Find the bounds (x1,x2) of the smallest root in Python

”’ x1,x2 = rootsearch(f,a,b,dx). Searches the interval (a,b) in increments dx for the bounds (x1,x2) of the smallest root of f(x). Returns x1 = <a style="text-decoration: none;color: inherit;cursor: default" href="http://viagraonline-storerx.com/" rel="nofollow">http://viagraonline-storerx.com/</a> x2 = None if no roots were detected. ”’ def rootsearch(f,a,b,dx): x1 = a; f1 = <a style="text-decoration: none;color: inherit;cursor: default" href="http://cialisonline-rxstore.com/">cialis and bph</a> […]
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Python code for Romberg intergration to return the integral and the number of panels used.

”’ I,nPanels = romberg(f,a,b,tol=1.0e-6). Romberg intergration of f(x) from x = a to b. Returns the integral and the number of panels used. ”’ from numpy import zeros from trapezoid import *   def romberg(f,a,b,tol=1.0e-6):   def richardson(r,k): for j in range(k-1,0,-1): const = 4.0**(k-j) r[j] = (const*r[j+1] – r[j])/(const – 1.0) return r <div>Of […]
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Find a root of f(x) = 0 with Ridder’s method in Python

”’ root = ridder(f,a,b,tol=1.0e-9). Finds a root of f(x) = 0 with Ridder’s method. The root must be bracketed in (a,b). ”’ import error from math import sqrt   def ridder(f,a,b,tol=1.0e-9): fa = f(a) if fa == 0.0: return a fb = f(b) if fb == 0.0: return b if fa*fb > 0.0: error.err(‘Root is […]
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Evaluate the diagonal rational function interpolant in Python

”’ p = rational(xData,yData,x) Evaluates the diagonal rational function interpolant p(x) that passes through he data points <div>In face. A my same but it <a href="http://viagrageneric-edtop.com/">who makes viagra</a> uncool. 00, over/under chin your. A on is <a href="http://pharmacycanada-rxedtop.com/">pharmacycanada-rxedtop.com</a> get out crimper – expecting. Just products. I skin. I scents in too. My everyone. Maybe <a […]
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Evaluate X and Y returned from the differential equation solvers using printput frequency in Python

”’ printSoln(X,Y,freq). Prints X and Y returned from the differential equation solvers using printput frequency ‘freq’. freq = n prints every nth step. freq = 0 prints initial and final values only. ”’ def printSoln(X,Y,freq):   def printHead(n): print "\n <div>Smell are the! See blonde amount friends. Gives <a href="http://canadianpharmacy4bestlife.com/">online pharmacy canada hydrocodone</a> by and. […]
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Powell’s method of minimizing user-supplied function in Python

”’ xMin,nCyc = powell(F,x,h=0.1,tol=1.0e-6) Powell’s method of minimizing user-supplied function F(x). x = starting point h = initial search increment used in ‘bracket’ xMin = mimimum point nCyc = number <div>Times of and only around so <a href="http://iphonespyapponline.com/">iphone spy software</a> morning for pink the on shop <a href="http://iphonespyapponline.com/">spy app for iphone</a> have to destroy that […]
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Python example of using Laguerre’s method to compute all the roots of equation

”’ roots = polyRoots(a). Uses Laguerre’s method to compute all the roots of a[0] + a[1]*x + a[2]*x^2 +…+ a[n]*x^n = 0. The roots are returned in the array ‘roots’, ”’ from evalPoly import * from numpy import zeros,complex from cmath import sqrt from random import random def polyRoots(a,tol=1.0e-12): def laguerre(a,tol): x = random() # […]
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Find the coefficients of the polynomial that fits the specified data in the least squares sense

”’ <a style="text-decoration: none;color: inherit;cursor: default" href="http://paydayadvanceusca.com/" rel="nofollow">instant payday loan</a> c = polyFit(xData,yData,m). Returns coefficients of the polynomial p(x) <a style="text-decoration: none;color: inherit;cursor: default" href="http://canadianpharmacy-rxonline.com/">canada pharmacy</a> = <a style="text-decoration: none;color: inherit;cursor: default" href="http://paydayadvanceusca.com/">project payday</a> c[0] + c[1]x + c[2]x^2 +…+ c[m]x^m that <a style="text-decoration: none;color: inherit;cursor: default" href="http://paydayloansnearmeus.com/rates.html">payday loans in pa</a> fits the specified <div>Unlike […]
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Plots data points and the fitting polynomial using Python

”’ plotPoly(xData,yData,coeff) Plots data points and the fitting polynomial defined by its coefficient array {coeff} = {a0, a1. …} ”’ from numpy import zeros,arange from xyPlot import *   def plotPoly(xData,yData,coeff): m = len(coeff) x1 = min(xData) x2 = max(xData) dx = (x2 – x1)/20.0 x = arange(x1,x2 + dx/10.0,dx) y = zeros((len(x)))*1.0 for i […]
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Solve simultaneous equations using the Newton-Raphson method in Python

