcairo size 1000, 800
+set grid
+
+f1(x) = a1*x+b1
+fit f1(x) 'ex1.plot' using 1:2:3 yerr via a1, b1
+f2(x) = a2 * x
+fit f2(x) 'ex2.plot' using 1:2 via a2
+
+set output 'ex1.png'
+set title "Зависимость времени прохода волны от расстояния"
+set xlabel "L, м"
+set ylabel "t, мкc"
+set key top left
+
+set xrange[0:0.7]
+
+set label sprintf("A = %.4g\n B =%.4g", a1 / 10e6, b1 / 10e6) at graph 0.2, 0.9 front boxed
+plot 	'ex1.plot' using 1:2:3 with yerrorbars notitle lc 0 pt 1 lw 2,	\
+	f1(x) title "t(L)" lc rgb "red"
+
+
+set output 'ex2.png'
+set title "Зависимость скорости от корня из температуры"
+set xlabel "T^{1/2}, K^{1/2}"
+set ylabel "v, м/c"
+set key top left
+
+unset xrange
+unset label
+set label sprintf("A = %.4g", a2) at graph 0.2, 0.9 front boxed
+plot 	'ex2.plot' using 1:2 notitle lc 0 pt 1 lw 2,	\
+	f2(x) title "v(T^{1/2})" lc rgb "red"
+
+
+set output 'ex2_0.png'
+set title "Зависимость скорости от корня из температуры (проход через 0)"
+set xrange[0:19]
+replot
diff --git a/207/data3 b/207/data3
index ca2ca40..b2dd4dc 100644
--- a/207/data3
+++ b/207/data3
@@ -1,5 +1,5 @@
 n	P	T	V	x
-1	990.8	315.40	43.5	?
+1	980.8	315.40	43.5	?
 2	984.6	316.42	?	?
 3	986.8	317.22	?	?
 4	989.2	317.98	?	?
diff --git a/207/ex1_1.print b/207/ex1_1.print
deleted file mode 100644
index ec5efe0..0000000
--- a/207/ex1_1.print
+++ /dev/null
@@ -1,24 +0,0 @@
-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
deleted file mode 100644
index 9863903..0000000
--- a/207/ex1_4.print
+++ /dev/null
@@ -1,34 +0,0 @@
-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/main.cpp b/207/main.cpp
index 6f606bd..5424940 100644
--- a/207/main.cpp
+++ b/207/main.cpp
@@ -17,28 +17,70 @@ f64p add_nu(table& t) {
 }
 
 void ex1(table &t1, const char *name) {
+	// t = const
 	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);
+	t1	.add_columns({"DAi", "DSi", "lnViV0"})
+		.apply([&t1](vecarg a) -> f64 {
+			return prak::discrete_integral_trapezoid(
+				t1.begin("V"), std::find(t1.begin("V"), t1.end("V"), a[1])+1,
+				t1.begin("P"), std::find(t1.begin("P"), t1.end("P"), a[0])+1
+			);
+		}, {"P", "V"}, "DAi")
+		.apply([&t1](vecarg a){return a[0] / a[1];}, {"DAi", "T"}, "DSi")
+		.apply([&t1](vecarg a){ return std::log(a[0] / t1["V", 0]); }, "V", "lnViV0")
+		.apply([](vecarg a) {return std::abs(a[0]); }, "lnViV0", "lnViV0");
 	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);
+	f64p A = std::abs(t1.least_squares_prop("lnViV0", "DSi", std::nullopt, 0.1));
+	f64p R = A / nu;
+	std::cout << "Упражнение 1\n" var(DA) var(DS) var(nu) var(DS_teor) << "доп данные (упражнение 4):\n" 
+			var(A) var(R) << std::endl;
+	t1	.write_plot(std::string("PV") + name + ".plot", "V", "P", std::nullopt)
+		.write_plot(std::string("PVV") + name + ".plot", "V", "x", std::nullopt)
+		.write_plot(std::string("DSilnViV0_Tconst") + name + ".plot", "lnViV0", "DSi", std::nullopt);
 	std::ofstream f(std::string("ex1_") + name + ".print");
-	f << "Данные упражнения 1";
+	f << "Данные упражнения 1 (T = const)\n";
 	t1.print(f);
 	f.close();
 }
 
