def _eval_laguerre_fxns(self):
"""
Evaluate matrix B
Rows: Memory size (self.M)
Cols: Number of Laguerre Fxns (self.num_laguerres)
"""
self.B = discrete_laguerre(self.alpha, self.num_laguerres, self.M)
def fit(self, y=None, order=2, method='LS'):
"""
Train method estimates the kernals of the system using orthogonal laguerre basis functions. Training is
carried out with the following:
* L basis functions are generated and evaluated - yields B matrix
* Convolve each ith Laguerre function, b_i, with input data x(t). - yields v_i(t) and V matrix
* Solve Y = C*V, where C is the coefficient matrix of the Laguerre functions. Solve using `method`
* Calculate kernels:
* k_0 = c_0
* k_1(m) = c_1* b(m)
* k_2(m_1, m_2) = b(m)^T * c_2 * b(m)
:param y: training output. If `None` it looks if self.y is array-like.
:type y: array-like
:param order: training output. If `None` it looks if self.y is array-like.
:type order: array-like
:param method: Method used to find the Laguerre coefficients, C
:type method: _LS_, _(more to be added)_
"""
try:
self.y = y if y is not None else self.y
assert len(self.y) == len(self.x)
except TypeError():
print "output y must be defined and of length len(x)"
# setup volterra matrix: B
self.B = discrete_laguerre(self.alpha, self.num_laguerres, self.M)
# setup convolved Volterra matrix with data: conv(B,x)V
self.V = np.array([np.convolve(self.B[:, l], self.x)[0:self.N] for l in range(self.num_laguerres)])
# perform regression to estimate the coefficients C for each laguerre
self._est_laguerre_coef()
# calc kernels
self._calculate_kernels()
def SISO_with_Laguerres(num_points=1024, memory=40, num_laguerres=3, laguerre_coef=(-0.5, 1., -1.5), alpha=0.5):
"""
Function used to generate SISO time series data. Default parameters are based off 'test_LET1' in the Lysis7.2 MATLAB
package.
:param num_points: Number of data points to generate. len(x) & len(y)=num_points
:type num_points: Integer, default _1024_
:param memory: Number of lags in series
:type memory: Integer, default _40_
:param num_laguerres: Number of generalized Laguerre functions to use in generating output.
:type laguerre_coef: Coefficients/weights in front each laguerre to formulate output
:param alpha: Scaling factor of the generalized Laguerre function
:type alpha: [-1, 1], default _0.5_
Returns
:param x: input data
:type x: Numpy array
:param y: output data
:type y: Numpy array
"""
#assert isinstance(num_points, (int, float))
#assert isinstance(memory, (int, float))
#assert isinstance(num_laguerres, (int, float))
N = int(num_points)
M = int(memory)
L = int(num_laguerres)
laguerre_coef = laguerre_coef[:num_laguerres] if len(laguerre_coef) >= num_laguerres else np.ones(num_laguerres)
#lags = range(M) # generate index memory
# psuedo gaussian white noise
x = randn(N)
dlf = discrete_laguerre(alpha, L, M)
h = (np.array(laguerre_coef) * dlf).sum(axis=1) #
v = np.convolve(x, h)
y = v[:N] + np.power(v[:N], 2)
return x,y