diff --git a/README.md b/README.md index bfed375..5117995 100644 --- a/README.md +++ b/README.md @@ -1,10 +1,22 @@ # pywdf + [![General badge](https://img.shields.io/badge/PDF-Paper-.svg)](https://repositori.upf.edu/handle/10230/57903) pywdf is a Python framework for modeling and simulating wave digital filter circuits. It allows users to easily create and analyze WDF circuit models in a high-level, object-oriented manner. The library includes a variety of built-in components, such as voltage sources, capacitors, diodes etc., as well as the ability to create custom components and circuits. Additionally, pywdf includes a variety of analysis tools, such as frequency response and transient analysis, to aid in the design and optimization of WDF circuits. Also included are several example circuits as shown below. + +## About *frantic0's* pywdf fork≈ + +This fork adds new examples of the Chua circuit that you can find in the structure below and a few extensions to the core *wdf.py*, including the following: +* a new element, `ChuaDiode`, a non-linear negative resistor that implements a piecewise-linear I-V relationship, +* a new two-port series adaptor with an embedded resistive voltage source, `SeriesVoltage` for exciting circuits with voltage impulses injection, useful for the Chua circuit, +* an implementation of the alpha transform for digitizing linear dynamic elements and testing different stability levels, with optional parameters for choosing between the bilinear and backward Euler transforms. + + + + ## Installation ``` pip install git+https://github.com/gusanthon/pywdf @@ -23,6 +35,9 @@ The core directory contains the main source code of the repository. │ ├── baxandalleq.py │ ├── diodeclipper.py │ ├── lc_oscillator.py +│ ├── chua.py implemented by @frantic0 +│ ├── chua_minimal.py implemented by @frantic0 +│ ├── chua_ODE.py implemented by @frantic0 │ ├── passivelpf.py │ ├── rca_mk2_sef.py │ ├── rclowpass.py @@ -33,6 +48,18 @@ The core directory contains the main source code of the repository. ├── setup.py ``` +## Interactive Debugging + + +``` +python3 -m debugpy --wait-for-client --listen 5678 pywdf/examples/chua_circuit.py +``` + + + + + + ## Usage ```python @@ -96,6 +123,7 @@ For further reading, check out: - Giovanni De Sanctis and Augusto Sarti, “Virtual analog modeling in the wave-digital domain,” IEEE transactions on audio, speech, and language processing, vol. 18, no. 4, pp. 715–727, 2009. [[URL]](https://ieeexplore.ieee.org/abstract/document/5276845) - Kurt James Werner, Vaibhav Nangia, Julius O Smith, and Jonathan S Abel, “A general and explicit formulation for wave digital filters with multiple/multiport nonlinearities and complicated topologies,” IEEE, 2015, pp. 1–5. [[URL]](https://ieeexplore.ieee.org/document/7336908) - D. Franken, Jörg Ochs, and Karlheinz Ochs, “Generation of wave digital structures for networks containing multiport elements,” Circuits and Systems I: Regular Papers, IEEE Transactions on, vol. 52, pp. 586 – 596, 04 2005. [[URL]](https://www.researchgate.net/publication/4018571_Generation_of_wave_digital_structures_for_connection_networks_containing_ideal_transformers) +- Klaus Meerkotter and Rheinhard Scholz, “Digital simulation of nonlinear circuits by wave digital filter principles”, 1989, IEEE International Symposium on Circuits and Systems (ISCAS) ## Contributions diff --git a/pywdf/__init__.py b/pywdf/__init__.py index 8132810..6d32c8b 100644 --- a/pywdf/__init__.py +++ b/pywdf/__init__.py @@ -1,13 +1,14 @@ from .core.circuit import * from .core.rtype import * from .core.wdf import * +from .core.solver import * from .examples.tr_808_hatresonator import TR_808_HatResonator from .examples.bassmantonestack import BassmanToneStack from .examples.baxandalleq import BaxandallEQ, UnadaptedBaxandallEQ from .examples.diodeclipper import DiodeClipper from .examples.lc_oscillator import LCOscillator -from .examples.passivelpf import PassiveLPF +from .examples.passive_lpf import PassiveLPF from .examples.rca_mk2_sef import RCA_MK2_SEF -from .examples.rclowpass import RCLowPass -from .examples.voltagedivider import VoltageDivider +from .examples.rc_lowpass import RCLowPass +from .examples.voltage_divider import VoltageDivider diff --git a/pywdf/core/circuit.py b/pywdf/core/circuit.py index 2dec46e..6641a6c 100644 --- a/pywdf/core/circuit.py +++ b/pywdf/core/circuit.py @@ -22,6 +22,7 @@ def __init__(self, source: baseWDF, root: rootWDF, output: baseWDF) -> None: self.root = root self.output = output + def process_sample(self, sample: float) -> float: """Process an individual sample with this circuit. @@ -38,6 +39,40 @@ def process_sample(self, sample: float) -> float: self.root.next.accept_incident_wave(self.root.propagate_reflected_wave()) return self.output.wave_to_voltage() + + + def process_sample_i_v(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.source.set_voltage(sample) + self.root.accept_incident_wave(self.root.next.propagate_reflected_wave()) + self.root.next.accept_incident_wave(self.root.propagate_reflected_wave()) + + return ( self.output.wave_to_voltage(), self.source.wave_to_current(), self.output.wave_to_current() ) + + + def process_i_v_signals(self, signal: np.array) -> np.array: + """Process an entire signal with this circuit. + + Args: + signal (np.array): incoming signal to process + + Returns: + (i,v) tuples list: processed signal + """ + self.reset() + l = [ self.process_sample_i_v(sample) for sample in signal] + return l + + def process_signal(self, signal: np.array) -> np.array: """Process an entire signal with this circuit. @@ -48,7 +83,10 @@ def process_signal(self, signal: np.array) -> np.array: np.array: processed signal """ self.reset() - return np.array([self.process_sample(sample) for sample in signal]) + + return np.array([ self.process_sample(sample) for sample in signal ]) + + def process_wav(self, filepath: str, output_filepath: str = None) -> np.array: fs, x = wavfile.read(filepath) @@ -67,8 +105,14 @@ def __call__(self, *args: any, **kwds: any) -> any: elif hasattr(args[0], "__iter__"): return self.process_signal(args[0]) + + + + + def get_impulse_response(self, delta_dur: float = 1, amp: float = 1) -> np.array: - """Get circuit's impulse response + """ + Get circuit's impulse response Args: delta_dur (float, optional): duration of Dirac delta function in seconds. Defaults to 1. @@ -81,6 +125,34 @@ def get_impulse_response(self, delta_dur: float = 1, amp: float = 1) -> np.array d[0] = amp return self.process_signal(d) + + + + + def plot_signal( + self, + signal: np.array, + n_samples: int = 500, + outpath: str = None, + title: str = "Signal", + ) -> None: + + plt.figure(figsize=(9, 5.85)) + plt.plot(signal[:n_samples]) + plt.xlabel("Sample [n]") + plt.ylabel("Amplitude [V]") + plt.title(title) + + plt.grid() + if outpath: + plt.savefig(outpath) + plt.show() + + + + + + def plot_impulse_response( self, n_samples: int = 500, @@ -120,14 +192,23 @@ def reset(self) -> None: if isinstance(self.