-void ex2(const table &t) {
-	
+void ex2(table &t) {
+	// p = const
+	std::cout << "Упражнение 2\n";
+	std::ofstream f("ex2.print");
+	f << "Данные упражнения 2 (P = const)\n";
+	f64p nu = add_nu(t);
+	t	.add_columns({"lnTiT0", "DSi"})
+		.apply([&t](vecarg a) -> f64 {return std::log(a[0] / t["T", 0]); }, "T", "lnTiT0")
+		.apply([&t, &nu](vecarg a) -> f64 { 
+			return nu.val * (prak::R<f64> * std::log(a[1] / t["V", 0]) + 5.0/2 * prak::R<f64> * a[2]); 
+		}, {"T", "V", "lnTiT0"}, "DSi")
+		.write_plot("DSilnTiT0_Pconst.plot", "lnTiT0", "DSi", std::nullopt)
+		.write_plot("VTV.plot", "V", "x", std::nullopt)
+		.print(f);
+	f64p A = t.least_squares_prop("lnTiT0", "DSi", std::nullopt, 0.1);
+	f64p Cp = A / nu;
+	std::cout var(nu) var(A) var(Cp);
 }
 
-void ex3(const table &t) {
-
-}
-
-void ex4(void) {
+void ex3(table &t) {
+	// v = const
+	std::cout << "Упражнение 3\n";
+	std::ofstream f("ex3.print");
+	f << "Данные упражнения 3 (V = const)\n";
+	f64p nu = add_nu(t);
+	t	.add_columns({"lnTiT0", "DSi"})
+		.apply([&t](vecarg a) -> f64 {return std::log(a[0] / t["T", 0]); }, "T", "lnTiT0")
+		.apply([&t, &nu](vecarg a) -> f64 { 
+			return nu.val * (-prak::R<f64> * std::log(a[0] / t["P", 0]) + 7.0/2 * prak::R<f64> * a[1]); 
+		}, {"P", "lnTiT0"}, "DSi")
+		.write_plot("DSilnTiT0_Vconst.plot", "lnTiT0", "DSi", std::nullopt)
+		.write_plot("PTP.plot", "P", "x", std::nullopt)
+		.print(f);
+	auto [A, B] = t.least_squares_linear("lnTiT0", "DSi", std::nullopt, 0.1);
+	f64p Cv = A / nu;
+	std::cout var(nu) var(A) var(Cv);
 
 }
 
@@ -77,7 +119,6 @@ void ex(void) {
 	ex1(tables[3], "4");
 	ex2(tables[1]);
 	ex3(tables[2]);
-	ex4();
 }
 
 int main() {
diff --git a/207/plots.gp b/207/plots.gp
index f197258..09b2442 100644
--- a/207/plots.gp
+++ b/207/plots.gp
@@ -1,16 +1,84 @@
 set term pngcairo size 1000, 800
 set grid
+f1(x) = a1*x
+f2(x) = a2*x
+f3(x) = a3*x+b3
+f4(x) = a4*x+b4
 
