{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Here's a little bit about inner products, the Gram-Schmidt method, and orthogonal projection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The dot product in $\\mathbb{R}^3$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use the sympy package for precise mathematical computations. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import sympy as sym " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Let's start with a basis for R^3\n", "v1 = sym.Array([1,0,3])\n", "v2 = sym.Array([1,0,5])\n", "v3 = sym.Array([-2,11,4])\n", "print('v1 =',v1)\n", "print('v2 =',v2)\n", "print('v3 =',v3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "v3[2]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Define an inner product\n", "def myip(v,w):\n", " return(v[0]*w[0]+v[1]*w[1]+v[2]*w[2])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def norm(v):\n", " return sym.sqrt(myip(v,v))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\sqrt{10}$" ], "text/plain": [ "sqrt(10)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(v1)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[sqrt(10)/10, 0, 3*sqrt(10)/10]\n" ] } ], "source": [ "e1 = 1/norm(v1)*v1\n", "print(e1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 1$" ], "text/plain": [ "1" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(e1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can define a vector b2 with the property that $span(e1,b2) = span(e1,v2)$ and $\\langle e1,b2 \\rangle =0$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-3/5, 0, 1/5]\n" ] } ], "source": [ "b2 = v2 - myip(v2,e1)*e1 ## you'd normally divide by but in this case, that number is 1.\n", "print(b2)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[sqrt(10)/10, 0, 3*sqrt(10)/10]\n" ] } ], "source": [ "print(e1)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myip(b2,e1)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\sqrt{10}}{5}$" ], "text/plain": [ "sqrt(10)/5" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(b2)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the vector e2 is [-3*sqrt(10)/10, 0, sqrt(10)/10] and has norm 1\n" ] } ], "source": [ "e2 = b2/norm(b2)\n", "print('the vector e2 is ',e2, 'and has norm', norm(e2))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 1, 0]\n" ] } ], "source": [ "b3 = v3 - myip(v3,e2)*e2 - myip(v3,e1)*e1 ## again, you'd normally have denominators and but those numbers are 1 here.\n", "e3 = b3/norm(b3)\n", "print(e3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is an orthonormal basis for $\\mathbb{R}^3$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "e1 = [sqrt(10)/10, 0, 3*sqrt(10)/10]\n", "e2 = [-3*sqrt(10)/10, 0, sqrt(10)/10]\n", "e3 = [0, 1, 0]\n" ] } ], "source": [ "obasis = [e1,e2,e3]\n", "print('e1 =',e1)\n", "print('e2 =',e2)\n", "print('e3 =',e3)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "i= 0 j= 0 inner product is 1\n", "i= 0 j= 1 inner product is 0\n", "i= 0 j= 2 inner product is 0\n", "i= 1 j= 0 inner product is 0\n", "i= 1 j= 1 inner product is 1\n", "i= 1 j= 2 inner product is 0\n", "i= 2 j= 0 inner product is 0\n", "i= 2 j= 1 inner product is 0\n", "i= 2 j= 2 inner product is 1\n" ] } ], "source": [ "## I think you can see that this is an orthonormal basis, but it doesn't hurt to have\n", "## the computer check it.\n", "for i in range(3):\n", " for j in range(3):\n", " print('i=',i,'j=',j,'inner product is',myip(obasis[i],obasis[j]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Now let's look at an example using the space of continuous functions on $[-\\pi,\\pi]$ with the inner product defined by\n", "\n", "$$\\langle f,g \\rangle := \\int_{-\\pi}^{\\pi} f(x)g(x) dx$$\n", "\n", "Let's just warm up with sympy" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x^{3} + \\sin{\\left(x \\right)}$" ], "text/plain": [ "x**3 + sin(x)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sym.Symbol(\"x\")\n", "myf = x**3+sym.sin(x)\n", "myf" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{x^{4}}{4} - \\cos{\\left(x \\right)}$" ], "text/plain": [ "x**4/4 - cos(x)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sym.integrate(myf, x)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 4 \\pi^{4}$" ], "text/plain": [ "4*pi**4" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sym.integrate(myf, (x,0,2*sym.pi))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\pi^{3}$" ], "text/plain": [ "pi**3" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myf.subs({x:sym.pi})" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 31.0062766802998$" ], "text/plain": [ "31.0062766802998" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myf.subs({x:sym.pi}).evalf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's redefine our inner product" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def myip(f, g):\n", " return sym.integrate(f*g, (x, -sym.pi, sym.pi))" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [], "source": [ "basis = [1, x, x**2, x**3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gram-Schmidt procedure\n", "It will be convenient to define the Gram-Schmidt process for any list of vectors and any inner product" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [], "source": [ "def gramschmidt(listofvectors, ip): # input a list of vectors and an innerproduct\n", " obasis = [] # we'll start with an empty list and add the vectors in our orthonormal basis as we create them\n", " for v in listofvectors:\n", " for e in obasis: ## think inductively. \n", " ## If we have e_1, e_2, ..., e_k and v=v_{k+1} we define e_{k+1} by\n", " ## e_{k+1}:= v - *e1 - *e2 - ... - *ek\n", " v -= ip(v, e) * e # take the old q and subtract e for each e in the obasis\n", " norm = ip(v,v) \n", " e = 1/sym.sqrt(norm) * v ## now normalize\n", " obasis.append(e)\n", " return(obasis)" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [], "source": [ "orth_basis = gramschmidt(basis,myip)" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[sqrt(2)/(2*sqrt(pi)),\n", " sqrt(6)*x/(2*pi**(3/2)),\n", " 3*sqrt(10)*(x**2 - pi**2/3)/(4*pi**(5/2)),\n", " 5*sqrt(14)*(x**3 - 3*pi**2*x/5)/(4*pi**(7/2))]" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "orth_basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The precision here of using numbers like $\\sqrt{14}$ and $4\\pi^{\\frac{7}{2}}$ are nice, but might make things look more complicated. Here are numerical approximations:" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.398942280401433,\n", " 0.219948406790773*x,\n", " 0.135577175410079*x**2 - 0.446031029038193,\n", " 0.0851039026947899*x**3 - 0.503965111551828*x]" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[e.evalf() for e in orth_basis]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that the result is orthonormal" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "i= 0 j= 0 inner product is 1\n", "i= 0 j= 1 inner product is 0\n", "i= 0 j= 2 inner product is 0\n", "i= 1 j= 0 inner product is 0\n", "i= 1 j= 1 inner product is 1\n", "i= 1 j= 2 inner product is 0\n", "i= 2 j= 0 inner product is 0\n", "i= 2 j= 1 inner product is 0\n", "i= 2 j= 2 inner product is 1\n" ] } ], "source": [ "for i in range(3):\n", " for j in range(3):\n", " print('i=',i,'j=',j,'inner product is',myip(orth_basis[i],orth_basis[j]))" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\sqrt{6}}{\\sqrt{\\pi}}$" ], "text/plain": [ "sqrt(6)/sqrt(pi)" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myip(orth_basis[1],sym.sin(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Orthonormal projection\n", "\n", "If $W$ is any subspace of an inner product space $V$ and $\\langle \\, ,\\, \\rangle$, we have an orthogonal projection operator $P:V \\to W$ that sends any vector $v$ to a vector $Pv \\in W$. The vector $Pv$ solves the _minimization problem_ in the sense that $Pv$ is the vector in $W$ closest to $v$. There is a simple formula for $Pv$ given by\n", "\n", "$$P(v):=\\langle v,e_1 \\rangle e_1 + \\langle v,e_2 \\rangle e_2 + \\cdots + \\langle v,e_k \\rangle e_k $$\n", "\n", "where $e_1, ..., e_k$ is any orthonormal basis for $W$." ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [], "source": [ "def project(func,onbasis,ip):\n", " n = len(onbasis)\n", " p = 0\n", " for e in onbasis:\n", " p += ip(func,e) * e \n", " return(p)" ] }, { "cell_type": "code", "execution_count": 124, "metadata": {}, "outputs": [], "source": [ "deg3p = project(sym.sin(x),orth_basis,myip)" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{3 x}{\\pi^{2}} + \\frac{5 \\sqrt{14} \\left(x^{3} - \\frac{3 \\pi^{2} x}{5}\\right) \\left(- \\frac{5 \\sqrt{14} \\left(- \\frac{2 \\pi^{3}}{5} + 6 \\pi\\right)}{4 \\pi^{\\frac{7}{2}}} + \\frac{5 \\sqrt{14} \\left(- 6 \\pi + \\frac{2 \\pi^{3}}{5}\\right)}{4 \\pi^{\\frac{7}{2}}}\\right)}{4 \\pi^{\\frac{7}{2}}}$" ], "text/plain": [ "3*x/pi**2 + 5*sqrt(14)*(x**3 - 3*pi**2*x/5)*(-5*sqrt(14)*(-2*pi**3/5 + 6*pi)/(4*pi**(7/2)) + 5*sqrt(14)*(-6*pi + 2*pi**3/5)/(4*pi**(7/2)))/(4*pi**(7/2))" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deg3p" ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - 0.0933876972831854 x^{3} + 0.85698332779525 x$" ], "text/plain": [ "-0.0933876972831854*x**3 + 0.85698332779525*x" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deg3p.evalf() # let's approximate the polynomial with decimal coefficients" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.plotting import plot\n", "plot(deg3p,sym.sin(x),x-1/6*x**3,(x,-sym.pi,sym.pi))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's find the degree five polynomial closest to