__dict__[key], baseWDF): self.__dict__[key].reset() + + + + def compute_spectrum(self, fft_size: int = None) -> np.ndarray: x = self.get_impulse_response() N2 = int(fft_size / 2 - 1) H = fft(x, fft_size)[:N2] return H + + + + def plot_freqz(self, outpath: str = None, fft_size: int = None): - """Plot the circuit's frequency response + """ + Plot the circuit's frequency response Args: outpath (str, optional): filepath to save figure. Defaults to None. @@ -171,6 +252,9 @@ def plot_freqz(self, outpath: str = None, fft_size: int = None): plt.savefig(outpath) plt.show() + + + def plot_freqz_list( self, values: list, @@ -241,6 +325,59 @@ def plot_freqz_list( plt.show() + + + + + def i_v_analysis( + self, + freq: float = 1000, + amplitude: float = 1, + t_ms: float = 5, + outpath: str = None, + ): + """Plot transient analysis of Circuit's response to sine wave + + Args: + freq (float, optional): frequency of sine wave. Defaults to 1000. + amplitude (float, optional): amplitude of sine wave. Defaults to 1. + t_ms (float, optional): time in ms of sine wave. Defaults to 5. + """ + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + + n_samples = int(t_ms * self.fs / 1000) + n = np.arange(0, 2, 1 / self.fs) + x = np.sin(2 * np.pi * freq * n) * amplitude + + y = self.process_i_v_signals(x) + + v, ii, io = zip(*y) + + v, ii, io = np.array(v), np.array(ii) * 100, np.array(io) * 0.01 + + ax.plot(x[:n_samples], label="input signal") + ax.plot(v[:n_samples], label="voltage out", alpha=0.75) + ax.plot(ii[:n_samples], label="current source through", alpha=0.75) + ax.plot(io[:n_samples], label="current output through", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("amplitude") + ax.set_yscale('log') + ax.set_ylim(0, 1000000) + + ax.set_title(loc="left", label="output signal vs input signal waveforms") + ax.grid(True) + ax.legend() + + if outpath: + plt.savefig(outpath) + + plt.show() + + + + + + def AC_transient_analysis( self, freq: float = 1000, diff --git a/pywdf/core/solver/__init__.py b/pywdf/core/solver/__init__.py new file mode 100644 index 0000000..58d077b --- /dev/null +++ b/pywdf/core/solver/__init__.py @@ -0,0 +1 @@ +__all__ = ['runge_kutta'] \ No newline at end of file diff --git a/pywdf/core/solver/runge_kutta.py b/pywdf/core/solver/runge_kutta.py new file mode 100644 index 0000000..e75341c --- /dev/null +++ b/pywdf/core/solver/runge_kutta.py @@ -0,0 +1,57 @@ +import numpy as np + +def rk4_step(f, t, y, h): + """ + Single step of fourth-order Runge-Kutta method + + Parameters: + f: function that defines dy/dt = f(t, y) + t: current time + y: current value of y + h: step size + + Returns: + y_next: next value of y + """ + k1 = h * f(t, y) + k2 = h * f(t + h/2, y + k1/2) + k3 = h * f(t + h/2, y + k2/2) + k4 = h * f(t + h, y + k3) + + y_next = y + (k1 + 2*k2 + 2*k3 + k4) / 6 + return y_next + +def rk4_solve(f, t_span, y0, h): + """ + Solve ODE using RK4 method + + Parameters: + f: function that defines dy/dt = f(t, y) + t_span: tuple (t_start, t_end) + y0: initial condition (scalar or array) + h: step size + + Returns: + t_values: array of time points + y_values: array of solution values + """ + t_start, t_end = t_span + t_values = np.arange(t_start, t_end + h, h) + + # Handle both scalar and vector initial conditions + y0 = np.asarray(y0) + if y0.ndim == 0: # Scalar case + y_values = np.zeros(len(t_values)) + else: # Vector case + y_values = np.zeros((len(t_values), len(y0))) + + # Initial condition + y_values[0] = y0 + + # Apply RK4 method + for i in range(len(t_values) - 1): + y_values[i + 1] = rk4_step(f, t_values[i], y_values[i], h) + + return t_values, y_values + + diff --git a/pywdf/core/wdf.py b/pywdf/core/wdf.py index d159af2..e02a838 100644 --- a/pywdf/core/wdf.py +++ b/pywdf/core/wdf.py @@ -1,10 +1,26 @@ from __future__ import annotations import numpy as np +from enum import Enum +import math + +class Transform(Enum): + BILINEAR = 1 + WARPED_BILINEAR = 2 + BACKWARD_EULER = 3 + ALPHA = 4 + MOBIUS = 5 class baseWDF: + ''' + The base one port object from which all wave digital elements will inherit. + ''' def __init__(self) -> None: - self.a, self.b = 0, 0 + self.a = 0.0 + self.b = 0.0 + # Added default values for impedance and admittance + self.Rp = 1.0e-9 # impedance + self.G = 1.0 / self.Rp # admittance self.parent = None def connect_to_parent(self, parent: baseWDF) -> None: @@ -19,7 +35,11 @@ def impedance_change(self) -> None: self.parent.impedance_change() def wave_to_voltage(self) -> float: - return (self.a + self.b) / 2.0 + return (self.a + self.b) * 0.5 + + # Added base class method to convert wave to current according to WDF parametric definition + def wave_to_current(self) -> float: + return (self.a - self.b) * 0.5 * self.G def reset(self) -> None: self.a, self.b = 0, 0 @@ -35,6 +55,11 @@ def __str__(self) -> str: class rootWDF(baseWDF): + ''' + The rootWDF class is a subclass of baseWDF that represents the root element in a WDF circuit. + It inherits from baseWDF but overwrites the connection of an element to a parent + and throws an error should this be attempted. + ''' def __init__(self, next: baseWDF) -> None: baseWDF.__init__(self) self.next = next @@ -54,8 +79,10 @@ def __init__(self): self.calc_impedance() def calc_impedance(self) -> None: - self.Rp = 0 - self.G = 1e16 + # self.Rp = 0 + # self.G = 1e16 + self.Rp = 1e-16 # short circuit has zero resistance, here we set it to a very small value + self.G = 1.0 / self.Rp # set the conductance to a very large value def accept_incident_wave(self, a: float) -> None: self.a = a @@ -74,8 +101,10 @@ def __init__(self): self.calc_impedance() def calc_impedance(self) -> None: - self.Rp = 0 - self.G = 1e16 + # self.Rp = 0 + # self.G = 1e16 + self.Rp = 1e16 # open circuit has infinite resistance, here we set it to a very large value + self.G = 1.0 / self.Rp # set the conductance to a very small value def accept_incident_wave(self, a: float) -> None: self.a = a @@ -111,7 +140,13 @@ def propagate_reflected_wave(self) -> float: class Capacitor(baseWDF): - def __init__(self, C: float, fs: int, tolerance: float = 0) -> None: + def __init__( + self, + C: float, + fs: int, + tolerance: float = 0, + alpha: float = 1.0 # 0.0 – Backward Euler; 1.0 – Bilinear Transform + ) -> None: baseWDF.