{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Part 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 1"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a =\n",
"\n",
" 1.2000 5.4000 6.0000 1.5000 9.0000\n",
"\n",
"b =\n",
"\n",
" 5.2000 3.1416 1.2000 1.5000 2.0000\n",
"\n"
]
}
],
"source": [
"a = [1.2 5.4 6 1.5 9]\n",
"b = [5.2 pi 1.2 1.5 2]"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1.0954 2.3238 2.4495 1.2247 3.0000\n",
"\n"
]
}
],
"source": [
"sqrt(a)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1.8221 14.8797 20.0855 2.1170 90.0171\n",
"\n"
]
}
],
"source": [
"e.^(a/2)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 6.4000 8.5416 7.2000 3.0000 11.0000\n",
"\n"
]
}
],
"source": [
"a + b"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 6.2400 16.9646 7.2000 2.2500 18.0000\n",
"\n"
]
}
],
"source": [
"a.* b"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"v1 =\n",
"\n",
" Columns 1 through 6:\n",
"\n",
" 0.00000 0.50000 1.00000 1.50000 2.00000 2.50000\n",
"\n",
" Columns 7 through 12:\n",
"\n",
" 3.00000 3.50000 4.00000 4.50000 5.00000 5.50000\n",
"\n",
" Columns 13 through 18:\n",
"\n",
" 6.00000 6.50000 7.00000 7.50000 8.00000 8.50000\n",
"\n",
" Columns 19 through 24:\n",
"\n",
" 9.00000 9.50000 10.00000 10.50000 11.00000 11.50000\n",
"\n",
" Columns 25 through 30:\n",
"\n",
" 12.00000 12.50000 13.00000 13.50000 14.00000 14.50000\n",
"\n",
" Columns 31 through 36:\n",
"\n",
" 15.00000 15.50000 16.00000 16.50000 17.00000 17.50000\n",
"\n",
" Columns 37 through 42:\n",
"\n",
" 18.00000 18.50000 19.00000 19.50000 20.00000 20.50000\n",
"\n",
" Columns 43 through 48:\n",
"\n",
" 21.00000 21.50000 22.00000 22.50000 23.00000 23.50000\n",
"\n",
" Columns 49 through 54:\n",
"\n",
" 24.00000 24.50000 25.00000 25.50000 26.00000 26.50000\n",
"\n",
" Columns 55 through 60:\n",
"\n",
" 27.00000 27.50000 28.00000 28.50000 29.00000 29.50000\n",
"\n",
" Column 61:\n",
"\n",
" 30.00000\n",
"\n"
]
}
],
"source": [
"v1 = 0 : 0.5 : 30"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"v =\n",
"\n",
" Columns 1 through 8:\n",
"\n",
" 1.0000 1.0101 1.0202 1.0303 1.0404 1.0505 1.0606 1.0707\n",
"\n",
" Columns 9 through 16:\n",
"\n",
" 1.0808 1.0909 1.1010 1.1111 1.1212 1.1313 1.1414 1.1515\n",
"\n",
" Columns 17 through 24:\n",
"\n",
" 1.1616 1.1717 1.1818 1.1919 1.2020 1.2121 1.2222 1.2323\n",
"\n",
" Columns 25 through 32:\n",
"\n",
" 1.2424 1.2525 1.2626 1.2727 1.2828 1.2929 1.3030 1.3131\n",
"\n",
" Columns 33 through 40:\n",
"\n",
" 1.3232 1.3333 1.3434 1.3535 1.3636 1.3737 1.3838 1.3939\n",
"\n",
" Columns 41 through 48:\n",
"\n",
" 1.4040 1.4141 1.4242 1.4343 1.4444 1.4545 1.4646 1.4747\n",
"\n",
" Columns 49 through 56:\n",
"\n",
" 1.4848 1.4949 1.5051 1.5152 1.5253 1.5354 1.5455 1.5556\n",
"\n",
" Columns 57 through 64:\n",
"\n",
" 1.5657 1.5758 1.5859 1.5960 1.6061 1.6162 1.6263 1.6364\n",
"\n",
" Columns 65 through 72:\n",
"\n",
" 1.6465 1.6566 1.6667 1.6768 1.6869 1.6970 1.7071 1.7172\n",
"\n",
" Columns 73 through 80:\n",
"\n",
" 1.7273 1.7374 1.7475 1.7576 1.7677 1.7778 1.7879 1.7980\n",
"\n",
" Columns 81 through 88:\n",
"\n",
" 1.8081 1.8182 1.8283 1.8384 1.8485 1.8586 1.8687 1.8788\n",
"\n",
" Columns 89 through 96:\n",
"\n",
" 1.8889 1.8990 1.9091 1.9192 1.9293 1.9394 1.9495 1.9596\n",
"\n",
" Columns 97 through 100:\n",
"\n",
" 1.9697 1.9798 1.9899 2.0000\n",
"\n"
]
}
],
"source": [
"v = linspace(1, 2)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"row1 =\n",
"\n",
" 10 12 14 16 18 20\n",
"\n",
"row2 =\n",
"\n",
" 20 18 16 14 12 10\n",
"\n",
"A =\n",
"\n",
" 10 12 14 16 18 20\n",
" 20 18 16 14 12 10\n",
"\n"
]
}
],
"source": [
"row1 = linspace(10, 20, 6)\n",
"row2 = linspace(20, 10, 6)\n",
"A = [row1; row2]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 50.655\n"
]
}
],
"source": [
"dot(a, b)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A =\n",
"\n",
" 1.2000 5.4000 6.0000 1.5000 9.0000\n",
" 5.2000 3.1416 1.2000 1.5000 2.0000\n",
"\n"
]
}
],
"source": [
"A = [a; b]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"y =\n",
"\n",
