Version 0.9.6

Variables

• eigvals

  eigvals = None
  
  

• lstsq

  lstsq = None
  
  

Classes

• poly1d - A one-dimensional polynomial class.

Function summary

• get_linalg_funcs()
• poly(seq_of_zeros)
• polyadd(a1, a2)
• polyder(p, m = 1)
• polydiv(u, v)
• polyfit(x, y, N)
• polyint(p, m = 1, k = None)
• polymul(a1, a2)
• polysub(a1, a2)
• polyval(p, x)
• roots(p)

Functions

• get_linalg_funcs()

  Look for linear algebra functions in numpy

• poly(seq_of_zeros)

  Return a sequence representing a polynomial given a sequence of roots.

  If the input is a matrix, return the characteristic polynomial.

  Example:

  >>> b = roots([1,3,1,5,6])
  >>> poly(b)
  array([1., 3., 1., 5., 6.])
  

• polyadd(a1, a2)

  Adds two polynomials represented as sequences

• polyder(p, m = 1)

  Return the mth derivative of the polynomial p.

• polydiv(u, v)

  Computes q and r polynomials so that u(s) = q(s)*v(s) + r(s) and deg r < deg v.

• polyfit(x, y, N)

  Do a best fit polynomial of order N of y to x. Return value is a vector of polynomial coefficients [pk ... p1 p0]. Eg, for N=2

  p2*x0^2 + p1*x0 + p0 = y1 p2*x1^2 + p1*x1 + p0 = y1 p2*x2^2 + p1*x2 + p0 = y2 ..... p2*xk^2 + p1*xk + p0 = yk

  Method: if X is a the Vandermonde Matrix computed from x (see http://mathworld.wolfram.com/VandermondeMatrix.html), then the polynomial least squares solution is given by the 'p' in

  X*p = y

  where X is a len(x) x N+1 matrix, p is a N+1 length vector, and y is a len(x) x 1 vector

  This equation can be solved as

  p = (XT*X)^-1 * XT * y

  where XT is the transpose of X and -1 denotes the inverse.

  For more info, see http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html, but note that the k's and n's in the superscripts and subscripts on that page. The linear algebra is correct, however.

  See also polyval

• polyint(p, m = 1, k = None)

  Return the mth analytical integral of the polynomial p.

  If k is None, then zero-valued constants of integration are used. otherwise, k should be a list of length m (or a scalar if m=1) to represent the constants of integration to use for each integration (starting with k[0])

• polymul(a1, a2)

  Multiplies two polynomials represented as sequences.

• polysub(a1, a2)

  Subtracts two polynomials represented as sequences

• polyval(p, x)

  Evaluate the polynomial p at x. If x is a polynomial then composition.

  Description:

  If p is of length N, this function returns the value: p[0]*(x**N-1) + p[1]*(x**N-2) + ... + p[N-2]*x + p[N-1]

  x can be a sequence and p(x) will be returned for all elements of x. or x can be another polynomial and the composite polynomial p(x) will be returned.

  Notice: This can produce inaccurate results for polynomials with significant variability. Use carefully.

• roots(p)

  Return the roots of the polynomial coefficients in p.

  The values in the rank-1 array p are coefficients of a polynomial. If the length of p is n+1 then the polynomial is p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]

Imported names