__init__(self) self.fs = fs @@ -119,8 +154,17 @@ def __init__(self, C: float, fs: int, tolerance: float = 0) -> None: rand_samp = np.random.normal(loc=0, scale=C * tolerance / 2) self.C = C + rand_samp self.z = 0 + self.setAlpha(alpha) self.calc_impedance() + + def setAlpha(self, alpha: float) -> None: + self.alpha = alpha + self.b_coef = (1.0 - alpha) / 2.0 + self.a_coef = (1.0 + alpha) / 2.0 + self.impedance_change() + + def prepare(self, new_fs: int) -> None: self.fs = new_fs self.impedance_change() @@ -131,8 +175,25 @@ def set_capacitance(self, new_C: float) -> None: self.C = new_C self.impedance_change() - def calc_impedance(self) -> None: - self.Rp = 1.0 / (2 * self.C * self.fs) + # def calc_impedance(self) -> None: + # ''' + # Local discretisation of capacitor using the warped bilinear transform method. + + # 1 + # Z_C = -------------- + # 2 * C * f_s + + # where f_s is the sampling frequency and C the capacitance. + # ''' + + # self.G = 1.0 / self.Rp + + + def calc_impedance( + self, + ) -> None: + + self.Rp = 1.0 / ( ( 1.0 + self.alpha ) * self.C * self.fs) self.G = 1.0 / self.Rp def accept_incident_wave(self, a: float) -> None: @@ -152,10 +213,20 @@ def reset(self) -> None: class Inductor(baseWDF): - def __init__(self, L: float, fs: int) -> None: + def __init__(self, + L: float, + fs: int, + alpha: float = 1.0 + ) -> None: + ''' + TODO: Why does inductor have a different constructor than capacitor? + ''' self.fs = fs self.L = L - self.z = 0 + self.z = 0.0 + self.alpha = alpha + self.b_coef = (1.0 - alpha) / 2.0 + self.a_coef = (1.0 + alpha) / 2.0 self.calc_impedance() def prepare(self, new_fs: int) -> None: @@ -163,21 +234,33 @@ def prepare(self, new_fs: int) -> None: self.impedance_change() self.reset() + def setAlpha(self, alpha: float) -> None: + self.alpha = alpha + self.b_coef = (1.0 - alpha) / 2.0 + self.a_coef = (1.0 + alpha) / 2.0 + self.impedance_change() + def set_inductance(self, new_L: float) -> None: if self.L != new_L: self.L = new_L self.impedance_change() - def calc_impedance(self) -> None: - self.Rp = 2 * self.L * self.fs - self.G = 1.0 / self.Rp + def calc_impedance( + self + ) -> None: + + self.Rp = (1.0 + self.alpha ) * self.L * self.fs + self.G = 1.0 / self.Rp + def accept_incident_wave(self, a: float) -> None: self.a = a self.z = self.a def propagate_reflected_wave(self) -> float: self.b = -self.z + self.b = self.b_coef * self.b - self.a_coef * self.z + return self.b def reset(self) -> None: @@ -189,7 +272,10 @@ def reset(self) -> None: class ParallelAdaptor(baseWDF): - def __init__(self, p1: baseWDF, p2: baseWDF) -> None: + def __init__(self, + p1: baseWDF, + p2: baseWDF + ) -> None: baseWDF.__init__(self) self.p1 = p1 self.p2 = p2 @@ -300,8 +386,41 @@ def propagate_reflected_wave(self) -> float: #################################################################################### +class SeriesVoltage(baseWDF): + + def __init__(self, p1: baseWDF) -> None: + baseWDF.__init__(self) + p1.connect_to_parent(self) + self.p1 = p1 + self.calc_impedance() + + def calc_impedance(self) -> None: + self.Rp = self.p1.Rp + self.G = 1.0 / self.Rp + + def set_voltage(self, new_V: float) -> None: + self.Vs = new_V + + def accept_incident_wave(self, a: float) -> None: + self.a = a + self.p1.accept_incident_wave( -a + -self.Vs ) # Incident wave is the negative of the voltage source + + def propagate_reflected_wave(self) -> float: + self.b = 0 - self.p1.propagate_reflected_wave() + -self.Vs + return self.b + + + +#################################################################################### + + class IdealVoltageSource(rootWDF): def __init__(self, next: baseWDF) -> None: + ''' + IdealVoltageSource is a subclass of rootWDF and not of baseWDF. + This is because there is delay free loop in the reflected wave and therefore + we can only use an ideal voltage source at the root of a connection tree, not as a leaf node. + ''' rootWDF.__init__(self, next) self.Vs = 0 self.calc_impedance() @@ -320,8 +439,35 @@ def propagate_reflected_wave(self) -> float: #################################################################################### +class IdealCurrentSource(rootWDF): + def __init__(self, next: baseWDF) -> None: + ''' + IdealCurrentSource is a subclass of rootWDF and not of baseWDF. + This is because there is delay free loop in the reflected wave + therefore we can only use an ideal current source at the root of a connection tree, not as a leaf node. + ''' + rootWDF.__init__(self, next) + self.Is = 0 + # self.Vs = 0 + self.calc_impedance() + + def set_current(self, new_I: float) -> None: + self.Is = new_I + + def accept_incident_wave(self, a: float) -> None: + self.a = a + + def propagate_reflected_wave(self) -> float: + self.b = 2.0 * self.Is + self.a + return self.b + + +#################################################################################### + + class ResistiveVoltageSource(baseWDF): - def __init__(self, Rval: float = None): + # def __init__(self, Rval: float = None): + def __init__(self, next: baseWDF = None, Rval: float = None) -> None: baseWDF.__init__(self) self.Rval = Rval if Rval else 1e-9 self.Vs = 0 @@ -347,14 +493,114 @@ def propagate_reflected_wave(self) -> None: #################################################################################### + +class ChuaDiode(rootWDF): + """ + Computes the Chua diode nonlinearity, a piecewise linear active resistance. + This class implements a Chua diode model for Wave Digital Filter (WDF) circuits. + The Chua diode is characterized by a piecewise linear current-voltage relationship. + """ + + def __init__( + self, + next: baseWDF, + g1: float, + g2: float, + v0: float, + r1: float + ) -> None: + """ + Initialize the Chua diode. + + Args: + next_element: The next WDF element in the circuit + g1: Slope of i(v) parameter of the chua diode + g2: Slope of i(v) parameter of the chua diode + v0: Voltage parameter of the chua diode + r1: Resistance value in Ohms + """ + rootWDF.__init__(self, next) + next.connect_to_parent(self) + self.set_Chua_parameters(g1, g2, r1, v0) + + + def set_Chua_parameters( + self, + g1: float, + g2: float, + r1: float, + v0: float + ) -> None: + """ + Sets diode specific parameters. + + Args: + g1: First conductance parameter + g2: Second conductance parameter + r1: Resistance parameter + """ + self.G1 = g1 + self.G2 = g2 + self.R1 = r1 + self.V0 = v0 + + def calc_impedance(self): + """Calculate impedance - implementation depends on specific circuit context""" + # Implementation would depend on the specific WDF framework + # This is a placeholder as the original C++ implementation is empty + pass + + + def incident(self, a: float): + """ + Set the incident wave. + + Args: + a: The incident wave value + """ + self.a = a + + + def propagate_reflected_wave(self) -> float: + """ + Compute the reflected wave using the Chua diode characteristic. + This implements the piecewise linear characteristic of the Chua diode + using the absolute value function to create the nonlinear behavior. + + Args: + a0: The incident wave value + + Returns: + The reflected wave value + """ + # TODO: g1 and g2 do not need to be calculated for every reflected calculation, just a_0 + g1 = (1.0 - self.G1 * self.R1) / (1.0 + self.G1 * self.R1) + g2 = (1.0 - self.G2 * self.R1) / (1.0 + self.G2 * self.R1) + a_0 = self.V0 * (1.0 + self.G2 * self.R1) + + self.b = ( g1 * self.a + 0.5 * (g2 - g1) * (abs( self.a + a_0 ) - abs( self.a - a_0 ))) + + return self.b + + + +#################################################################################### + + class Diode(rootWDF): def __init__( - self, next: baseWDF, Is: float, Vt: float = 25.85e-3, n_diodes: float = 1 + self, + next: baseWDF, + Is: float, + Vt: float = 25.85e-3, + n_diodes: float = 1 ) -> None: + rootWDF.