" 6.2400 16.9646 7.2000 2.2500 18.0000\n",
" 27.0400 9.8696 1.4400 2.2500 4.0000\n",
"\n"
]
}
],
"source": [
"y = A.* b"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"M =\n",
"\n",
"Diagonal Matrix\n",
"\n",
" 1.2000 0 0 0 0\n",
" 0 5.4000 0 0 0\n",
" 0 0 6.0000 0 0\n",
" 0 0 0 1.5000 0\n",
" 0 0 0 0 9.0000\n",
"\n",
"M1 =\n",
"\n",
" 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000\n",
" 1.20000 0.00000 0.00000 0.00000 0.00000 0.00000\n",
" 0.00000 5.40000 0.00000 0.00000 0.00000 0.00000\n",
" 0.00000 0.00000 6.00000 0.00000 0.00000 0.00000\n",
" 0.00000 0.00000 0.00000 1.50000 0.00000 0.00000\n",
" 0.00000 0.00000 0.00000 0.00000 9.00000 0.00000\n",
"\n",
"M2 =\n",
"\n",
" 0.00000 1.20000 0.00000 0.00000 0.00000 0.00000\n",
" 0.00000 0.00000 5.40000 0.00000 0.00000 0.00000\n",
" 0.00000 0.00000 0.00000 6.00000 0.00000 0.00000\n",
" 0.00000 0.00000 0.00000 0.00000 1.50000 0.00000\n",
" 0.00000 0.00000 0.00000 0.00000 0.00000 9.00000\n",
" 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000\n",
"\n"
]
}
],
"source": [
"M = diag(a)\n",
"M1 = diag(a, -1)\n",
"M2 = diag(a, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 2"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"col =\n",
"\n",
" 3\n",
" 3\n",
" 3\n",
"\n",
"M =\n",
"\n",
" 2 2 2\n",
" 2 2 2\n",
" 2 2 2\n",
"\n",
"M =\n",
"\n",
" 2 2 2 3\n",
" 2 2 2 3\n",
" 2 2 2 3\n",
"\n"
]
}
],
"source": [
"col = [3 3 3]'\n",
"M = 2 * ones(3)\n",
"M = [M, col]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"B =\n",
"\n",
"Diagonal Matrix\n",
"\n",
" 2 0 0\n",
" 0 2 0\n",
" 0 0 2\n",
"\n",
"row =\n",
"\n",
" 1 2 3 4 5 6 7 8 9 10\n",
"\n",
"M =\n",
"\n",
" 1 2 3 4 5 6 7 8 9 10\n",
" 1 2 3 4 5 6 7 8 9 10\n",
" 1 2 3 4 5 6 7 8 9 10\n",
"\n",
"M =\n",
"\n",
" 2 0 0 1 2 3 4 5 6 7 8 9 10\n",
" 0 2 0 1 2 3 4 5 6 7 8 9 10\n",
" 0 0 2 1 2 3 4 5 6 7 8 9 10\n",
"\n"
]
}
],
"source": [
"B = 2 * eye(3)\n",
"row = [1 2 3 4 5 6 7 8 9 10]\n",
"M = [row; row; row]\n",
"M = [B, M]"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a =\n",
"\n",
" 2 2 2 2 2\n",
"\n",
"b =\n",
"\n",
" -1 -1 -1 -1\n",
"\n",
"C =\n",
"\n",
"Diagonal Matrix\n",
"\n",
" 2 0 0 0 0\n",
" 0 2 0 0 0\n",
" 0 0 2 0 0\n",
" 0 0 0 2 0\n",
" 0 0 0 0 2\n",
"\n",
"D =\n",
"\n",
" 0 0 0 0 0\n",
" -1 0 0 0 0\n",
" 0 -1 0 0 0\n",
" 0 0 -1 0 0\n",
" 0 0 0 -1 0\n",
"\n",
"E =\n",
"\n",
" 0 -1 0 0 0\n",
" 0 0 -1 0 0\n",
" 0 0 0 -1 0\n",
" 0 0 0 0 -1\n",
" 0 0 0 0 0\n",
"\n",
"F =\n",
"\n",
" 2 -1 0 0 0\n",
" -1 2 -1 0 0\n",
" 0 -1 2 -1 0\n",
" 0 0 -1 2 -1\n",
" 0 0 0 -1 2\n",
"\n"
]
}
],
"source": [
"a = [2 2 2 2 2]\n",
"b = [-1 -1 -1 -1]\n",
"C = diag(a)\n",
"D = diag(b, -1)\n",
"E = diag(b, 1)\n",
"F = C + D + E"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"row =\n",
"\n",
" 2 2 3 3\n",
"\n",
"base =\n",
"\n",
" 0 0\n",
" 0 0\n",
"\n",
"block =\n",
"\n",
"Diagonal Matrix\n",
"\n",
" 5 0\n",
" 0 5\n",
"\n",
"D =\n",
"\n",
" 2 2 3 3\n",
" 2 2 3 3\n",
" 0 0 0 0\n",
" 0 0 0 0\n",
" 0 0 5 0\n",
" 0 0 0 5\n",
"\n"
]
}
],
"source": [
"row = [2 2 3 3]\n",
"base = zeros(2)\n",
"block = 5 * eye(2)\n",
"D = [row; row; base base; base block]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 3"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 5151\n",
"a = 5151\n"
]
}
],
"source": [
"n = 0 : 101;\n",
"sum(n)\n",
"\n",
"a = 0;\n",
"for(i = 0:101)\n",
" a += i;\n",
"endfor\n",
"a"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 4"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"function retval = transform(n)\n",
" if (n > 1)\n",
" if (mod(n, 2) == 0)\n",
" retval = n./2;\n",
" else\n",
" retval = 3 .* n + 1;\n",
" endif\n",
" else\n",
" error (\"expecting value > 1\");\n",
" endif\n",
"endfunction"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 2\n"
]
}
],
"source": [
"transform(4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In mathematics, the Fibonacci numbers, commonly denoted $Fn$, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from $0$ and $1$. That is,\n",
"\n",
"$$ F_{0}=0, F_{1}=1 $$\n",
"\n",
"and \n",
"\n",
"$$ F_{n} = F_{n-1} + F_{n-2} $$ for $n > 1$. "