sin(x)" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " numerical approx of the solution is 0.00564311797634678*x**5 - 0.155271410633428*x**3 + 0.987862135574673*x\n" ] } ], "source": [ "basis = [1, x, x**2, x**3,x**4,x**5]\n", "orth_basis = gramschmidt(basis,myip)\n", "deg5p = project(sym.sin(x),orth_basis,myip)\n", "print('\\n numerical approx of the solution is',deg5p.evalf())\n" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(deg5p,sym.sin(x),(x,-sym.pi-0.5,sym.pi+0.5)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the result is so close, it's hard to distinguish the graph of the sine function from the graph of our degree five approximation on the interval $[\\pi,\\pi]$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Let's change the inner product \n", "By changing the inner product, we will arrive at a different notion of distance and then orthonormal projection onto $W$, the subspace of polynomials of degree less than or equal to $5$, will result in a different approximation of the sine function. I'll use the inner product\n", "\n", "$$\\langle f, g \\rangle := f(0)g(0)+f(2)g(2)+f(4)g(4)+f(6)g(6)+f(8)g(8)+f(10)g(10)$$\n", "\n", "Notice that this formula for $\\langle f, g \\rangle$ defines an inner product on the subspace $W$. On the space $V$ of all continuous functions, it's not non-degenerate since there are functions $f$ that are not the zero function for which $\\langle f, f \\rangle = 0$. For example, $$f(x)=\\frac{x(x-2)(x-4)(x-6)(x-8)(x-10)e^{x^2+1}}{\\sqrt{1+3x^4}}$$. In class (and in the notes I posted) I prove that in the context of this kind of \"almost\" inner product that the formula for orthogonal projection still solves the minimization problem.\n", "\n", "Now, before going on, let me illustrate how you evaluate a function of x at a particular value in sympy." ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1020\n", "sin(10)\n", "-0.544021110889370\n" ] } ], "source": [ "print((x**3+2*x).subs({x:10}))\n", "print((sym.sin(x)).subs({x:10}))\n", "print((sym.sin(x)).subs({x:10.0})) # putting in a floating point number automatically returns a numerical approx" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [], "source": [ "def myip2(f, g):\n", " values = [f.subs({x:i})*g.subs({x:i}) for i in [0,2,4,6,8,10]] # make the list of products of values\n", " return sum(values).evalf() # then add them up and return the result" ] }, { "cell_type": "code", "execution_count": 138, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle -24901.4232151138$" ], "text/plain": [ "-24901.4232151138" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myip2(sym.sin(x),x**5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since this inner product involes substituting numerical values for the variable x, we'll express the number 1 (which is our first basis vector) as $x^0$ since otherwise, we'll get a python error. Look:" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "ename": "AttributeError", "evalue": "'int' object has no attribute 'subs'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m/Users/John/Code/Numerical_Analysis/inner_products.ipynb Cell 53\u001b[0m line \u001b[0;36m2\n\u001b[1;32m 1\u001b[0m f\u001b[39m=\u001b[39m\u001b[39m1\u001b[39m\n\u001b[0;32m----> 2\u001b[0m f\u001b[39m.\u001b[39;49msubs({x:\u001b[39m3\u001b[39m})\n", "\u001b[0;31mAttributeError\u001b[0m: 'int' object has no attribute 'subs'" ] } ], "source": [ "f=1\n", "f.subs({x:3})" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 1$" ], "text/plain": [ "1" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f=(x**0)\n", "f.subs({x:3})" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1, x, x**2, x**3, x**4, x**5]" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "basis=[x**0, x, x**2, x**3, x**4, x**5]\n", "basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Be careful: notice that both the integer 1 and x**0 are printed the same way, as \"1\" even though they have different types." ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "int" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(1)" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sympy.core.numbers.One" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(x**0)" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [], "source": [ "orth_basis2 = gramschmidt(basis,myip2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that in the definition of my inner product myip2, I use evalf() to return numerical approximations. This was probably not necessary, and possibly even a bad decision for it makes our gram-schmidt process return something very very close to an orthonormal basis, but not quite:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "i= 0 j= 0 inner product is 1.00000000000000\n", "i= 0 j= 1 inner product is -1.94289029309402e-16\n", "i= 0 j= 2 inner product is 5.55111512312578e-17\n", "i= 