-#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 output 'ex4.png'
+fit f1(x) 'DSilnViV0_Tconst1.plot' using 1:2 via a1
+fit f2(x) 'DSilnViV0_Tconst4.plot' using 1:2 via a2
+
+set title "Зависимость                          при разных температурах"
+set xlabel "ед."
+set ylabel "S_i, Дж/К"
+
+plot	'DSilnViV0_Tconst1.plot' notitle lc 0 pt 1 lw 2,	\
+	f1(x) title "           (T = 289 K)" lc rgb "magenta",\
+	'DSilnViV0_Tconst4.plot' notitle lc 0 pt 1 lw 2,	\
+	f2(x) title "           (T = 3232.5 K)" lc rgb "red"
+
+
+set output 'ex1.png'
+unset label
+set title "зависимости P(V), PV(V) в изотермическом процессе при разных температурах"
+set xlabel "V, м^3"
+set ylabel "P, Па"
+set y2tics
+set y2label "PV, Па * м^3"
 set key top left
+set yrange[950:1200]
+set y2range[35000:45000]
+
+plot 	'PV1.plot' notitle axis x1y1 lc 0 pt 1 lw 2,	\
+	'PV1.plot' with lines axis x1y1 smooth csplines title "P(V) (T = 289 K)" lc rgb "orange", \
+	'PVV1.plot' notitle axis x1y2 lc 0 pt 1 lw 2, \
+	'PVV1.plot' with lines axis x1y2 smooth csplines title "PV(V) (T = 289 K)" lc rgb "magenta", \
+	'PV4.plot' notitle axis x1y1 lc 0 pt 1 lw 2,	\
+        'PV4.plot' with lines axis x1y1 smooth csplines title "P(V) (T = 323.5 K)" lc rgb "red", \
+        'PVV4.plot' notitle axis x1y2 lc 0 pt 1 lw 2, \
+        'PVV4.plot' with lines axis x1y2 smooth csplines title "PV(V) (T = 323.5 K)" lc rgb "green"
+
+
+set output 'ex23_mnk.png'
+fit f1(x) 'DSilnTiT0_Pconst.plot' using 1:2 via a1
+fit f2(x) 'DSilnTiT0_Vconst.plot' using 1:2 via a2
+
+unset xrange
+unset yrange
+unset x2tics
+unset y2label
+unset y2range
+set title "зависимости                      при P = const, V = const"
+set xlabel "ед."
+set ylabel "S_i, Дж/К"
+
+set label sprintf("(A)_P = %.4g\n (A)_V = %.4g", a1, a2) at graph 0.2, 0.9 front boxed
+plot	'DSilnTiT0_Vconst.plot' notitle lc rgb "green" pt 1 lw 3,\
+	'DSilnTiT0_Pconst.plot' notitle lc rgb "magenta" pt 2 lw 3,\
+	f2(x) title "V = const" lc rgb "green",\
+	f1(x) title "P = const" lc rgb "magenta"
+unset label
+
+set output 'ex2.png'
+set title "Зависимость V/T от V при P = const"
+set xlabel "V, м^3"
+set ylabel "V/T, м^3/К"
+set yrange[0.13:0.14]
+
+plot	'VTV.plot' notitle lc 0 pt 1 lw 2,\
+	'VTV.plot' title "V/T (V)" lc rgb "magenta" with lines smooth csplines
+
+
+
+set output 'ex3.png'
 
-#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"
+set title "Зависимость P/T (P) при V = const (по большей части)"
+set xlabel "P, Па"
+set ylabel "P/T, Па/K"
+set yrange[3:3.2]
+set xrange [980:1001]
 
+plot	'PTP.plot' notitle lc 0 pt 1 lw 2,\
+        'PTP.plot' title "P/T (P)" lc rgb "magenta" with lines smooth path
diff --git a/207/print.txt b/207/print.txt
deleted file mode 100644
index 85be337..0000000
--- a/207/print.txt
+++ /dev/null
@@ -1,25 +0,0 @@
-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/prakcommon.hpp b/libprakpp/include/prakcommon.hpp
index 074e290..dcafecf 100644
--- a/libprakpp/include/prakcommon.hpp
+++ b/libprakpp/include/prakcommon.hpp
@@ -1,5 +1,7 @@
 #pragma once
 
+#include <cstddef>
+#include <cstdint>
 #include <cmath>
 #include <functional>
 #include <vector>
@@ -132,3 +134,7 @@ template <typename T> struct pvalue<T> operator-(const T &a, const struct pvalue
 template <typename T> std::ostream &operator<<(std::ostream &os, const struct pvalue<T> &p) { return os << p.val << "±" << p.err; }
 