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"function retval = fibonacci_rec(n)\n",
" if(n == 0)\n",
" retval = 0;\n",
" elseif(n == 1)\n",
" retval = 1;\n",
" else\n",
" retval = fibonacci_rec(n - 1) + fibonacci_rec(n - 2);\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"function f_0 = fibonacci(n)\n",
"f_1 = 1;\n",
"f_2 = 0;\n",
"i = 1;\n",
" while i < n\n",
" f_0 = (f_1) + (f_2);\n",
" f_2 = f_1;\n",
" f_1 = f_0;\n",
" i = i + 1;\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 46368\n",
"elapsed_time = 1.0456\n",
"ans = 46368\n",
"elapsed_time = 0.0019200\n"
]
}
],
"source": [
"tic()\n",
"fibonacci_rec(24)\n",
"elapsed_time = toc()\n",
"tic()\n",
"fibonacci(24)\n",
"elapsed_time = toc()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An algorithm for computing the midpoint"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"beta = 10;\n",
"t = 2;\n",
"a = 0.96e-01;\n",
"b = 0.99e-01;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first algorithm uses: $$a + \\frac{b-a}{2} $$"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c = 0.19500\n"
]
}
],
"source": [
"c = a + b\n",
"# a = vpa(a, 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This means that the result obtained with this equation does not belong to the range $[0.096-0.099]$ and thus is incorrect. Another way of computing the midpoint is this: \n",
"$$a + \\frac{b- a}{2} $$"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d = 0.097500\n"
]
}
],
"source": [
"d = a + (b - a) / 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This time a correct result is obtained, considering the approximation of $fl_a$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 7"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Algorithm of Archimedes for computing $\\pi$. This algorithm provides approximations to $\\pi$ through the use of the succession $\\{A_i\\}_{i = 1,...,n}$. This succession computes the "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"L'algoritmo di Archimede per il calcolo di pigreco implementato dalla funzione `archimede(n)` soffre di instabilità numerica poiché il valore di pigreco diverge in modo progressivamente maggiore dal valore reale di pigreco a partire dal passo `n = 15`. \n",
"\n",
"In particolare si nota che il valore dell'errore relativo subisce un brusco aumento a partire dal passo `n = 16`."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"function A=archimede(n)\n",
"b(1)=2;\n",
"s(1)=1;\n",
" for i=1:n\n",
" A(i)=b(i)*s(i);\n",
" s(i+1)=sqrt( (1-sqrt(1-s(i)^2) )/2 );\n",
" b(i+1)=2*b(i);\n",
" end\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"La funzione `myarchimede(n)` rappresenta una variante dell'algoritmo di Archimede che riesce a porre rimedio all'instabilità di cui soffriva la precedente versione. Ciò è dovuto alla diversa strategia adottata per il calcolo del valore della cella i-esima del vettore `s`.\n",
"\n",
"L'espressione:\n",
"\n",
"$$\\sqrt{\\frac{1-\\sqrt{1-s^2_{t-1}}}{2}}$$\n",
"\n",
"si riformula in:\n",
"\n",
"$$\\frac{s_{i-1}}{\\sqrt{2 \\left( 1+\\sqrt{1-s^2_{i-1}} \\right)}}$$"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"function A=myarchimede(n)\n",
"b(1)=2;\n",
"s(1)=1;\n",
" for i=1:n\n",
" A(i)=b(i)*s(i);\n",
" s(i+1)=s(i)/sqrt( 2*(1+sqrt(1-s(i)^2)) );\n",
" b(i+1)=2*b(i);\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 24;\n",
"A=archimede(n);\n",
"err=abs(A-pi)/pi; % formula per il calcolo dell'errore relativo di A\n",
"\n",
"Anew=myarchimede(n);\n",
"errnew=abs(Anew-pi)/pi; % formula per il calcolo dell'errore relativo di A*\n",
"\n",
"figure(1)\n",
"semilogy(1:n,err,'ks-',1:n,errnew,'ro-')\n",
"legend('A','A*')\n",
"box off"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 2.0000 2.0000\n",
" 2.8284 2.8284\n",
" 3.0615 3.0615\n",
" 3.1214 3.1214\n",
" 3.1365 3.1365\n",
" 3.1403 3.1403\n",
" 3.1413 3.1413\n",
" 3.1415 3.1415\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1416 3.1416\n",
" 3.1417 3.1416\n",
" 3.1418 3.1416\n",
" 3.1425 3.1416\n",
"\n"
]
}
],
"source": [
"[A.' Anew.'] "