__init__(self, next) next.connect_to_parent(self) self.set_diode_params(Is, Vt, n_diodes) + def set_diode_params(self, Is: float, Vt: float, n_diodes: float) -> None: self.Is = Is self.n_diodes = n_diodes @@ -407,7 +653,11 @@ def omega4(self, x: float) -> float: class DiodePair(Diode): def __init__( - self, next: baseWDF, Is: float, Vt: float = 25.85e-3, n_diodes: float = 2 + self, + next: baseWDF, + Is: float, + Vt: float = 25.85e-3, + n_diodes: float = 2 ) -> None: Diode.__init__(self, next, Is, Vt, n_diodes) diff --git a/pywdf/examples/__init__.py b/pywdf/examples/__init__.py index b8a1dd0..b842ad6 100644 --- a/pywdf/examples/__init__.py +++ b/pywdf/examples/__init__.py @@ -8,4 +8,5 @@ "rca_mk2_sef", "rclowpass", "voltagedivider", + "chua_circuit", ] diff --git a/pywdf/examples/bassmantonestack.py b/pywdf/examples/bassmantonestack.py index 4f7e518..1b2084f 100644 --- a/pywdf/examples/bassmantonestack.py +++ b/pywdf/examples/bassmantonestack.py @@ -66,7 +66,8 @@ def _impedance_calc(self,R: RTypeAdaptor): Rb, Rc, Rd, Re, Rf, Rg = R.get_port_impedances() # This scattering matrix was derived using the R-Solver python script (https://github.com/jatinchowdhury18/R-Solver), # invoked with command: r_solver.py --adapt 0 --out ./test_outputs/bassman_test.txt --pywdf ./netlists/bassman_netlist.txt - R.set_S_matrix([[0,-(Rc*Rd + (Rc + Rd)*Re + Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + Rb*Re + (Rb + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Re - Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + (Rb + Rc + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rc*Rd + (Rb + Rc + Rd)*Re)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -1,], + R.set_S_matrix([ + [0,-(Rc*Rd + (Rc + Rd)*Re + Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + Rb*Re + (Rb + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Re - Rc*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rb*Rd + (Rb + Rc + Rd)*Rf)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -(Rc*Rd + (Rb + Rc + Rd)*Re)/((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf), -1,], [-(Rb*Rc*Rd + Rb*Rc*Rf + (Rb*Rc + Rb*Rd)*Re)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg), -(Rb*Rb*Rc*Rd*Rd + (Rb*Rb*Rc + Rb*Rb*Rd)*Re*Re + (Rb*Rb*Rc - Rc*Rc*Rd - Rc*Rd*Rd + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re)*Rf*Rf + (2*Rb*Rb*Rc*Rd + Rb*Rb*Rd*Rd)*Re + (2*Rb*Rb*Rc*Rd - Rc*Rc*Rd*Rd + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc - Rc*Rd*Rd + (Rb*Rb - Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb - Rc*Rc)*Rd*Rd + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re*Re + (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Rf*Rf - 2*(Rc*Rd*Rd - (Rb*Rb - Rc*Rc)*Rd)*Re - 2*(Rc*Rd*Rd - (Rb*Rb - Rc*Rc)*Rd - (Rb*Rb - Rc*Rc - 2*Rc*Rd - Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rb*Rc*Rd*Rd + (Rb*Rb*Rc + Rb*Rb*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf*Rf + (2*Rb*Rb*Rc*Rd + Rb*Rb*Rd*Rd)*Re + (2*Rb*Rb*Rc*Rd + Rb*Rc*Rd*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (2*Rb*Rb*Rc + Rb*Rd*Rd + 3*(Rb*Rb + Rb*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Rd + (Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (Rb*Rb + Rb*Rc + Rb*Rd)*Rf*Rf + (Rb*Rd*Rd + 2*(Rb*Rb + Rb*Rc)*Rd)*Re + (Rb*Rd*Rd + 2*(Rb*Rb + Rb*Rc)*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rb*Rc*Rd*Re + (Rb*Rb*Rc + Rb*Rb*Rd)*Re*Re + (2*Rb*Rb*Rc + Rb*Rc*Rc + 2*Rb*Rc*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf*Rf + (2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (2*Rb*Rb*Rc + Rb*Rc*Rc)*Rd + (3*Rb*Rb*Rc + Rb*Rc*Rc + (2*Rb*Rb + 3*Rb*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Re + (Rb*Rb + Rb*Rc + Rb*Rd)*Re*Re + (Rb*Rb + Rb*Rc + Rb*Rd)*Rf*Rf + ((Rb*Rb + Rb*Rc)*Rd + 2*(Rb*Rb + Rb*Rc + Rb*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rb*Rc*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rc*Rd)*Rf*Rf + (Rb*Rb*Rc*Rd + Rb*Rb*Rd*Rd)*Re - (Rb*Rc*Rc*Rd - Rb*Rc*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc - Rb*Rb*Rd - Rb*Rd*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Rd + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Re + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((2*Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (2*(Rb*Rb + Rb*Rc)*Rd*Rd + (3*Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd)*Re + (2*Rb*Rc*Rd*Rd + (2*Rb*Rb*Rc + Rb*Rc*Rc)*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + 2*Rb*Rd*Rd + (2*Rb*Rb + 3*Rb*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + Rb*Rc)*Rd*Rd + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Re + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rc*Rd + Rb*Rc*Rf + (Rb*Rc + Rb*Rd)*Re)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg),], [-(Rb*Rc*Rd + Rb*Rc*Re + (Rb*Rc + Rc*Rd)*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg), (Rb*Rc*Rc*Rd*Rd + (Rb*Rc*Rc + Rb*Rc*Rd)*Re*Re + (Rb*Rc*Rc + Rc*Rc*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf*Rf + (2*Rb*Rc*Rc*Rd + Rb*Rc*Rd*Rd)*Re + (2*Rb*Rc*Rc*Rd + Rc*Rc*Rd*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (2*Rb*Rc*Rc + Rc*Rd*Rd + 3*(Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (Rb*Rc + Rc*Rc + Rc*Rd)*Rf*Rf + (Rc*Rd*Rd + 2*(Rb*Rc + Rc*Rc)*Rd)*Re + (Rc*Rd*Rd + 2*(Rb*Rc + Rc*Rc)*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rc*Rc*Rd*Rd + (Rb*Rc*Rc - Rb*Rb*Rd - Rb*Rd*Rd)*Re*Re + (Rb*Rc*Rc + Rc*Rc*Rd - (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re)*Rf*Rf + (2*Rb*Rc*Rc*Rd - Rb*Rb*Rd*Rd)*Re + (2*Rb*Rc*Rc*Rd + Rc*Rc*Rd*Rd - (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rc*Rc - Rb*Rd*Rd - (Rb*Rb - Rc*Rc)*Rd)*Re)*Rf - ((Rb*Rb - Rc*Rc)*Rd*Rd + (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re*Re + (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Rf*Rf + 2*(Rb*Rd*Rd + (Rb*Rb - Rc*Rc)*Rd)*Re + 2*(Rb*Rd*Rd + (Rb*Rb - Rc*Rc)*Rd + (Rb*Rb - Rc*Rc + 2*Rb*Rd + Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd*Re + (Rb*Rb*Rc + 2*Rb*Rc*Rc + 2*Rb*Rc*Rd)*Re*Re + (Rb*Rc*Rc + Rc*Rc*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf*Rf + (Rb*Rc*Rc*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (Rb*Rb*Rc + 3*Rb*Rc*Rc + (3*Rb*Rc + 2*Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Re + (Rb*Rc + Rc*Rc + Rc*Rd)*Re*Re + (Rb*Rc + Rc*Rc + Rc*Rd)*Rf*Rf + ((Rb*Rc + Rc*Rc)*Rd + 2*(Rb*Rc + Rc*Rc + Rc*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd)*Rf*Rf + (2*Rb*Rc*Rd*Rd + (Rb*Rb*Rc + 2*Rb*Rc*Rc)*Rd)*Re + (2*(Rb*Rc + Rc*Rc)*Rd*Rd + (2*Rb*Rb*Rc + 3*Rb*Rc*Rc)*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + 2*Rc*Rd*Rd + (3*Rb*Rc + 2*Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Rd + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Re + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (Rb*Rc*Rc*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rc*Rd)*Re*Re - (Rb*Rb*Rc*Rd - Rb*Rc*Rd*Rd)*Re + (Rb*Rc*Rc*Rd + Rc*Rc*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc - Rc*Rc*Rd - Rc*Rd*Rd)*Re)*Rf + 2*((Rb*Rc + Rc*Rc)*Rd*Rd + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Re + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rc*Rd + Rb*Rc*Re + (Rb*Rc + Rc*Rd)*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg),], [-(Rb*Rd*Re - Rc*Rd*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg), (Rb*Rc*Rd*Rd*Re + (Rb*Rc*Rd + Rb*Rd*Rd)*Re*Re + (2*Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((2*Rb + 3*Rc)*Rd*Rd + (3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + 2*((Rb + Rc)*Rd*Rd*Re + ((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + ((Rb + Rc)*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb + 2*Rb*Rc)*Rd*Rd*Re + (2*Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rc*Rd + Rc*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + (Rb*Rc*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((3*Rb + 2*Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc)*Rd)*Re)*Rf + 2*((Rb + Rc)*Rd*Rd*Re + ((Rb + Rc)*Rd + Rd*Rd)*Re*Re + ((Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + ((Rb + Rc)*Rd*Rd + 2*((Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -((Rb*Rb + 2*Rb*Rc)*Rd*Rd*Re + (Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd - (Rb*Rb*Rc + Rb*Rc*Rc - Rb*Rd*Rd)*Re*Re - (Rb*Rb*Rc + Rb*Rc*Rc - Rc*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re)*Rf*Rf + ((2*Rb*Rc + Rc*Rc)*Rd*Rd - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re*Re - 2*(Rb*Rb*Rc + Rb*Rc*Rc - (Rb + Rc)*Rd*Rd)*Re)*Rf + (2*(Rb + Rc)*Rd*Rd*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re*Re - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd - (Rb*Rb + 2*Rb*Rc + Rc*Rc - Rd*Rd)*Re)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), (2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rc*Rd*Rd + (Rb*Rc + Rc*Rc)*Rd)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((3*Rb*Rc + 2*Rc*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + ((Rb + 2*Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + 2*Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rd*Rd + (Rb*Rb + Rb*Rc)*Rd)*Re*Re + ((2*Rb*Rb + 3*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + ((2*Rb + Rc)*Rd*Rd + (2*Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + 2*((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + ((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Rf)*Rg)/((Rb*Rb*Rc + Rb*Rc*Rc)*Rd*Rd + (Rb*Rb*Rc + Rb*Rc*Rc + Rb*Rd*Rd + (Rb*Rb + 2*Rb*Rc)*Rd)*Re*Re + (Rb*Rb*Rc + Rb*Rc*Rc + Rc*Rd*Rd + (2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf*Rf + ((Rb*Rb + 2*Rb*Rc)*Rd*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd)*Re + ((2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + 2*(Rb*Rb*Rc + Rb*Rc*Rc)*Rd + 2*(Rb*Rb*Rc + Rb*Rc*Rc + (Rb + Rc)*Rd*Rd + (Rb*Rb + 3*Rb*Rc + Rc*Rc)*Rd)*Re)*Rf + ((Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re*Re + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Rf*Rf + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd)*Re + 2*((Rb + Rc)*Rd*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc)*Rd + (Rb*Rb + 2*Rb*Rc + Rc*Rc + 2*(Rb + Rc)*Rd + Rd*Rd)*Re)*Rf)*Rg), -(Rb*Rd*Re - Rc*Rd*Rf)/(Rb*Rc*Rd + (Rb*Rc + Rb*Rd)*Re + (Rb*Rc + Rc*Rd + (Rb + Rc + Rd)*Re)*Rf + ((Rb + Rc)*Rd + (Rb + Rc + Rd)*Re + (Rb + Rc + Rd)*Rf)*Rg),], diff --git a/pywdf/examples/capacitor.py b/pywdf/examples/capacitor.py new file mode 100644 index 0000000..e5ca088 --- /dev/null +++ b/pywdf/examples/capacitor.py @@ -0,0 +1,91 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + + +class _Capacitor(Circuit): + + def __init__( + self, + sample_rate: int, + cutoff: float + ) -> None: + + self.fs = sample_rate + self.cutoff = cutoff + + self.C = 47e-9 # capacitance in Farads + self.R = 1.0 / (2 * np.pi * self.C * self.cutoff) + self.Vs = ResistiveVoltageSource(self.R) + + self.C1 = Capacitor(self.C, self.fs) + self.S1 = SeriesAdaptor(self.Vs, self.C1) + + super().__init__(self.Vs, self.S1, self.C1) + # super().__init__(self.Vs, self.Vs, self.C1) + + + def process_sample_i_v(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vs.set_voltage(sample) + self.Vs.accept_incident_wave(self.S1.propagate_reflected_wave()) + self.S1.accept_incident_wave(self.Vs.propagate_reflected_wave()) + + return ( self.source.wave_to_voltage(), self.source.wave_to_current(), self.output.wave_to_current() ) + + + + +if __name__ == "__main__": + + fs = 44100 + f = 4 + # duration = .25 + duration = 1.0 + + cap = _Capacitor(fs, 1000) + + # cap.plot_freqz() + # cap.plot_freqz_list(range(1000, 10000, 1000), cap.set_cutoff, param_label="cutoff") + # cap.AC_transient_analysis() + + t = np.linspace(0, duration, int(fs * duration), endpoint=False) + + sine = np.sin(2 * np.pi * f * t) + + y = cap.process_i_v_signals(sine) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + ax.plot(sine, color="r", label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + color = 'tab:blue' + ax2 = ax.twinx() + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + ax2.plot(i, color=color, label="current through", alpha=0.75) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through capacitor C1 ") + ax.legend() + ax2.legend() + ax.grid(True) + + plt.savefig("./tests/capacitor.png") + plt.show() \ No newline at end of file diff --git a/pywdf/examples/chua.py b/pywdf/examples/chua.py new file mode 100644 index 0000000..841af00 --- /dev/null +++ b/pywdf/examples/chua.py @@ -0,0 +1,184 @@ +# Chua's Circuit example using WDF following the principles of Meerkotter and Scholz 1989. +# "Digital simulation of nonlinear circuits by wave digital filter principles" + + +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class Chua(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.C1_value = 5.5e-9 + self.R2_value = 1.3e3 + # self.R2_value = 1.428e3 + self.L3_value = 7.07e-3 + self.C4_value = 49.5e-9 + + self.C1 = Capacitor(self.C1_value, self.fs) # fs, needs local discretization + self.R2 = Resistor(self.R2_value) + self.L3 = Inductor(self.L3_value, self.fs) # fs, needs local discretization + self.C4 = Capacitor(self.C4_value, self.fs) # fs, needs local discretization + + self.Vs = SeriesVoltage(self.C4) + + self.P2 = ParallelAdaptor(self.L3, self.Vs) + self.S1 = SeriesAdaptor(self.P2, self.R2) + self.P1 = ParallelAdaptor(self.S1, self.C1) + + self.g1 = -500.0e-6 + self.g2 = -800.0e-6 + self.v0 = 1.0 + self.R_NL = 569.2 + + self.NL = ChuaDiode( + self.P1, + g1=self.g1, # parameter 1 + g2=self.g2, # parameter 2 + v0=self.v0, # Voltage parameter + r1=self.R_NL, # Resistance in Ohms + ) + + # init and set circuit + super().