def 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] """ # If input is scalar, this makes it an array p = atleast_1d(p) if len(p.shape) != 1: raise ValueError,"Input must be a rank-1 array." # find non-zero array entries non_zero = NX.nonzero(NX.ravel(p))[0] # Return an empty array if polynomial is all zeros if len(non_zero) == 0: return NX.array([]) # find the number of trailing zeros -- this is the number of roots at 0. trailing_zeros = len(p) - non_zero[-1] - 1 # strip leading and trailing zeros p = p[int(non_zero[0]):int(non_zero[-1])+1] # casting: if incoming array isn't floating point, make it floating point. if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)): p = p.astype(float) N = len(p) if N > 1: # build companion matrix and find its eigenvalues (the roots) A = diag(NX.ones((N-2,), p.dtype), -1) A[0, :] = -p[1:] / p[0] roots = _eigvals(A) else: roots = NX.array([]) # tack any zeros onto the back of the array roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype))) return roots
def roots(p): """ Return the roots of a polynomial with coefficients given 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 described by p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n] Parameters ---------- p : array_like of shape(M,) Rank-1 array of polynomial co-efficients. Returns ------- out : ndarray An array containing the complex roots of the polynomial. Raises ------ ValueError: When `p` cannot be converted to a rank-1 array. Examples -------- >>> coeff = [3.2, 2, 1] >>> print np.roots(coeff) [-0.3125+0.46351241j -0.3125-0.46351241j] """ # If input is scalar, this makes it an array p = atleast_1d(p) if len(p.shape) != 1: raise ValueError,"Input must be a rank-1 array." # find non-zero array entries non_zero = NX.nonzero(NX.ravel(p))[0] # Return an empty array if polynomial is all zeros if len(non_zero) == 0: return NX.array([]) # find the number of trailing zeros -- this is the number of roots at 0. trailing_zeros = len(p) - non_zero[-1] - 1 # strip leading and trailing zeros p = p[int(non_zero[0]):int(non_zero[-1])+1] # casting: if incoming array isn't floating point, make it floating point. if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)): p = p.astype(float) N = len(p) if N > 1: # build companion matrix and find its eigenvalues (the roots) A = diag(NX.ones((N-2,), p.dtype), -1) A[0, :] = -p[1:] / p[0] roots = eigvals(A) else: roots = NX.array([]) # tack any zeros onto the back of the array roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype))) return roots
def roots(p): """ Return the roots of a polynomial with coefficients given 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 described by p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n] Parameters ---------- p : array_like of shape(M,) Rank-1 array of polynomial co-efficients. Returns ------- out : ndarray An array containing the complex roots of the polynomial. Raises ------ ValueError: When `p` cannot be converted to a rank-1 array. Examples -------- >>> coeff = [3.2, 2, 1] >>> print np.roots(coeff) [-0.3125+0.46351241j -0.3125-0.46351241j] """ # If input is scalar, this makes it an array p = atleast_1d(p) if len(p.shape) != 1: raise ValueError, "Input must be a rank-1 array." # find non-zero array entries non_zero = NX.nonzero(NX.ravel(p))[0] # Return an empty array if polynomial is all zeros if len(non_zero) == 0: return NX.array([]) # find the number of trailing zeros -- this is the number of roots at 0. trailing_zeros = len(p) - non_zero[-1] - 1 # strip leading and trailing zeros p = p[int(non_zero[0]):int(non_zero[-1]) + 1] # casting: if incoming array isn't floating point, make it floating point. if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)): p = p.astype(float) N = len(p) if N > 1: # build companion matrix and find its eigenvalues (the roots) A = diag(NX.ones((N - 2, ), p.dtype), -1) A[0, :] = -p[1:] / p[0] roots = eigvals(A) else: roots = NX.array([]) # tack any zeros onto the back of the array roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype))) return roots
#prefix = 'data/tallinn_201s_title_rdist_10000' X, y = load_data(prefix + '.train', feature_list=feature_list) #print y.shape #X, y = load_svmlight_file(prefix + '.train') testX, testY = load_data(prefix + '.test', feature_list=feature_list) X = vstack((X, testX)) X = preprocessing.scale(X) print X #y = vstack((y, testY)) #y = y + testY #y = y.transpose() #print y.shape, testY.shape y = hstack((y, testY)) print y if options.data: log('loading ' + str(options.data)) X, y = load_data(options.data, feature_list=feature_list) if False: pos_start = 0 pos_end = 1500 neg_start = 2000 neg_end = 1000000 # tmp tmp = X[pos_start:pos_end, :] tmp = vstack((tmp, X[neg_start:neg_end])) X = tmp