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans = 3.141592653589793\n"
]
}
],
"source": [
"format long\n",
"pi"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 8"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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glHr69Olnn3/+/Jtv2j/gLDc91Nra2vn5uf3njVyVQCK0YEjjTWvBH4odoJttc8X13Auyw+G+eXFxkS3+fvfu3eqHH04NBib61mMwh4RrWNcAX3ixciEfb6w49mj6BufNXJ6KlCSXixwKp01pLesIpGgQM/DU7EGS2MKoVN39TmYmlaySUCz7BuAhXcdDfkVRIEeBpW+6mddFIEUhkB0DEfMritTVYF2zK00IKpLstoNAwjSmkSCKd1GU8X4PcvG+E0gAhCp0iT4dJGlpqssiyd0hAIEUPo/2ZARp6brtWYLGrGryfndz+r4TSABcmu399J3KaZveNLKdygLGRgmkwHl/vIaY5AWTj9us3/uajEMALh2EEu3vQwNkqnfTiy//I3ybNJRGWs86nUNSQUqFBMA9MV1iEx7XRsLedyqkkHm8nwCeML2XmSqSJBVGOQIJgEtZx5h/IXhYroTMY77iZb6L/679d4Wrox8fH+e3MLeDQApWy11F+JA9vLB0I8x7xeyL/J8XrKVRgyJp6v1838zKN+o4ODjo9/sEEgCUEHWQZLk2ys4ObvsodcboVldXp25hbgGLGgC4JG8iYzkJI3WLo7n0fxOVqvlnIk/Z3NwkkKCHhB0GkQt1I3T3uq4984ImXMv4q9NdvQh+AgmAM170kkWepaxv7y9zSAHStc+IGrIHVPTbZI3VDSJXdS9FhQTADe86TD/KoyRRKk2yFRDtsvv4+FhLi6ojkADo50ffXYeQV7TkiqtJ4vWNmAik0AjZbYCQeLBbCbhWd3vMIWGRyIfsYU7j8Tr726S0NCqZSap8uqtwVEhBkbbnIE4hbYfSX0sQhVGOQAJgmy/LGcSm0eVMkvLkfayMITsAKCE2jZRSKkkuIyksBFI4RO8/iIaF7dDCNJLcvanytbp9RCBhCdY1QC/543Wi06gQRTbuJ2sXgRQIubsQ4BWhu1KSpCqcxQvzEEgA7BFeHolNI5WmpbVQYEUSgRQCoXsR4mPxnnX6R5Il7kd+XpKuMQIJyzGNhOAJTaMKixdCKpI4DwmAJWKP9cWlUbvTXecdPtZ6jcfHx0dHR3fu3On3+82a0QAVkvfE7UuIlaeboqxmN1rVPVskpTNqteL4+Pjly5f3798/PT0dDAa1/rYNKiQANmgvj7KR5JZZIi6NZDTm4uLiq6+++uijj5RSR0dH1p6XQPKbrN0J8Iqg3af1JemW3JaipmyY7t27d0+fPn3+/LmeB62AQEIlWo5GATkEbc+NkqR0oij/2Zz/nbv4YfatGAwGR0dHg8Egq5PsIJAAaLC4fxczFnVJShq1KIxK25+9z6WvrtZLPjg4OD09PTg4aNCwNljU4DEpOxXgFSk7joFL0ulaAr6/v//mzZvNzc3NzU0WNQAIh7nyqMFIsog0Mn8To5YnDtqvjTIEkq9E7FeAUsqfrdFBO6eyx3wUpany5NMoQSChKtY1oAFps0f2FLMnr1cifS+qYg4JQBQcHE5NPZ2tZ/f3YkIEkpeoVIBMxQst2t5l8sKweOUFT1PCIgIJQCsL+noh43XODuBKR+2s8DT+CCT/OCyPuOw3vONmf8kvnFB8agnhLBuLGgAYIaE8clkbTRUpOppR93AwSVKlfDqCJJAANCdhOnPe+k/HaaQ0l0QNXkuSNPkrhxiy84yE/R+Qz30aCeDdTBKBBEA/t92ymzQSebtxvzKJQPKJhPKIdQ0Qzlka6b4wXYQIJAANzev67dcJ+XGSyzSSyqMiiUACEAjSyHcEkjckjNcBkjm4cKonaeRLkUQgoTamkaAkjdep1ndbaPaUTBpp1zaQRqPRZDLR0hQsQHkEzJPtHVaPkzwpjIq8KJJanRi7tbXV6XTOzs6+/PLLjY2N/Ocff/xxt9tVSnW73SdPnrRtIwBP2O+o3dziyLc08kXzQDo8POx0Os+ePRuPxzs7O3kgjcfjbrf76tUrPQ0EII+Qkt3BNbyVx5ekyy+wJ1bzQBqNRuvr60qpTqdzcnKS/3w8Hq+srOzs7Ny4caPf76+srGhoZtyE7PzAYpY7O2d3lIAxreaQOp1O9sW9e/fyH04mk5s3b/Z6vQ8++GB7e3ve3yYFbdoAJ1jXALdK08jgZhlKGgmfSWo1hzQej7MvihVSr9fr9XpKqY2NjcPDw3l/yyF/RZRHwBRqozYkD9w1r5DW19ffvn2rriaN8p/v7e0Nh0MNTQMg0pxLa1vq46ymkT9nGoWheYXU6/X29vZ2d3dPTk4eP36slBoOh48ePfrhhx+2t7cfPHhwdnb28OFDfU0FEDvbaRRoFIktktp+usPhsNPp5JNJS3+eWVtbOz8/b/O8kRA+Xie8eTBk9nO307tV2d60bZMyO2x9ZL4+Nx0KgVSR8B5fePNggsPxuorbm4bNUmZvrZvAV8mlg+Siuwdy9nYHgf10NAgkAK1Y6MAtpVFkSxgELgFvtewb5lAeARl7acQe5xoVEprj9NjY2F/O0CCNmmyWsaaRtCKJQAIgFLVRbAgkiRivA2zsBZFNGpUSVSQxhwSgEpvjdZbSKO4oEohAEsev8igbr/eowRBl3mRPyy1q+WZJGhXIuXADgQSgCV1d2EzVZX78SEjvK4mQTGIOCYAUxqttJo1kI5BkYfgLMlnYMm2kUZqSRvNIWN1AIAGoTXuZoT2Nps9GojDyAYEkiKflEafHoiVLtRGWcV4kEUgAlpgKDM+6d8+aGzVW2QFwKSuvTRXZpFFNbpfbEUhSeDpeh9ho761MbfZJcnk2kpFHhxEM2UEDppHQgMGDMAqjFhzOJBFIIlAeQSz/Nk7SyFsEEoCqNHb1RnKO8141cVUkEUgAbDOVRjPnvTKY3JiTTCKQ3PNvSATRKG6cumoPg2kEzxFI0INDUThDGplhv0hi2bdjlEeIiuYNPusv2YNCQYUEoJz28Tr9acTFUg2zXCQRSABsMJJGFTCY7BECyaXAxuvY80Mlbo5GXINCZrNIYg4JgHHajr2YNAoaFZIzgZVHCIzG7VNnGjFp5IK1IolAArBIy+ExzWnUCIPJviCQAIjHpJFrdookAsmNUMfrOBQNQ759iiiPSKNoEEgAjNCQRlwsVRILRRKB5ECo5REC0yYL9KSRviUM1O5amM4kAgmAZk3SKCuGit9y0BYfzkOCZpf3jaY38ZaDjy+PnzyT2H5Eyj6fqSJJ42dFhWQbnTW80LhEqb2Fzz4TO4hg2YeTDaZq/6AIJADaNEmj4tdZJ2dmmoJpJF3MzSQRSFZRHkG4bBNtVh612ryJChBIAFzKp47yASCWM/jA0EdEINkTT3nE2EiEtJ0Di4ixyg7ANQ1KlOZpNLW+zvARG0tA2zN6zEAgAbiUTyA1+Ktmz/c+gQgJH5j+lAgkSzgugxcszeBwWyOUYQ4JRjCNFImGF2XgtkYoQyDZQHkE+Rpspc3TyB0OlSQjkABcqhUWPqYRhCOQAFhBGmEZAsk4xuvgC4PlEWmECggkmMJgvUeSJFGqamD4nkZsmWIRSGZRHsEXFbdT39MIknEeEgAzONkINRFIQOyqj9fVKI8ojFAfQ3YGMV7HYL0vqmynpBFMI5AALBdYGnGoJBOBZArlEbygeUP1IY0gFoEEYImqoUUaoR0CCcAipBGsIZCMYLwux2C9ZEs/mYDTiC1TIJZ9AzFrfeTEyUbQh0DSj/IIXtBQHnlYGEEyhuwAlCCNYB+BBOMYrJdqbuREkkZsmdIQSJoxXgcvtOqHg0gjCEQgAbhmyUEVaQRjCCSdKI/ghQWZQhrBIQIJiFFp8ESYRkwjiUIgwQZ2e++FmEaQhkDShvE6eGFesszdgJOENIIdnBgLRGc2exalEVEEW6iQ9KA8ghdK8yXyNGI8WQ4CCZaw28sUeRpBFAIJiEWNiCGN4AKBpAHjdfBIcXMt33RJIzhCIAGRIo1yjCcLQSC1RXkEL0wFDWkEgQgk2MNxqHOcbATJOA+pFcojeGFJeUQUQQYqJCAupBHEIpCAuJBGpRhPloBAao7xOnghD53pDpc0gjAEEqziONSt94dQpBHkIZAaojyCF8rLI9IIIhFIQPiyNEqvook0KkX57hyBBMSENIJgBFITjNe1wXGoNVn6vN9cSSPIxomxQMiyNOIQCl6gQqqNfRteSBKlVJKmqaIerYzy3S1TgTQajSaTiaEHB1AVw3Twh5FA2tra+v777x89ejQcDk08vmXJdWr2BENAmMvySCnSCB7RH0iHh4edTufZs2fffvvtYDDQ/vhOpFfU1JVX0AgDIxbkacQgM3yhP5BGo9H6+rpSqtPpnJycaH98AItdhj0h1AhHSw4ZGbLrdDrZF/fu3TPx+K5wpAlPsJ3CS0aWfY/H4+yLBRVS8RiEvQfQ43K3Sgs/4CgK3tBfIa2vr799+1YpNR6Pu93uvF9LC7S3wZA0TSnldWFgRL8kSZRKOMCDt/RXSL1eb29vb3d39+Tk5PHjx9ofH0CJJEk4ZtKEU4ldMfWmD4fDTqeTTyZNWVtbOz8/N/G8JpQeyLOxtsc+r02SqKs+dMndylEN75sTpi4dtLGxYeiR7ZvaLjnRELKQRggFlw6qjUuxQJBCGrluCtAWF1eFM4zU1zZ7KFR4D6ndNWLjdIJAAjwxMx63OH/oT+EdAqmJbNSOnR1u5BdiuFpZ57pBgB7MIQFeuX5ZoDyNOEJCAAikhljaoAWnx9Zzeeqryi88D4SEQAJ88v6q80rliTRbHjGB1B5HS/YRSM1RJMGerGvMtrmEGx0hTAQSIF6xAkrTy2QCgkMgtUKRBOOuj8fNjsUxXodgEEhwjJH6RZalEYxi47SM85AAkebc9XWqf2S1N0JCILXFSbLQb84mNVsezR6+U0XBXwzZAcKUpVFpzHAkhMAQSBqwtKElRurfq5xGsION0yYCCRCDNELcCCQ9KJLQVs0BuNJfJ73gNQIJEGBOGhEwiAqBBDiVJA3SiOUMNjGNZA3LvrVh/Xcbkd6gc/4WU3pFhtlvr9+xL743EGGhQgIcqX/8kqaX/xRXs0OICCSdWNqAqham0eJah0IcoSKQAOtapBGcYBrJDgJJM4qkxmLZ59ul0by/JsYQAAIJsIjaCJiPVXb6sdwOJeZcvbvBY8RQRiJOBBJgXoUjlKXl0YIDHUorCyI9M8EuhuwAw3SkUbWHAfxGIBnB0oZmAlzXoCmNgBgQSIAx+ooayiPEgEAyhSIpdtUypH15RIGFYBBIgAFa04jySIgAh5SFIZAMokhqIIR93lZtBASGZd+APpVPNtKVRqQaQkIgAZqYGVljvA7xYMjOLEbtYlEnNyhr/BXCkLJgBBLQmrE0ojxCVAgk4yiS6vLsINRdbUSlhcAQSEALJtOI8gixIZBsoEgKE4kRJc8qeK+wyg6or/69JLSXR4zXITxUSJZQJNUi+iA0ywqTaQTEiUAC6qg/TNcgjRgLRJwIJKAyMUFByeWW6AreZwSSPYza+a1RGlEeAdURSEAFttIIiBmr7KzKiiT6qCqyURERHbrFNFrwVFNjRNm3It4fQBMqJGC+JBFVG6Vpmj1s/gVcYRrJBALJNmaSvFF/ebeWJwSiRSABZVqEg5SRRsA3BJIDFEkVORsVcZFGFZ+TtEPACCTgOsG1EWkkCtNI2rHKDihwlEbVn5YeEAEjkNxg/bdE4j8SyiOEjSE7QCnVNo1Ml0cM1iEGBJIzLG2owsYwfdOTjQoPwNQRoAGBhLi1PtmoZVpw3yOvsa5BLwLJJYokx8RPGgFRIZAQKx1pxGAdoBGBBOmMjIrISKPFrSCNEBsCyTFG7RyQkUZuHx+6MI2kEYGEyIhJo8V3miCNECECyT2KJEtaL+8GYBRXakAc9EUR5RFgCBWSCBRJizUZps/qoeyvhKWRw8eHCUwj6UKFhOBkXUPerctLo3ktIo0QOSokKSiSdJpKIx3vLGkBmEYgIVwilzBQHgHzEEjwQ71het0L6pg6wmJMI2lBIAnCqJ1O+uaQNKZFaVtIIyDDogaEJe/y82wXk0YAFiOQZOFOss1NLa6T9yZSHgGLMWSHILS+rdGcR2XqCFUxjdQegSQOM0nzzN3hzRSVetNito2kETCFQILnfEgj+48P+Ig5JHhratJI5wNrTgvmBYEqqJAkYtRuOTOTRnZQHoWKaaSWqJDgk2yHT5XBRXSmyyPSCJiHCkkoiqRyxobprh6eqSPAGQIJ/jA8FWMiLZg9AqojkOSiSLrGwzSy/xRwjmmkNphDgniGh+nMKWYoaQQsRYUkGkXS7Go6E0egTB0BEhBIEMzKDAxpAQhBIEEqz9OocNlxAg+ohECSLsZRO92313OINIoQ6xoaY1EDhLEYRabLI9IIqIUKyQMRFUnV0kjLESgLGQBp2gbSaDSaTCZamoKo2R2mM5oWoQw3Ara1GrLb2trqdDpnZ2dffvnlxsZG/vOPP/642+0qpbrd7pMnT9q2EcHfSdbua+McWJh2edFFtoGamgfS4eFhp9N59uzZeDze2dnJA2k8Hne73VevXulpIIIXVtImiVKKnghoonkgjUaj9fV1pVSn0zk5Ocl/Ph6PV1ZWdnZ2bty40e/3V1ZWNDQTQWpxCYbGR6Dmj1tJI6ChVnNInU4n++LevXv5DyeTyc2bN3u93gcffLC9vT3vb5OCNm2IR2hLG1zc0Mj8QgZzjw2Er3aFNBwOf/zxx1u3bimlxuNx9sNihdTr9Xq9nlJqY2Pj8PBw3uNwFBk1F8N0Vsb0KY9wiWmkBmoH0sbGRjZddHh4OBqN1NWkUf4Le3t73W63uMYBugSytCHQNKL3AVpqPofU6/X29vZ2d3dPTk4eP36slBoOh48ePfrhhx+2t7cfPHhwdnb28OFDfU2F/7y9bvdSSZIoFeDrAmxqe0w3HA47nU4+mbT055m1tbXz8/M2zxszX4skA+2uWJRYOAeWQWjMCq9oLp3y1/ga3bxfBFIbXgaSmUaX7vCm95nSZhBIKJq3Vsv3rWR2j9MbulzLzj+ezSS5GKbL95BsbzG6kpM0Qqlsmyj216woXopAgkk+JWcTV4Hnuh1AO9XDMv9NE0dhBBKMMZ9Gi1fW2rl8auiZC81k1kkV9xTT+xSB5CXpo3YCVtOFN58MTxUTiM1yMQIJugmISmtnHQl4rRCtuB2GkUZGKzwCyVdCiyTXbcr3FtMLGQLoWYC6TG/2BBL0EZBGFnIifxbXLxeiyZwrEo5A8pigIsndpFG+roGqBXKwKTZDIKE1AaloLY0ojwBz2t7CHLGT0TFbTiMAJhBIfnN5k6QkkZBG1kbqSSPANIbs0IiAKFLXBtBsnANb+FbCqwdCQ4XkPQdFkoz+mJIFCAwVEuoQcAmGjM00ojwC7KBCCoGlIinriQV0xg7TCIA5VEioRkZdkC1hcJhGMt4GIExUSIEwWyTJ6IazeChNI9M3PQJgARUSFopy0mjeM8rIZSBYBBLmE9MBS0gjAKYxZBcOzaN2pNH0D4W8H0CwCCTMkHEJhkz1NGIaCfAdQ3ZBaXL977wTz/5MTBQpR+NmlEeAKwRS3IodrZj1Cxk5aQTADobsQlNjJmk2jcQQlUaUR4AdBBIEXYIhIyqNAFhDIMVN0vqFTJtgMLGuQdjbA4SMOaQA1VvaIKa7tXxZoKmnpjwCnCOQopSvX8gqpJy7TtlhJCx4asojwCYCKUxzi6SppXQyuluZaQTAMgIpGsJWdef0RkI2jaTlASmPAMtY1BCsa+u/ha2jy7ktUCiPAFGokEIntTBSrvNg8bNTHgH2EUjhSpJUqcTNsrXlJKcRACcIpBAVqyJZV2C4JDyNKI8AJ5hDCo7U6aKc6TTist+ApwikgJRddsHsrc3rcz5W5rwBAOZhyC4IglcuFDkPgyoNYLwOcIVA8lyFKGpykyTdHF4WqNgGaiNAMgLJZ85