__init__(self.Vs, self.NL, self.C1) + + + def process_sample( + self, + sample: float + ) -> float: + + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage() + + + def process_sample_chua(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage(), self.C4.wave_to_voltage(), self.L3.wave_to_current() + + + def set_params( + self, + frequency: float, + decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + # self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + # self.L1.set_inductance(self.L) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + # fs = 48e3 # doesn't work for this sample rate + # fs = 96e3 + fs = 100e3 + + chua_circuit = Chua(fs) + # chua_circuit.set_params(frequency, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{fs}Hz.png" + + + a = np.ones(1) # impulse signal + b = np.zeros(2400) + samples = np.concatenate((a, b)) + + i_list, v1_list, v2_list = [], [], [] + + for s in samples: + v1, v2, i = chua_circuit.process_sample_chua(s) + v1_list.append(v1) + v2_list.append(v2) + i_list.append(i) + + # Plotting + fig, axes = plt.subplots(1, 3, figsize=(15, 4)) + axes[0].plot(v1_list, label='C1 [V]', color='r') + axes[1].plot(v2_list, label='C4 [V]', color='g') + axes[2].plot(i_list, label='L3 [I]', color='b') + + + for ax in axes: + ax.legend() + ax.grid(True) + ax.set_xlabel("Sample [n]") + + axes[0].set_ylabel("Output") + + # Centered title + fig.suptitle("Chua impulse response", fontsize=14) + plt.tight_layout(rect=[0, 0, 1, 0.95]) # Leave space for suptitle + + # Save and show + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + + # 3D Phase Portrait + fig = plt.figure(figsize=(8, 6)) + ax = fig.add_subplot(111, projection='3d') + ax.plot(v1_list, v2_list, i_list, lw=1.0) + ax.set_title("3D Phase Portrait of Chua's Circuit WDF") + ax.set_xlabel("x C1 [V]") + ax.set_ylabel("y C4 [V]") + ax.set_zlabel("z L3 [I]") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_WDF_attractor.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() diff --git a/pywdf/examples/chua_minimal.py b/pywdf/examples/chua_minimal.py new file mode 100644 index 0000000..4ea32fa --- /dev/null +++ b/pywdf/examples/chua_minimal.py @@ -0,0 +1,185 @@ +# Chua's Circuit example using WDF following the principles of Meerkotter and Scholz 1989. +# "Digital simulation of nonlinear circuits by wave digital filter principles" + + +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class Chua(Circuit): + + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + self.Vin_prev_i = 0.0 + + # initialize wdf + self.C1_value = 5.5e-9 + self.R2_value = 1.3e3 + + self.R2_value = 1.428e3 + + self.L3_value = 7.07e-3 + self.C4_value = 49.5e-9 + + self.C1 = Capacitor(self.C1_value, self.fs) # fs, needs local discretization + self.C4 = Capacitor(self.C4_value, self.fs) # fs, needs local discretization + self.L3 = Inductor(self.L3_value, self.fs) # fs, needs local discretization + + self.Vin = ResistiveVoltageSource( None, self.R2_value ) + + self.P2 = ParallelAdaptor(self.L3, self.C4) + self.S1 = SeriesAdaptor(self.P2, self.Vin) + self.P1 = ParallelAdaptor(self.S1, self.C1) + + self.g1 = -500.0e-6 + self.g2 = -800.0e-6 + self.v0 = 1.0 + self.R_NL = 569.2 + + self.NL = ChuaDiode( self.P1, g1=self.g1, # parameter 1 + g2=self.g2, # parameter 2 + v0=self.v0, # Voltage parameter + r1=self.R_NL, # Resistance in Ohms + ) + + # init and set circuit + super().__init__(self.Vin, self.NL, self.C1) + + + def process_sample( + self, + sample: float + ) -> float: + + # self.Vs.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage() + + + def process_sample_chua(self, sample: float) -> float: + """Process an individual sample with this circuit. + + Note: not every circuit will follow this general pattern, in such cases users may want to overwrite this function. See example circuits + + Args: + sample (float): incoming sample to process + + Returns: + (i, v) I-V tupple: processed sample + """ + self.Vin.set_voltage(sample) + self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + return self.output.wave_to_voltage(), self.C4.wave_to_voltage(), self.L3.wave_to_current() + + + def set_params( + self, + frequency: float, + decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + # self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + # self.L1.set_inductance(self.L) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + # fs = 48e3 # doesn't work for this sample rate + # fs = 96e3 + fs = 100e3 + + chua_circuit = Chua(fs) + # chua_circuit.set_params(frequency, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "tests" / "plots" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{fs}Hz.png" + + + a = np.ones(1) # impulse signal + b = np.zeros(2400) + samples = np.concatenate((a, b)) + + i_list, v1_list, v2_list = [], [], [] + + for s in samples: + v1, v2, i = chua_circuit.process_sample_chua(s) + v1_list.append(v1) + v2_list.append(v2) + i_list.append(i) + + # Plotting + fig, axes = plt.subplots(1, 3, figsize=(15, 4)) + axes[0].plot(v1_list, label='C1 [V]', color='r') + axes[1].plot(v2_list, label='C4 [V]', color='g') + axes[2].plot(i_list, label='L3 [I]', color='b') + + + for ax in axes: + ax.legend() + ax.grid(True) + ax.set_xlabel("Sample [n]") + + axes[0].set_ylabel("Output") + + # Centered title + fig.suptitle("Chua impulse response", fontsize=14) + plt.tight_layout(rect=[0, 0, 1, 0.95]) # Leave space for suptitle + + # Save and show + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() + + + # 3D Phase Portrait + fig = plt.figure(figsize=(8, 6)) + ax = fig.add_subplot(111, projection='3d') + ax.plot(v1_list, v2_list, i_list, lw=1.0) + ax.set_title("3D Phase Portrait of Chua's Circuit WDF") + ax.set_xlabel("x C1 [V]") + ax.set_ylabel("y C4 [V]") + ax.set_zlabel("z L3 [I]") + plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_WDF_attractor.png" + plt.savefig(out_path.with_suffix('.png')) + plt.show() diff --git a/pywdf/examples/diodeclipper.py b/pywdf/examples/diodeclipper.py index dd2767a..c417831 100644 --- a/pywdf/examples/diodeclipper.py +++ b/pywdf/examples/diodeclipper.py @@ -11,8 +11,12 @@ class DiodeClipper(Circuit): def __init__( - self, sample_rate: int, cutoff: float = 1000, input_gain_db: float = 0, - output_gain_db: float = 0, n_diodes: float = 2 + self, + sample_rate: int, + cutoff: float = 1000, + input_gain_db: float = 0, + output_gain_db: float = 0, + n_diodes: float = 2 ) -> None: self.fs = sample_rate @@ -38,7 +42,7 @@ def __init__( def process_sample(self, sample: float) -> float: sample *= self.input_gain - return -(super().process_sample(sample) * self.output_gain) ### ¡! phase inverted !