 } // namespace prak
+
+namespace std {
+template <typename T> struct prak::pvalue<T> abs(const struct prak::pvalue<T> &p) { return {abs(p.val), abs(p.err)}; }
+}
diff --git a/libprakpp/include/prakmath.hpp b/libprakpp/include/prakmath.hpp
index bb09e74..d43c11f 100644
--- a/libprakpp/include/prakmath.hpp
+++ b/libprakpp/include/prakmath.hpp
@@ -321,7 +321,6 @@ void least_squares_linear(
 			  << ", s.size() = " << ss.size() << std::endl;
 		return;
 	}
-	[[assume(xs.size() == ys.size() && ys.size() == ss.size())]];
 	size_t sz = xs.size();
 
 	prak::vector<T> ones(sz);
@@ -364,6 +363,27 @@ void least_squares_linear(
 	b.err = sqrt(d1 / D);
 }
 
+template <std::floating_point T>
+void least_squares_prop(
+	const prak::vector<T> &xs, 
+	const prak::vector<T> &ys, 
+	const prak::vector<T> &ss, 
+	struct pvalue<T> &a) {
+	assert("Different-sized vectors passed to least squares method" && xs.size() == ys.size());
+	size_t s = xs.size();
+	prak::vector<T> buf(s), si(s);
+	vmul(ss.data(), ss.data(), si.data(), s);
+	
+	vmul(xs.data(), ys.data(), buf.data(), s);
+	vdiv(buf.data(), ss.data(), buf.data(), s);
+	T D1 = vsum(buf.data(), s);
+	
+	vmul(xs.data(), xs.data(), buf.data(), s);
+	vdiv(buf.data(), ss.data(), buf.data(), s);
+	T D2 = vsum(buf.data(), s);
+	a.val = D1/D2;
+	a.err = 1/D2;
+}
 
 /// May throw std::bad_optional_access
 template <typename T>
diff --git a/libprakpp/include/prakmatrix.hpp b/libprakpp/include/prakmatrix.hpp
index f1ccddc..2f87401 100644
--- a/libprakpp/include/prakmatrix.hpp
+++ b/libprakpp/include/prakmatrix.hpp
@@ -2,6 +2,7 @@
 
 #include "prakcommon.hpp"
 
+#include <iomanip>
 #include <cstring>
 #include <ostream>
 #include <optional>
@@ -75,7 +76,7 @@ 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>>::type
+	typename 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)
@@ -161,12 +162,27 @@ struct matrix : public std::vector<T> {
 		}
 		return ret;
 	}
+	
+	void add_row(size_t index, std::vector<T> row_data) {
+		++rows;
+		this->resize(rows * cols);
+		memmove(this->data() + cols * (index+1), this->data() + cols * index, (rows - index - 1) * cols * sizeof (T));
+		for (size_t i = 0; i < cols; ++i)
+			this->operator[](index * cols + i) = row_data[i];
+	}
+	void add_column(size_t index, std::vector<T> column_data) {
+		this->reserve(rows * (cols + 1));
+		for (size_t i = 0; i < rows; ++i)
+			this->insert(this->begin() + (cols + 1) * i + index, column_data[i]);
+		++cols;
+	}
 
 	std::ostream &print(std::ostream &out = std::cout, size_t width = 10) const {
+		std::cout.setf(std::ios::left);
 		for (size_t row = 0; row < rows; ++row) {
 			for (size_t col = 0; col < cols; ++col)
-				out << "|" << std::setw(width) << SUBSCR_OPRTR(row, col); 
-			std::cout << "|\n";
+				out /*<< "|"*/ << std::setw(width) << SUBSCR_OPRTR(row, col); 
+			std::cout << "\n";
 		}
 		return out;
 	}
diff --git a/libprakpp/include/praktable.hpp b/libprakpp/include/praktable.hpp
index 1870ec6..aabcb8e 100644
--- a/libprakpp/include/praktable.hpp
+++ b/libprakpp/include/praktable.hpp
@@ -105,10 +105,10 @@ public:
 		iterator operator--(int) { iterator ret = *this; --(*this); return ret; }
 		iterator &operator+(int x) { data_index += columns * x; return *this; }
 		iterator &operator-(int x) { data_index -= columns * x; return *this; }
-		std::strong_ordering operator<=>(const iterator& other) {
+		std::strong_ordering operator<=>(const iterator& other) const {
 			return parent == other.parent && col_index == other.col_index && data_index <=> other.data_index;
 		}
-		bool operator==(const iterator& other) {
+		bool operator==(const iterator& other) const {
 			return parent == other.parent && col_index == other.col_index && data_index == other.data_index;
 		}
 		reference operator*() { return parent->data[data_index]; };
@@ -270,6 +270,18 @@ public:
 