zphr7SdD49FhP3lEgTMwh+anmVbodziQJqUuENAPAAlRIvvFkuigjJAYqNoPyCHCLQPKHV1Gk3KVRvuabxd+AXxiy80Trs4ssj9q5rY2yp07TtHobKI8A56iQxPOtMFKu0yiTnx7LebKALwgkwXRHkZ313xLSKFexJZRHgAQEkkgeVkUZH9MIgBDMIclj8mJ0RmeSRKVRdZRHgBBUSJJ4WxgpYWnEpBHgIwJJBotRpH0mScJlgYpqtYTyCJCDQHLN56pICSuMAHiNQHLK8+Nz39PI87cfCA2LGhypeTE6vbQsbfA9jQBIQ4VknedjdJkA0ojyCJCGQLJIUhS1WdoQQBoBEIhAsiWUA/Iw0iiUTwMICnNI5jmdLlqgwUxSGGkEQCYqJJMkjdG1F0waiTw8AEAgGeJDFGVtnCqS5jU5mDQCIBaBZIA/R+BTSxvmjeCFlEb+fDhAdAgkrXwojGqRdlkgAAEjkDTxNooWrP8OqTACIB+BpIP/w0D5YF3+UoJMI/8/KCBkBFJleZ9d7NK8LYyKinNIhbXgaekrBgBDCKRqpqb+8247zK56ujaquBJPOMojQDgCqYLZniyUvm12WV3pSN3sq1/8CwDQAIFUR14VBXJD0pJXUWXeaPZX5JdQoRxCACEjkOoIrksrxk+b235TQgFoj0CqQPtNv+XJRuraZFKRtBIq9E8PCASBVFmIaxnyBDK9wpsSCsBSBFI1V+fmvP/aZ9ZyaB6bJRTlEeALAqkOzzu2qRzSNUCnxeISyvM3HkAlBFL4FtRDojKpqM0QX9ladiIN8ACBFKyl43IeXRmo7hDfnGtPABCNQAqN8/khOxaXUHkOBf0eAKEhkAIRSQ7NM3V9QaoiwEcEkt8iz6EFeD8A7xBIXiKHAISHQPIJOVQR43WAjwgkD5BDtfAmAZ4ikOQihwBEhUAShxwCECcCSQpyCEDkCCTHyCEAyBBIbpBDADCFQLKKHAKAeQgkG8ghAFiKQDKIHAKA6v7H0ONOJpPxeGzowWXK4ye5kl5x27CWxN4zqSVel194XR5p/KJMBdL+/v53331n6MEtS8os+M0wcggALDMSSJ9++umLFy9MPLIr6XXF/ypGFDkEAI0ZCaTXr19/8cUXJh5ZjsDG5QDAucRQT7q7u6uUevLkSen/rq2tmXhSAIAQ5+fndf9E2yq74XD4448/3rp16+HDh0t/+aeffip+K7y8yMqg0i9Kfy0wvC6/8Lr8EuTravyitAXSxsbGxsZGxV/29ANY3GxPX9RSvC6/8Lr8EuTravyiTK2yAwCglgCrRe1KF3nzvgGAXgQSAEAEl0N24/F4MvJd0KwAAAKGSURBVJk4bIAJw+EwvBellBqNRuFdeiPI64mMRqPwtsAgPykV6G6lWnSD//unP/1Jd2MqmUwmv/nNb/74xz86eXYTJpPJ7373uzRN//znP//iF7/45S9/6bpFemSv69///vdf//rXf/zjH7/+9a9dt0ibv/zlL6enpyG9oq2trfF4vLe31+l0Op2O6+ZoE94nFepu1bYbTB35+uuvP/nkk//85z+uGqDdYDAYDAZpmr59+/b3v/+96+ZoMxgMvvnmm+zrTz75xG1jNPrtb3/7q1/9Kn9pAfjb3/729ddfp8FtgeF9Umm4u1XLbtDN1b739vZu3bo1Ho9XVlacNMCEx48fZ1+MRqOQDk4fPHiQfRHYQNDr16+z07eDMRqN1tfXlVKdTufk5MR1c7QJ75NS4e5WLbtBB3NIo9FoNBrl7Q7M7u7uixcvsn4hDNngz3A4fPToUb/fd90cLJJ3Affu3XPbEiwW9m7VuBu0VyHll3IYDoc3b97c3d0dj8c7Ozv9ft/femL2+hRPnjzp9/ubm5tVrlgh1tTr2t3d/de//vXtt9/6+0llal1PxEf5DHlIFVKogtmtZjXuBu0FUn4ph263+9///lcpdXJy0uv1bty4Ya0N2hWvT7Gzs7OxsdHr9QIYhyy+ru+//z7bbdw2SYta1xPxzvr6+mg0UkqNx+Nut+u6OVgkpN2qqGU36GAOKa/jbty4EVLv8PDhw+3t7dFodHZ2FlINnq1M3drayr599eqVy9Zgvl6vt7e3t7u7e3JyEuqQeDBC3a1adoOcGKvTZDI5OzsLbMUt/DIcDtkC4VCbbpBAAgCIwMVVAQAiEEgAABEIJACACAQSAEAEAgkAIML/B4UdV4BmIwiIAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k = 1/3; # 1/2, 1, 2\n",
"x = -pi : pi;\n",
"y = sin(k*x);\n",
"\n",
"figure(1)\n",
"plot( x,sin(1/2*x),'ks-',\n",
" x,sin(1/3*x),'ro-',\n",
" x,sin(x), 'bs-',\n",
" x,sin(2*x),'ks-')\n",
"legend('1/2','1/3', '1', '2')\n",
"box off"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Lo script grafica una funzione scelta\n",
"dall\"utente tra le seguenti:\n",
" \n",
" 1) y = x^3-3x per -3 <= x <=3\n",
" 2) y = 3x cos(2x) per 0 <= x <= 2pi\n",
" 3) y = sin(x)/x per -8pi <= x <= 8pi\n",
" \n"
]
},
{
"name": "stdin",
"output_type": "stream",
"text": [
"Scegliere una tra le funzioni indicate, digitandone il numero: 2\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"disp('Lo script grafica una funzione scelta');\n",
"disp('dall\"utente tra le seguenti:');disp(' ');\n",
"disp(' 1) y = x^3-3x per -3 <= x <=3');\n",
"disp(' 2) y = 3x cos(2x) per 0 <= x <= 2pi');\n",
"disp(' 3) y = sin(x)/x per -8pi <= x <= 8pi');disp(' ');\n",
"scelta = input('Scegliere una tra le funzioni indicate, digitandone il numero: ');\n",
"\n",
"switch scelta\n",
"\n",
"case 1\n",
" f=@(x) x.^3-3*x;\n",
" x = [-3:0.05:3];\n",
" y = f(x);\n",
" plot(x,y,'r')\n",
" box off\n",
" xlabel('x'); ylabel('y');\n",
" title('Grafico della funzione 1');\n",
" legend('y=x^3-3*x');\n",
"\n",
"case 2\n",
" f=@(x) 3*x.*cos(2*x);\n",
" x = [0:pi/50:2*pi];\n",
" y = f(x);\n",
" plot(x,y,'b')\n",
" box off\n",
" xlabel('x'); ylabel('y');\n",
" title('Grafico della funzione 2');\n",
" legend('y=3*x*cos(2x)');\n",
" \n",
"case 3\n",
" f=@(x) sin(x)./x;\n",
" x = [-8*pi:pi/50:8*pi];\n",
" y = f(x);\n",
" plot(x,y,'m')\n",
" box off\n",
" xlabel('x'); ylabel('y');\n",
" title('Grafico della funzione 3');\n",
" legend('y=sin(x)/x'); \n",
" \n",
"end "