¡ + return -( super().process_sample(sample) * self.output_gain) ### ¡! phase inverted !¡ def set_cutoff(self, new_cutoff: float) -> None: if self.cutoff != new_cutoff: diff --git a/pywdf/examples/inductor.py b/pywdf/examples/inductor.py new file mode 100644 index 0000000..cb7f957 --- /dev/null +++ b/pywdf/examples/inductor.py @@ -0,0 +1,104 @@ +import matplotlib.pyplot as plt +from pathlib import Path +import sys + +script_path = Path(__file__).resolve() +src_dir = script_path.parent.parent + +sys.path.append(str(src_dir)) + +from core.wdf import * +from core.circuit import Circuit + + +class _Inductor(Circuit): + def __init__( + self, + sample_rate: int, + frequency: float = 442, + decibels: float = -18, + closed: bool = True, + ) -> None: + + self.fs = sample_rate + self.frequency = frequency + self.decibels = decibels + self.gain = self.decibels_to_gain() + self.closed = closed + + # initialize wdf + self.L = 1.0e3 + self.twopi = 2 * np.pi + + self.L1 = Inductor(self.L, self.fs) + + self.Vs = ResistiveVoltageSource() + self.S1 = SeriesAdaptor(self.Vs, self.L1) + + # self.SW1 = Switch(self.S1) + + # init and set circuit + super().__init__(self.Vs, self.S1, self.C1) + # super().__init__(self.Vs, self.SW1, self.C1) + self.set_params(self.frequency, self.closed, self.decibels) + + def process_sample(self, sample: float) -> float: + return super().process_sample(sample) * self.gain + + def set_params( + self, frequency: float, switch_closed: bool, decibels: float + ) -> None: + + # update frequency + if self.frequency != frequency: + self.frequency = frequency + + self.L = 1.0 / (np.square(self.twopi * frequency) * self.C) + self.L1.set_inductance(self.L) + + # update switch status + if switch_closed != self.closed: + self.SW1.set_closed(switch_closed) + + # update gain + if self.decibels != decibels: + self.decibels = decibels + self.gain = self.decibels_to_gain() + + def decibels_to_gain(self): + return 10 ** (self.decibels / 20.0) + + +if __name__ == "__main__": + + # set params + fs = 48e3 + frequency = 440 + decibels = 0 + switch_closed = True + + _inductor = _Inductor(fs) + _inductor.set_params(frequency, switch_closed, decibels) # update params + + # plot transfer function + plt_dir = src_dir.parent / "data" / "plot" + plt_dir.mkdir(exist_ok=True, parents=True) + out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" + _inductor.plot_freqz(out_path) + + # generate sinusoid + out = _inductor.process_signal(np.ones((int(fs)))) + out = out - 1 # remove DC offset [0, 2] + + plt.figure(figsize=(10, 4)) + plt.plot(out) + plt.xlim([0, fs]) + plt.title(f"{frequency}Hz sinewave") + plt.tight_layout() + plt.show() + + # estimate pitch using zerocrossing + zero_crossings = np.where(np.diff(np.sign(out)))[0] + T = (zero_crossings[2] - zero_crossings[0]) / fs + f = 1 / T + print(f"T = {T:.6f}[s]\nf = {f:.3f}[Hz]") diff --git a/pywdf/examples/lc_oscillator.py b/pywdf/examples/lc_oscillator.py index 5d37520..4136d52 100644 --- a/pywdf/examples/lc_oscillator.py +++ b/pywdf/examples/lc_oscillator.py @@ -12,6 +12,7 @@ class LCOscillator(Circuit): + def __init__( self, sample_rate: int, @@ -34,21 +35,41 @@ def __init__( self.C1 = Capacitor(self.C, self.fs) self.L1 = Inductor(self.L, self.fs) self.S2 = SeriesAdaptor(self.C1, self.L1) + # self.S2 = ParallelAdaptor(self.C1, self.L1) self.Vs = ResistiveVoltageSource() self.S1 = SeriesAdaptor(self.Vs, self.S2) + # self.S1 = ParallelAdaptor(self.Vs, self.S2) self.SW1 = Switch(self.S1) # init and set circuit super().__init__(self.Vs, self.SW1, self.C1) + self.set_params(self.frequency, self.closed, self.decibels) - def process_sample(self, sample: float) -> float: + + + def process_sample( + self, + sample: float + ) -> float: + + # self.Vs.set_voltage(sample) + # self.NL.accept_incident_wave(self.P1.propagate_reflected_wave()) + # self.P1.accept_incident_wave(self.NL.propagate_reflected_wave()) + + # return self.output.wave_to_voltage() + + return super().process_sample(sample) * self.gain + def set_params( - self, frequency: float, switch_closed: bool, decibels: float + self, + frequency: float, + switch_closed: bool, + decibels: float ) -> None: # update frequency @@ -75,7 +96,7 @@ def decibels_to_gain(self): # set params fs = 48e3 - frequency = 440 + frequency = 10 decibels = 0 switch_closed = True @@ -83,24 +104,28 @@ def decibels_to_gain(self): lc_oscillator.set_params(frequency, switch_closed, decibels) # update params # plot transfer function - plt_dir = src_dir.parent / "data" / "plot" + plt_dir = src_dir.parent / "tests" / "plots" plt_dir.mkdir(exist_ok=True, parents=True) out_path = plt_dir / f"{script_path.stem}_{frequency}Hz.png" - lc_oscillator.plot_freqz(out_path) + + lc_oscillator.plot_freqz( + out_path + ) + + a = np.ones(1) # impulse signal + b = np.zeros(24000) + samples = np.concatenate((a, b)) # generate sinusoid - out = lc_oscillator.process_signal(np.ones((int(fs)))) + out = lc_oscillator.process_signal(samples) out = out - 1 # remove DC offset [0, 2] plt.figure(figsize=(10, 4)) plt.plot(out) plt.xlim([0, fs]) - plt.title(f"{frequency}Hz sinewave") + plt.title(f"LC Oscillator {frequency}Hz sinewave") plt.tight_layout() + out_path = plt_dir / f"{script_path.stem}_signal.png" + plt.savefig(out_path.with_suffix('.png')) plt.show() - # estimate pitch using zerocrossing - zero_crossings = np.where(np.diff(np.sign(out)))[0] - T = (zero_crossings[2] - zero_crossings[0]) / fs - f = 1 / T - print(f"T = {T:.6f}[s]\nf = {f:.3f}[Hz]") diff --git a/pywdf/examples/passive_apf.py b/pywdf/examples/passive_apf.py index 16bf56d..dacee09 100644 --- a/pywdf/examples/passive_apf.py +++ b/pywdf/examples/passive_apf.py @@ -12,7 +12,7 @@ script_dir = Path(__file__).resolve().parent wdf_dir = script_dir.parent -plot_dir = wdf_dir.parent / "data" / "plot" +plot_dir = wdf_dir.parent / "tests" / "plots" # add path to PYTHONPATH sys.path.append(str(wdf_dir)) @@ -283,8 +283,14 @@ def set_cutoff(self, cutoff: float) -> None: if __name__ == "__main__": + apf = PassiveAPF(48000) + apf.plot_freqz() + apf.plot_freqz_list( - [100, 