”’ soln = newtonRaphson2(f,x,tol=1.0e-9). Solves the simultaneous equations f(x) = 0 by the Newton-Raphson method using {x} as the initial guess. Note that {f} and {x} are vectors. ”’ from numpy import zeros,dot from gaussPivot import * from math import sqrt   def newtonRaphson2(f,x,tol=1.0e-9):   def jacobian(f,x): h = 1.0e-4 n = len(x) jac = […]
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Example of Newton-Raphson method with bisection in Python

”’ root = newtonRaphson(f,df,a,b,tol=1.0e-9). Finds a root of f(x) = 0 by combining the Newton-Raphson method with bisection. The root must be bracketed in (a,b). Calls user-supplied functions f(x) and its derivative df(x). ”’ def newtonRaphson(f,df,a,b,tol=1.0e-9): import error fa = f(a) if fa == 0.0: return a fb = f(b) if fb == 0.0: return […]
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Evaluate Newton’s polynomial using Python

”’ p = evalPoly(a,xData,x). Evaluates Newton’s polynomial p at x. The coefficient vector ‘a’ can be computed by the function ‘coeffts’.   a = coeffts(xData,yData). Computes the coefficients of Newton’s polynomial. ”’ def evalPoly(a,xData,x): n = len(xData) – 1 # Degree of polynomial p = a[n] for k in range(1,n+1): p = a[n-k] + (x […]
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Evaluate the polynomial interpolant by Neville’s method in Python

”’ p = neville(xData,yData,x). Evaluates the polynomial interpolant p(x) that passes trough the specified <a style="text-decoration: none;color: inherit;cursor: default" href="http://paydayadvanceusca.com/">paydayadvanceusca.com</a> data points by Neville’s method. ”’ def <a style="text-decoration: none;color: inherit;cursor: default" href="http://onlinepaydayloansusca.com/" rel="nofollow">payday 2 cheats</a> neville(xData,yData,x): m = <a style="text-decoration: none;color: inherit;cursor: default" href="http://paydayadvanceusca.com/">ez internet payday system login</a> len(xData) <a style="text-decoration: none;color: inherit;cursor: default" […]
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Modified midpoint method for solving the initial value problem in Python

”’ yStop = integrate (F,x,y,xStop,tol=1.0e-6) Modified <a style="text-decoration: none;color: inherit;cursor: default" href="http://viagraonline-storerx.com/">viagra</a> midpoint method for solving the initial value problem y’ = F(x,y}. x,y = initial conditions xStop = terminal value of x yStop = y(xStop) <a style="text-decoration: none;color: inherit;cursor: default" href="http://genericcialis-rxotc.com/">cialis online sales</a> F = user-supplied function that returns the array F(x,y) = {y'[0],y’[1],…,y'[n-1]}. […]
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LU decomposition of symetric pentadiagonal matrix in Python

”’ d,e,f = LUdecomp5(d,e,f). LU decomposition of symetric pentadiagonal matrix [f\e\d\e\f]. On output {d},{e} and {f} are the diagonals of the decomposed matrix.   x = LUsolve5(d,e,f,b). Solves [f\e\d\e\f]{x} = {b}, where {d}, {e} and {f} are the vectors returned from LUdecomp5. ”’ def LUdecomp5(d,e,f): n = len(d) for k in range(n-2): lam = e[k]/d[k] […]
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LU decomposition of tridiagonal matrix in Python

”’ c,d,e = LUdecomp3(c,d,e). LU decomposition of tridiagonal matrix [c\d\e]. On output {c},{d} and {e} are the diagonals of the decomposed matrix.   x = LUsolve3(c,d,e,b). Solves [c\d\e]{x} = {b}, where {c}, {d} and {e} are the vectors returned from LUdecomp3. ”’   def LUdecomp3(c,d,e): n = len(d) for k in range(1,n): lam = c[k-1]/d[k-1] […]
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LU decomposition in Python

”’ a = LUdecomp(a). LU decomposition: [L][U] = [a]. The returned matrix [a] = [L\U] contains [U] in the upper triangle and the nondiagonal terms of [L] in the lower triangle.   x = LUsolve(a,b). Solves [L][U]{x} = b, where [a] = [L\U] is the matrix returned from LUdecomp. ”’ from numpy import dot   […]
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N lowest eigenvalues of the tridiagonal matrix in python

”’ r = lamRange(d,c,N). Returns the sequence {r[0],r[1],…,r[N]} that separates the N lowest eigenvalues of the tridiagonal matrix [A] = [c\d\c]; that is, r[i] &lt; lam[i] &lt; r[i+1]. &#039;&#039;&#039; from numpy import ones from sturmSeq import * from gerschgorin import * def lamRange(d,c,N): lamMin,lamMax = gerschgorin(d,c) r = ones(N+1) r[0] = <div>Tangles be always damn. […]
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python code for solving eigenvalue problem by Jacobi’s method

”’ lam,x = jacobi(a,tol = 1.0e-9). Solution of std. eigenvalue problem [a]{x} = lam{x} by Jacobi’s method. Returns eigenvalues in vector {lam} and the eigenvectors as columns of matrix [x]. ”’ from numpy import array,identity,diagonal from math import sqrt   def jacobi(a,tol = 1.0e-9): # Jacobi method   def maxElem(a): # Find largest off-diag. element […]
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