Exemplo n.º 1
0
def inv_transform(xs, ys, zs, M):
    iM = linear_algebra.inverse(M)
    vec = vec_pad_ones(xs, ys, zs)
    vecr = nx.matrixmultiply(iM, vec)
    try:
        vecr = vecr / vecr[3]
    except OverflowError:
        pass
    return vecr[0], vecr[1], vecr[2]
Exemplo n.º 2
0
def mfuncC(f, x):
    """
	mfuncC(f, x) : matrix function with possibly complex eigenvalues.
	Note: Numeric defines (v,u) = eig(x) => x*u.T = u.T * Diag(v)
	This function is needed by sqrtm and allows further functions.
	"""

    x = array(x)
    (v, u) = numerix.mlab.eig(x)
    uT = transpose(u)
    V = numerix.mlab.diag(f(v + 0j))
    y = matrixmultiply(uT, matrixmultiply(V, linear_algebra.inverse(uT)))
    return approx_real(y)
Exemplo n.º 3
0
def mfuncC(f, x):
	"""
	mfuncC(f, x) : matrix function with possibly complex eigenvalues.
	Note: Numeric defines (v,u) = eig(x) => x*u.T = u.T * Diag(v)
	This function is needed by sqrtm and allows further functions.
	"""
	
	x      = array(x) 
	(v, u) = numerix.mlab.eig(x)
	uT     = transpose(u)
	V      = numerix.mlab.diag(f(v+0j))
	y      = matrixmultiply(
           uT, matrixmultiply(
           V, linear_algebra.inverse(uT)))
	return approx_real(y)
Exemplo n.º 4
0
def 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

    """

    x = asarray(x)+0.
    y = asarray(y)+0.
    y = reshape(y, (len(y),1))
    X = Matrix(vander(x, N+1))
    Xt = Matrix(transpose(X))
    c = array(linear_algebra.inverse(Xt*X)*Xt*y)  # convert back to array
    c.shape = (N+1,)
    return c
Exemplo n.º 5
0
def 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

    """

    x = asarray(x) + 0.
    y = asarray(y) + 0.
    y = reshape(y, (len(y), 1))
    X = Matrix(vander(x, N + 1))
    Xt = Matrix(transpose(X))
    c = array(linear_algebra.inverse(Xt * X) * Xt * y)  # convert back to array
    c.shape = (N + 1, )
    return c