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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2JSOKVsc+BjxE2y/BCqlMpNG62MeAh2j7RQik0pBGG2NywkO0/XMEUgk4NNoekxMeou3nEEjbIopKxJslwze8R/gsAmkrpFG52FuHh2j7KQJpQ2zTVYfJCQ/R9opA2oyrH/YqB5MTHqLtCaS1sTDSg711eMjztieQ1kMa6cTeOjzkc9sTSKvi0MgUbycnfOZn2/PWQasiigxi8OEhD99kiBUSAAjl2/ad3YE0Ho+zLDNdBaAVbe8bfzLJ4kBqt9t3d3enp6dJkpiuBdCEtveTJ5lk6xnScDgMguDi4iJN0263G0WR6YqAytH2PvPhSMnWFdJ4PG42m0qpIAhGo5HpcgAdaHvPOX+kZOsKSSkVBEHxoNVqvfgDtVpt9ss8zyuvCaiY/rZ3+OnPUkUmOblOsjiQ0jQtHix6qUgCwT36297JJz6ruZpGyt4tu2az+fT0pJRK0zQMQ9PlADrQ9nA4jZS9K6Q4jvv9fq/XG41GZ2dnpssBdKDtfeb8FQ3K3kBSSg0GgyRJTk5OprvqgPNoez+5vTCasjiQlFJc9goP0fa+8SSNlL1nSADgA3/SSNm+QgIAV/lwaDSHQAIAcbxaGE2xZQcAsviZRooVEgDI4eE23SwCCQBE8HZhNMWWHQCYRxopAgkAjCONCmzZCVXFWyzT8YA0nh8azSGQ5Cq3R/kQAUAaFkZz2LIDAANIo+dYIQGAVmzTLUIgAYA+LIyWYMsOADQhjZYjkABAB9Loj9iyA4BqcWi0IgIJACrEwmh1bNkBQFVIo7UQSABQCdJoXWzZAUDJODTaDIEEAGViYbQxtuwAoDSk0TZYIQFACdim2x6BBADbYmFUCrbsAGArpFFZCCQA2BxpVCKLt+wODg7CMFRKhWF4fn5uuhxAB9peDg6NSmdrIKVpGobhzc2N6UIAfWh7OVgYVcHiQKrX691u99WrV+/fv6/X66YrAipH2wtBGlXE1jOkLMt2d3fjON7Z2el0OqbLAXSg7SUgjapj2QopSZKHh4e9vb3j4+M4jpVSURQNh8MXf7hWq81+mee5jhKBstH2QnBoVDXLAimKoiiKlFL9fj8Mw+LxIkxFuIG2l4CFkQaWBdJUq9XqdDqHh4eTyeT4+Nh0OYAOtL0ppJEetgZSs9n8/v17kiQnJydBEJguB9CBttePbTqdbA2kwvK9C8BJtL02LIw0s/UqOwCoFGmkH4EEAPNIIyPs3rIDULXiEMU3pJERBBKAhXx7XmZhZBZbdgCgFGkkAIEEAKSRCGzZAfAadxrJQSAB8BcLI1HYsgPgKdJIGlZIpSn96lj5/yBgL9JIIAKpHHQ2YBfmrEBs2QEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQwbJAyrIsTdPpl+PxOMsyg/WsolarmS5BKcr4nZAyVkTbb4wyZgkpYwnLAun+/v729rZ43G637+7uTk9PkyQxWxVQKdoenrApkI6Oji4vL4vHw+EwCIKLi4urq6vr62uzhQHVoe3hD5sCaTAYvHv3rng8Ho+bzaZSKgiC0WhktC6gQrQ9/PGX6QI2FwRB8aDVar34A41GQ2M5C+3v70uohDLmyjBdwoZoe8rYpgzTJfyB6EBKkuTh4WFvb+/4+Pj5d6fHvC++VHx8fKy2OKAatD28JTqQoiiKoujFbzWbzfF4rJRK0zQMQ711ARWi7eEt0YG0RBzH/X6/1+uNRqOzszPT5QA60PZwWy3Pc9M1bC5JkiAIprvqgA9oe7jK7kACADjDpsu+V2fjne1VYxDUs8ZQbg0Lbf8cg6Csavv/fvr0yXQN5fvy5cvPnz9fv36tlGq322ma9vt9U7scBwcHSZJ8/fr1169fRUn6GR+EgvGhmG0MJWZYykLbzzE+CAXjQ2FT2+fOefPmzf7+/ufPn/M8//bt28ePH/M8f3p6evv2rf5iTP3/zjI+CAXjQzHbGLmYYSkLbT/H+CAUjA+FXW3v4JadqDvb0zSt1+vdbrfX65laIxsfhILxoZhtDCVmWMpC288xPggF40NhV9s7GEhz/nhne6WyLNvd3Y3jeGdnp9Pp6C+gYHYQCkKGYpaEYakIba9MD0JByFDMkjAsi9h6H9KcJTe3L7+zXUM9cRwrpaIoGg6H2gqYY2QQ5sRxLGEoZkkYlm3Q9stJ+PvS9mtxJJAW3dxu6s72aT39fj8Mw0U33ush5PZ+CUMxS8iwbIO2X0LI31fCUMwSMiyLOBJIixi/s73VanU6ncPDw8lk8uJbk2lgfBAKEoZilpBhqYLxX03C39r4IBQkDMUsIcOyiBc3xhq/s914AUJqkFPGlLR6SmT8VzNegJAa5JQxJa2eKS8CCQAgn/tX2QEArEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQAQCCQAgAoEEABCBQAIAiEAgAQBEIJAAACIQSAAAEQgkAIAIBBIAQATLAinLsjRNp1+Ox+MsywzWA2hA28MTlgXS/f397e1t8bjdbt/d3Z2eniZJYrYqoFK0PTxhUyAdHR1dXl4Wj4fDYRAEFxcXV1dX19fXZgsDqkPbwx82BdJgMHj37l3xeDweN5tNpVQQBKPRyGhdQIVoe/jDpkCaEwRB8aDVaj3/bqPRqP1Ob3VAJWh7OOwv0wVsbnrMu+ilYp7nGssBdKDt4TBbV0jNZvPp6UkplaZpGIamywF0oO3hNltXSHEc9/v9Xq83Go3Ozs5MlwPoQNvDbTWrF/hJkgRBMN1Vn9VoNB4fH/WXBFSNtoerbF0hFaIoMl0CoBttD1fZeoYEAHAMgQQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgEEgBABAIJACACgQQAEIFAAgCIQCABAEQgkAAAIhBIAAARCCQAgAgEEgBABLs/oA+AQbUPP0yX4IL88m/TJUhBIAHYnPAn09qHH+VWWMU/WOK/Zju27AAAIrBCkm72BZTwV6MAsA0CSbrZEJpb3ZNPAFxCINlkLoHIJwAuIZAsll/+XWRSEUXkEwCrEUi2mo2iwpL1E+EEQD4CyT7Po+hFHD4BsAuBZI1pqGwQJxw+AZCPQLLAikui1ZFPAASyOJAODg7CMFRKhWF4fn5uupxKlB5FL+LwySI+tD28ZWsgpWkahuHNzY3pQqqiJ4pexOGTWM63PTxncSDV6/Vut/vq1av379/X63XTFZXGYBQ9x+aeKA63PaDsDaQsy3Z3d1+/fj2ZTDqdzouvGWu12uyXeZ5rKm4j21yzoA35ZJZ7bQ/MsjWQ4jiO41gpFUXRcDh88WdsmYqilkRrIZ80c6ntgedsDaR+vx+GYRRFpgvZir1R9CIujqiaG20PLGJrILVarU6nc3h4OJlMjo+PTZezNsei6EVcHFE629seWM7WQGo2m9+/f0+S5OTkJAgC0+WswYcoeo7NvVLY2/bAKmwNpIJFexdWXLOgDfm0DYvaHliL3YFkBT+XRGvh8AmAIpAqRRRt5vnhE2MI+IBAqgRPo2WZfuYTAOcRSCUjigBgMwRSObhmoSK1Dz8YUsATBNK2WBIBQCkIpM0RRQBQIgJpE0SRHuzXAV4hkNZDFAFARQiklXDNAgBUjUD6A5ZEprBfB/iGQFqIKAIAnQikFxBFAKAfgfQvDorkYL8O8BCBpBRLIgAQwPdAIooAt/HmvBbxN5CIIrHYr0NZaCS7+BhIRBEACPQf0wWYITaNah9+sMMAwE8+BpLMz3wrokhsUmrDIADe8nHLTv0/kyQ88T2/1lxObQCgk6eBpAQ87y85yjJeGwDo528gGbTKVRV+ZpKHvzKAKa8DSf+TPhf4AcAiXgeS0pVJm70pkZ+LJADesjuQxuNxEAT1en2bf6TS5/0tl0ReZZI/v+mWSml7QCCLA6ndbgdBMJlMPnz4EEWR6XLmlbU751Um4Y+Etz2wDVsDaTgcBkFwcXGRpmm3291yZpb7pM9BESpSbtsD0th6Y+x4PG42m0qpIAhGo9H2/2Apd8tOb24tN41k3slbLlaBqyi97QFRbF0hKaWCICgetFqtF3+gVqvNfpnneUWVaPggJTbuUJDT9kDpLA6kNE2LB4teKq47FTd40md3DpqV3vaAHLZu2TWbzaenJ6VUmqZhGJb1z66+OVbR7twSDm/csfhbUUVtDwhh6wopjuN+v9/r9Uaj0dnZWYn/8h/XSQZXRWzcea66tgcksDWQlFKDwSBJkpOTk+muetUkbNC5l0mO/TpV09/2gDYWB5JSqqLLXuee9DVcswCsjqu94Sq7A6k6swc20nLIvUUSACh7L2rQoHjGl/m878wFDiQrsIgbc3wtBJJ9+GxZ6OTh06IEfs5xtuyWkbY5JuGqCvhmuhyn8bQR9bSjE4H0B0IyyclnBAkDi1UUfyb+Xnr4PM4E0p8ZzCSxF1bAQ0JenDnMydedayGQhKI1IRDbd9Uh7BWBtCKdrw09mfBMP0uxfVcFxrNAIK1KQyZ5EkVwgDM3HkhAGk1x2fd6KpqE+t+qFdgSvbo9XoPOYYW0htJfFXp7zQIvCd3AkdI2mAXPEUjrKWvjjmkMN3CktBlG7EUE0tq2zCSiCO7hivDV8QywBIGkD41Y4JnLSWTSKhii5QikTaw794gi+IAjpeVIoz8ikDa0SiZ5e80CvMWR0iKMySoIpM0tySReJy7CtPQB23ezeDZYHYFUMpoPUGzf/R/BvBYCaSuzrwSZfsAstu98/t03QyBti1eCq2N+esjb7Ts/f+st8dZBJaDtgCV8e+M7PtN5Y6yQAFTOn40EomgbrJDK4dtrwA0wUT1XvHew29OEJt8SgVQa5ycbsD1XpwnbdKUgkMrk6mTbHsOCKfemCZ8dUxbOkFAt3q4Cz7l0pMTCqESskErm3qu/jfGpg1jCjSMl0qhcFq+QDg4OwjBUSoVheH5+brqcf3l748WUMy9+BRLb9puxd7LQ5FWwNZDSNA3D8ObmxnQh+Nei3TlLn3EEcrLtbdy+o6UrYnEg1ev1brf76tWr9+/f1+t10xX9xt7XfZux7gnFUsLbfmN2vcmQLXXayNYzpCzLdnd34zje2dnpdDov/kztd5ordGB/fBUcFOkkv+23YcWUIY0qVcvz3HQNa0iS5OHhYW9v7/j4ePofj46OBoPB3E82Go3Hx0e91b3A4fZdcVXk8AhoY13bb0Nsw7ANoIFlW3ZRFEVRpJTq9/thGBaPoROXcevnVdvLPFISG5OOsSyQplqtVqfTOTw8nEwmsy8bpXHpMEng04RvbGn7LUk7UpJTifMs27KbkyRJEARBEDz/lqi9C9sbmigSxZa2357xiUPna2Z3IC0hbWYan1qbYULaRVrbb8/gxLF0zlrN1i07VI0oggSmjpRIIyMIJE1sOUzimgVIo/9IyYqp6iQCSR/hmcSSCJLpmT7MArMIJK1kZhKTEFaoevtO4Nz0DYHkNaIIdqlu+440ksDWtw6yl5D3R+Etf2Cv0icRaSQEKyQDDG7ccc0C3FDWJGKTQBQCyRdMPDhm+yMlFkbSEEhm6FwkEUVw1TZHSqSRQASSMRoyiSiCD9adSswLsQgkk6rLJKYcvLL6VGJhJBmB5BSuWYC3VjlSIo2EI5AM42IhoCzLj5RII/kIJPO2zCSiCJj1fEIxR2xBIImwWSYxzYAXzW7fsTCyCIFkJaIIWE7ax85iFQSSFKu8lOOaBWAtzBS7EEiCLMkklkQAnEcgycJ5LABvEUhyEUUAvEIgiVP1p5ABgEwEkkREEQAP8QF9AAARCCQAgAgEEgBABMsCKcuyNE2nX47H4yzLDNazilqtZroEpSjjd0LKWBFtvzHKmCWkjCUsC6T7+/vb29vicbvdvru7Oz09TZLEbFVApWh7eMKmQDo6Orq8vCweD4fDIAguLi6urq6ur6/NFgZUh7aHP2wKpMFg8O7du+LxeDxuNptKqSAIRqOR0bqACtH28IfF9yEFQVA8aLVaL/5Ao9HQWM5C+/v7EiqhjLkyTJewIdqeMrYpw3QJfyA6kJIkeXh42NvbOz4+fv7d6THviy8VHx8fqy0OqAZtD2+JDqQoiqIoevFbzWZzPB4rpdI0DcNQb11AhWh7eEt0IC0Rx3G/3+/1eqPR6OzszHQ5gA60PdxWy/PcdA2bS5IkCILprjrgA9oerrI7kAAAzrDpsu/V2Xhne9UYBPWsMZRbw0LbP8cgKKva/r+fPn0yXUP5vnz58vPnz9evXyul2u12mqb9ft/ULsfBwUGSJF+/fv3161dRkn7GB6FgfChmG0OJGZay0PZzjA9CwfhQ2NT2uXPevHmzv7//+fPnPM+/ffv28ePHPM+fnp7evn2rvxhT/7+zjA9CwfhQzDZGLmZYykLbzzE+CAXjQ2FX2zu4ZSfqzvY0Tev1erfb7fV6ptbIxgehYHwoZhtDiRmWstD2c4wPQsH4UNjV9g4G0pw/3tleqSzLdnd34zje2dnpdDr6CyiYHYSCkKGYJWFYKkLbK9ODUBAyFLMkDMsitt6HNGfJze3L72zXUE8cx0qpKIqGw6G2AuYYGYQ5cRxLGIpZEoZlG7T9chL+vrT9WhwJpEU3t5u6s31aT7/fD8Nw0Y33egi5vV/CUMwSMizboO2XEPL3lTAUs4QMyyKOBNIixu9sb7VanU7n8PBwMpm8+NZkGhgfhIKEoZglZFiqYPxXk/C3Nj4IBQlDMUvIsCzixY2xxu9sN16AkBrklDElrZ4SGf/VjBcgpAY5ZUxJq2fKi0ACAMjn/lV2AAArEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIhAIAEARCCQAAAiEEgAABEIJACACAQSAEAEAgkAIAKBBAAQgUACAIjwP0LK6tr/fGEDAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Pa = [-6, -6, -7, 0, 7, 6, 6, -3, -3, 0, 0, -6;\n",
"-7, 2, 1, 8, 1, 2, -7, -7, -2, -2, -7, -7];\n",
"\n",
"row1 = Pa(1,:);\n",
"row2 = Pa(2,:);\n",
"subplot(2,2,1)\n",
"plot(row1, row2)\n",
"box off\n",
"\n",
"alpha_vett=[pi/2, pi/3, pi]; \n",
"\n",
"for k=1:length(alpha_vett)\n",
"alpha = alpha_vett(k);\n",
"\n",
"% rotazione in senso antiorario di angolo alpha\n",
"% A=[cos(alpha) -sin(alpha); sin(alpha) cos(alpha)];\n",
"\n",
"% rotazione in senso orario di angolo alpha\n",
"A=[cos(-alpha) -sin(-alpha); sin(-alpha) cos(-alpha)];\n",
"\n",
"subplot(2,2,k+1);\n",
"Prot = A * Pa;\n",
"plot(Prot(1,:),Prot(2,:)) \n",
"box off\n",
"end"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Octave",
"language": "octave",
"name": "octave"
},
"language_info": {
"file_extension": ".m",
"help_links": [
{
"text": "GNU Octave",
"url": "https://www.gnu.org/software/octave/support.html"
},
{
"text": "Octave Kernel",
"url": "https://github.com/Calysto/octave_kernel"
},
{
"text": "MetaKernel Magics",
"url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
}
],
"mimetype": "text/x-octave",
"name": "octave",
"version": "5.2.0"
}
},
"nbformat": 4,
"nbformat_minor": 4
}