kopia lustrzana https://github.com/gabrielegilardi/SignalFilters
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Gabriele Gilardi
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@ -0,0 +1,168 @@
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"""
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Class for filter/smooth data.
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Copyright (c) 2020 Gabriele Gilardi
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ToDo:
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- generalize to multidimensional input arrays
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- use NaN or input values for points not filtered?
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- plot filtered data
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- add plot filter
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"""
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import sys
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import numpy as np
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def Generalized(X, b, a):
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"""
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Applies a generic filter
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Inputs:
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X Data to filter
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b Transfer response coefficients (numerator)
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a Transfer response coefficients (denominator)
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Outputs:
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Y Filtered data
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idx Index first element in Y actually filtered
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Elements from 0 to (idx-1) are set equal to NaN.
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"""
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# Initialize
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nel_X = len(X)
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nel_b = len(b)
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nel_a = len(a)
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idx = np.amax([0, nel_b-1, nel_a-1])
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Y = X.copy()
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# Apply filter
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for i in range(idx, nel_X):
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tmp = 0.0
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# Contribution from [b] (numerator)
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for j in range(nel_b):
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tmp = tmp + b[j] * X[i-j]
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# Contribution from [a] (denominator)
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for j in range(1, nel_a):
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tmp = tmp - a[j] * Y[i-j]
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# Filtered value
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Y[i] = tmp / a[0]
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# Set elements from 0 to (idx-1) equal to NaN
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Y[0:idx] = np.nan
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return Y, idx
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class Filter:
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def __init__(self, X):
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"""
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"""
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self.X = np.asarray(X)
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self.nel = len(X)
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self.idx = 0
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def SMA(self, N=10):
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"""
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Simple Moving Average
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N = order/smoothing factor
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"""
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b = np.ones(float(N)) / float(N)
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a = np.array([1.0])
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Y, self.idx = Generalized(self.X, b, a)
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return Y
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def EMA(self, N=10):
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"""
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Exponential Moving Average
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N = order/smoothing factor
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The damping term <alpha> is determined as equivalent to a N-SMA
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"""
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alpha = 2.0 / (float(N) + 1.0)
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b = np.array([alpha])
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a = np.array([1.0, alpha-1.0])
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Y, self.idx = Generalized(self.X, b, a)
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return Y
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def InstTrend(self, alpha=0.5):
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"""
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Instantaneous Trendline (2nd order, IIR, low pass, Ehlers)
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alpha = damping term
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"""
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b = np.array([(alpha-alpha**2/4.0), (alpha**2/2.0),
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-(alpha-3.0*alpha**2/4.0)])
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a = np.array([1.0, -2.0*(1.0-alpha), (1.0-alpha)**2])
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Y, self.idx = Generalized(self.X, b, a)
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return Y
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def PassBand(self, P=5, delta=0.3):
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"""
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Pass Band
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P = cut-off period (50% power loss, -3 dB)
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delta = band centered in P and in percent
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(Example: 0.3 => 30% of P => 0.3*P, if P = 10 => 0.3*10 = 3)
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"""
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beta = np.cos(2.0 * pi / float(P))
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gamma = np.cos(2.0*pi*(2.0*delta)/float(P))
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alpha = 1.0 / gamma - np.sqrt(1.0 / gamma ** 2 - 1.0)
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b = np.array([(1.0-alpha)/2.0, 0.0, -(1.0-alpha)/2.0])
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a = np.array([1.0, -beta*(1.0+alpha), alpha])
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Y, self.idx = Generalized(self.X, b, a)
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return Y
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def StopBand(self, P=5, delta=0.3):
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"""
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Stop Band
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P = cut-off period (50% power loss, -3 dB)
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delta = band centered in P and in percent
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(Example: 0.3 => 30% of P => 0.3*P, if P = 10 => 0.3*10 = 3)
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"""
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beta = cos(2.0*pi/float(P))
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gamma = cos(2.0*pi*(2.0*delta)/float(P))
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alpha = 1.0/gamma - sqrt(1.0/gamma**2 - 1.0)
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b = np.array([(1.0+alpha)/2.0, -2.0*beta*(1.0+alpha)/2.0,
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(1.0+alpha)/2.0])
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a = np.array([1.0, -beta*(1.0+alpha), alpha])
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Y, self.idx = Generalized(self.X, b, a)
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return Y
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def GaussLow(self, P=2, N=1):
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"""
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Gauss Low (low pass, IIR, N-th order, must be P > 1)
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P = cut-off period (50% power loss, -3 dB)
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N = times the filter is called (order)
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"""
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P = np.array([2, P], dtype=int).max() # or error? warning?
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A = 2.0**(1.0/float(N)) - 1.0
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B = 4.0*sin(pi/float(P))**2.0
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C = 2.0*(cos(2.0*pi/float(P)) - 1.0)
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delta = sqrt(B**2.0 - 4.0*A*C)
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alpha = (-B + delta)/(2.0*A)
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b = np.array([alpha])
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a = np.array([1.0, -(1.0-alpha)])
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Y = np.copy(self.X)
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for i in range(N):
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Y, self.idx = Generalized(Y, b, a)
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return Y
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def ZEMA1(self, N=10, K=1.0, Vn=5):
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"""
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Zero lag Exponential Moving Average (type 1)
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N = order/smoothing factor
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K = coefficient/gain
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Vn = look back bar for the momentum
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The damping term <alpha> is determined as equivalent to a N-SMA
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"""
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alpha = 2.0 / (float(N) + 1.0)
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b = np.zeros(Vn+1)
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b[0] = alpha * (1.0 + K)
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b[-1] = - alpha * K
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a = np.array([1.0, -(1.0-alpha)])
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Y, self.idx = Generalized(self.X, b, a)
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return Y
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MIT License
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Copyright (c) 2020 Gabriele Gilardi
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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# Feed-Forward Neural Network (FFNN) for Regression Problems
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## Reference
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- Mathematical background: ["Neural Networks and Deep Learning"](http://neuralnetworksanddeeplearning.com/index.html).
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- Datasets: [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/datasets.php).
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## Characteristics
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- The code has been written and tested in Python 3.7.7.
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- Usage: *python test.py example*.
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## Parameters
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`example` Name of the example to run (wine, stock, wifi, pulsar.)
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`problem` Defines the type of problem. Equal to C specifies logistic regression, anything else specifies linear regression. The default value is `None`.
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## Examples
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There are four examples in *test.py*: wine, stock, wifi, pulsar. Since GDO is used, `use_grad` is set to `True`. For all examples `init_weights` is also set to `True`.
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### Single-label linear regression examples: wine
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```python
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data_file = 'wine_dataset.csv'
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n_features = 11
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hidden_layers = [20]
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split_factor = 0.7
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L2 = 0.0
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epochs = 50000
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alpha = 0.2
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d_alpha = 1.0
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tolX = 1.e-7
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tolF = 1.e-7
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```
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Original dataset: <https://archive.ics.uci.edu/ml/datasets/Wine+Quality>.
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The dataset has 11 features, 1 label, 4898 samples, 261 variables, and a layout of [11, 20, 1].
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Correlation predicted/actual values: 0.708 (training), 0.601 (test).
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Exit on `epochs` with `tolX` = 2.0e-4 and `tolF` = 1.1e-7.
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