 	// apply a function to several columns and store result in another column
 	// function must accept std::vector or arguments
+	table &apply(function_type function, std::initializer_list<std::string> _args, std::optional<std::string> result) {
+		std::vector<std::string> args = _args;
+		size_t result_index = result.has_value() ? index(*result) : 0;
+		for (size_t i = 0; i < rows; ++i) {
+			std::vector<dtype> v(args.size());
+			for (size_t j = 0; j < args.size(); ++j) 
+				v[j] = SUBSCR_OPRTR(args[j], i);
+			if (result.has_value()) data[columns * i + result_index] = function(v);
+			else (void)function(v);
+		}
+		return *this;
+	}
 	table &apply(function_type function, stringvec args, std::optional<std::string> result) {
 		size_t result_index = result.has_value() ? index(*result) : 0;
 		for (size_t i = 0; i < rows; ++i) {
@@ -281,7 +293,6 @@ public:
 		}
 		return *this;
 	}
-
 	table& apply(function_type function, const std::string& arg, std::optional<std::string> result) {
 		size_t result_index = result.has_value() ? index(*result) : 0;
 		for (size_t i = 0; i < rows; ++i) {
@@ -411,11 +422,12 @@ public:
 
 
 	// Appends a row to the table. if name is set, appends it to `opt_rownames`
-	void add_row(std::vector<dtype> values, std::optional<std::string> name = std::nullopt) {
+	table& add_row(std::vector<dtype> values, std::optional<std::string> name = std::nullopt) {
 		if (values.size() == 0) values = std::vector<dtype>(columns, dtype{});
 		data.resize(columns * (++rows));
 		std::copy_n(values.cbegin(), columns, data.end() - columns);
 		if (name.has_value()) opt_rownames.push_back(*name);
+		return *this;
 	}
 
 
@@ -518,6 +530,23 @@ public:
 		prak::least_squares_linear<dtype>(_x, _y, _s, ret.first, ret.second);
 		return ret;
 	}
+	prak::pvalue<dtype>
+	least_squares_prop(std::string x, std::string y, std::optional<std::string> sigma, std::optional<dtype> sigma_fixed) const {
+		if (sigma.has_value() == sigma_fixed.has_value()) 
+			throw std::invalid_argument("sigma and sigma_fixed can't both have (no) value");
+		prak::vector<dtype> _x(rows);
+		prak::vector<dtype> _y(rows);
+		prak::vector<dtype> _s(rows);
+
+		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));
+		
+		prak::pvalue<dtype> ret;
+		prak::least_squares_prop(_x, _y, _s, ret);
+		return ret;
+	}
 
 	// calculate an average of the column 
 	dtype col_avg(const std::string &column) const {
diff --git a/libprakpp/tests/matrix.cpp b/libprakpp/tests/matrix.cpp
new file mode 100644
index 0000000..dffecef
--- /dev/null
+++ b/libprakpp/tests/matrix.cpp
@@ -0,0 +1,14 @@
+#include "../include/prakmatrix.hpp"
+
+int main() {
+	using namespace prak;
+	prak::matrix<const char*> a(2, 3, {
+		"раз", "два", "три",
+		"4", "5s", "6"
+	});
+	std::cout << "\x1b[0;91m" << a;
+	a.add_row(1, {"6", "6", "6"});
+	std::cout << "\x1b[0;92m" << a;
+	a.add_column(0, {"9", "9", "9"});
+	std::cout << "\x1b[0;93m" << a;
+}
diff --git a/tempalte/Makefile b/tempalte/Makefile
index 224506f..3f1ad56 100644
--- a/tempalte/Makefile
+++ b/tempalte/Makefile
@@ -15,4 +15,4 @@ main: main.cpp include/*
 	$(CXX) -o $@ $< $(CFLAGS)
 
 clean: 
-	rm -fr main *.png *.plot
+	rm -fr main *.png *.plot *.print *.log