0 j= 3 inner product is 1.94289029309402e-16\n", "i= 0 j= 4 inner product is -3.52357032440409e-14\n", "i= 1 j= 0 inner product is -1.94289029309402e-16\n", "i= 1 j= 1 inner product is 1.00000000000000\n", "i= 1 j= 2 inner product is 3.88578058618805e-16\n", "i= 1 j= 3 inner product is 2.77555756156289e-17\n", "i= 1 j= 4 inner product is -2.25097718242750e-14\n", "i= 2 j= 0 inner product is 5.55111512312578e-17\n", "i= 2 j= 1 inner product is 3.88578058618805e-16\n", "i= 2 j= 2 inner product is 1.00000000000000\n", "i= 2 j= 3 inner product is 5.82867087928207e-16\n", "i= 2 j= 4 inner product is -3.26128013483640e-15\n", "i= 3 j= 0 inner product is 1.94289029309402e-16\n", "i= 3 j= 1 inner product is 2.77555756156289e-17\n", "i= 3 j= 2 inner product is 5.82867087928207e-16\n", "i= 3 j= 3 inner product is 1.00000000000000\n", "i= 3 j= 4 inner product is -1.10883524584438e-14\n", "i= 4 j= 0 inner product is -3.52357032440409e-14\n", "i= 4 j= 1 inner product is -2.25097718242750e-14\n", "i= 4 j= 2 inner product is -3.26128013483640e-15\n", "i= 4 j= 3 inner product is -1.10883524584438e-14\n", "i= 4 j= 4 inner product is 0.999999999999991\n" ] } ], "source": [ "for i in range(5):\n", " for j in range(5):\n", " print('i=',i,'j=',j,'inner product is',myip2(orth_basis2[i],orth_basis2[j]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try to clean up these inner products a bit and organize them into a table:" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "╒══════════════╤══════════════╤══════════════╤══════════════╤══════════════╕\n", "│ 1 │ -1.94289e-16 │ 5.55112e-17 │ 1.94289e-16 │ -3.52357e-14 │\n", "├──────────────┼──────────────┼──────────────┼──────────────┼──────────────┤\n", "│ -1.94289e-16 │ 1 │ 3.88578e-16 │ 2.77556e-17 │ -2.25098e-14 │\n", "├──────────────┼──────────────┼──────────────┼──────────────┼──────────────┤\n", "│ 5.55112e-17 │ 3.88578e-16 │ 1 │ 5.82867e-16 │ -3.26128e-15 │\n", "├──────────────┼──────────────┼──────────────┼──────────────┼──────────────┤\n", "│ 1.94289e-16 │ 2.77556e-17 │ 5.82867e-16 │ 1 │ -1.10884e-14 │\n", "├──────────────┼──────────────┼──────────────┼──────────────┼──────────────┤\n", "│ -3.52357e-14 │ -2.25098e-14 │ -3.26128e-15 │ -1.10884e-14 │ 1 │\n", "╘══════════════╧══════════════╧══════════════╧══════════════╧══════════════╛\n" ] } ], "source": [ "from tabulate import tabulate\n", "table = [[myip2(orth_basis2[i],orth_basis2[j]) for i in range(5)] for j in range(5)]\n", "print(tabulate(table, tablefmt='fancy_grid'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Better yet, let's zero out those floating point numbers that are almost zero to machine precision. We'll use the function available in the math library called \"isclose\". I'm not saying it's a good practice to first call a numerical approximation like evalf() and then go back and return 0 if a later result is close to 0. I just want to show you some of the things you can do in python." ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [], "source": [ "from math import isclose\n", "def makezeroifclose(x):\n", " if isclose(x,0,abs_tol=1e-9): return 0 ## return 0 if |x| < 10^(-9)\n", " else: return x" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.442" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "makezeroifclose(3.442)" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "makezeroifclose(9.4323e-13)" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "╒═══╤═══╤═══╤═══╤═══╕\n", "│ 1 │ 0 │ 0 │ 0 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 1 │ 0 │ 0 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 0 │ 1 │ 0 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 0 │ 0 │ 1 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 0 │ 0 │ 0 │ 1 │\n", "╘═══╧═══╧═══╧═══╧═══╛\n" ] } ], "source": [ "from tabulate import tabulate\n", "table = [[makezeroifclose(myip2(orth_basis2[i],orth_basis2[j])) for i in range(5)] for j in range(5)]\n", "print(tabulate(table, tablefmt='fancy_grid'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's do the orthogonal projection using this other inner product" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "solution \n", " 0.000997277281565862*x**5 - 0.0357554009431181*x**4 + 0.427647172081707*x**3 - 2.00632974849076*x**2 + 3.02680629310743*x + 1.7576218258597e-14\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deg5p2 = project(sym.sin(x),orth_basis2,myip2)\n", "print('solution \\n', deg5p2)\n", "plot(sym.sin(x),deg5p2,(x,-1,11),ylim=[-1.5,1.5])" ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.plotting import plot\n", "plot(sym.sin(x),deg5p2,deg5p,(x,-1,11),ylim=[-1.5,1.5])" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.plotting import plot\n", "plot(sym.sin(x),deg5p2,deg5p,(x,-sym.pi-0.5,sym.pi+0.5),ylim=[-1.5,1.5])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 2 }