250, 500, 1000, 2000, 4000, 8000], apf.set_cutoff, param_label="cutoff", outpath=plot_dir / "passive_apf-cutoff_list.png" + [100, 250, 500, 1000, 2000, 4000, 8000], + apf.set_cutoff, + param_label="cutoff", + outpath=plot_dir / "passive_apf-cutoff_list.png" ) diff --git a/pywdf/examples/passivelpf.py b/pywdf/examples/passive_lpf.py similarity index 87% rename from pywdf/examples/passivelpf.py rename to pywdf/examples/passive_lpf.py index 99c260f..142ec59 100644 --- a/pywdf/examples/passivelpf.py +++ b/pywdf/examples/passive_lpf.py @@ -37,5 +37,12 @@ def set_cutoff(self, new_cutoff: float) -> None: self.C2.set_capacitance(self.C) if __name__ == '__main__': + lpf = PassiveLPF(44100, 1000) - lpf.plot_freqz_list(range(1000,10000,1000),lpf.set_cutoff,param_label='cutoff') \ No newline at end of file + + lpf.plot_freqz_list( + range(1000,10000,1000), + lpf.set_cutoff, + param_label='cutoff', + outpath="tests/passive_lpf_freqz_list.png" + ) \ No newline at end of file diff --git a/pywdf/examples/rc_highpass.py b/pywdf/examples/rc_highpass.py index d4701ad..f510954 100644 --- a/pywdf/examples/rc_highpass.py +++ b/pywdf/examples/rc_highpass.py @@ -44,7 +44,25 @@ def set_cutoff(self, new_cutoff: float): if __name__ == "__main__": + lpf = RCHighPass(44100, 1000) - lpf.plot_freqz() - # lpf.plot_freqz_list(range(1000, 10000, 1000), lpf.set_cutoff, param_label="cutoff") - # lpf.AC_transient_analysis() + + lpf.plot_freqz( outpath="tests/rc_highpass_freqz.png" ) + + lpf.plot_freqz_list( + range(1000, 10000, 1000), + lpf.set_cutoff, + param_label="cutoff", + outpath="tests/rc_highpass_freqz_list.png" + ) + + lpf.AC_transient_analysis( + freq = 1000, + amplitude = 1, + t_ms = 5, + outpath="tests/rc_highpass_ac_analysis.png" + ) + + lpf.plot_impulse_response( outpath="tests/rc_pass_impulse_response.png" ) + + print("done") \ No newline at end of file diff --git a/pywdf/examples/rclowpass.py b/pywdf/examples/rc_lowpass.py similarity index 65% rename from pywdf/examples/rclowpass.py rename to pywdf/examples/rc_lowpass.py index 96a2b92..ca4ca10 100644 --- a/pywdf/examples/rclowpass.py +++ b/pywdf/examples/rc_lowpass.py @@ -35,7 +35,25 @@ def set_cutoff(self, new_cutoff: float): if __name__ == "__main__": + lpf = RCLowPass(44100, 1000) - lpf.plot_freqz() - lpf.plot_freqz_list(range(1000, 10000, 1000), lpf.set_cutoff, param_label="cutoff") - lpf.AC_transient_analysis() + + lpf.plot_freqz( outpath="tests/rc_lowpass_freqz.png" ) + + lpf.plot_freqz_list( + range(1000, 10000, 1000), + lpf.set_cutoff, + param_label="cutoff", + outpath="tests/rc_lowpass_freqz_list.png" + ) + + lpf.AC_transient_analysis( + freq = 1000, + amplitude = 1, + t_ms = 5, + outpath="tests/rc_lowpass_ac_analysis.png" + ) + + lpf.plot_impulse_response( outpath="tests/rc_lowpass_impulse_response.png" ) + + print("done") \ No newline at end of file diff --git a/pywdf/examples/resistor.py b/pywdf/examples/resistor.py new file mode 100644 index 0000000..7fd9483 --- /dev/null +++ b/pywdf/examples/resistor.py @@ -0,0 +1,61 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + +class _Resistor(Circuit): + + def __init__( + self, + fs: int, + R1_val: float + ) -> None: + + self.fs = fs + + self.R1 = Resistor(R1_val) + + self.Vs = IdealVoltageSource(self.R1) + + super().__init__(self.Vs, self.Vs, self.R1) + + def set_R1(self, new_R): + self.R1.set_resistance(new_R) + + # def process_sample(self, sample: float) -> float: + # return super().process_sample_i_v(sample) + + +if __name__ == '__main__': + + r = _Resistor(44100, 1e4) + + vs = np.arange(0.0, 6.0, 0.01) + + y = r.process_i_v_signals(vs) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + ax.plot(v, label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + color = 'tab:blue' + ax2 = ax.twinx() + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + ax2.plot(i, color=color, label="current through output", alpha=0.75) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through resistor R1 ") + ax.grid(True) + ax.legend() + + plt.savefig("./tests/resistor.png") + plt.show() + + diff --git a/pywdf/examples/voltagedivider.py b/pywdf/examples/resistor_parallel.py similarity index 81% rename from pywdf/examples/voltagedivider.py rename to pywdf/examples/resistor_parallel.py index b088db1..b7a182d 100644 --- a/pywdf/examples/voltagedivider.py +++ b/pywdf/examples/resistor_parallel.py @@ -24,6 +24,11 @@ def set_R1(self,new_R): def set_R2(self,new_R): self.R2.set_resistance(new_R) + + def process_sample(self, sample: float) -> float: + # return super().process_sample(sample) + self.R1.wave_to_voltage() + self.C1.wave_to_voltage() + pass + if __name__ == '__main__': vd = VoltageDivider(44100, 1e5, 1e10) vd.plot_freqz() \ No newline at end of file diff --git a/pywdf/examples/resistor_series.py b/pywdf/examples/resistor_series.py new file mode 100644 index 0000000..a00902c --- /dev/null +++ b/pywdf/examples/resistor_series.py @@ -0,0 +1,69 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + + +class ResistorSeries(Circuit): + + def __init__( + self, + fs: int, + R1_val: float, + R2_val: float + ) -> None: + + self.fs = fs + + self.R1 = Resistor(R1_val) + self.R2 = Resistor(R2_val) + + self.S1 = SeriesAdaptor(self.R1, self.R2) + self.I1 = PolarityInverter(self.S1) + self.Vs = IdealVoltageSource(self.I1) + + super().__init__(self.Vs, self.Vs, self.R2) + + def set_R1(self,new_R): + self.R1.set_resistance(new_R) + + def set_R2(self,new_R): + self.R2.set_resistance(new_R) + + +if __name__ == '__main__': + + rs = ResistorSeries(44100, 1e4, 1e4) + + vs = np.arange(0.0, 6.0, 0.01) + + y = rs.process_i_v_signals(vs) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + + # ax.plot(vs, label="voltage across", alpha=0.75) + ax.plot(v, label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + + color = 'tab:blue' + ax2 = ax.twinx() + ax2.plot(i, color=color, label="current through output", alpha=0.75) + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through resistor R1 ") + ax.grid(True) + ax.legend() + + plt.savefig("./tests/resistor_series.png") + plt.show() + + diff --git a/pywdf/examples/sallenkeyfilter.py b/pywdf/examples/sallenkeyfilter.py index 597f555..6062fb4 100644 --- a/pywdf/examples/sallenkeyfilter.py +++ b/pywdf/examples/sallenkeyfilter.py @@ -48,7 +48,9 @@ def __impedance_calc(self, R: RTypeAdaptor) -> float: Ro = 1.0e-1 Rb, Rc, Rd = R.get_port_impedances() - R.set_S_matrix ([ [ 0, -(Rc * Rd + ((Ag + 1) * Rc + (Ag + 1) * Rd) * Ri - Rc * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), -(Rb * Rd + ((Ag + 1) * Rb - Ag * Rd) * Ri - (Rb + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), (((Ag + 1) * Rb + Ag * Rc) * Ri - (Rb + Rc + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro) ], + + R.set_S_matrix ([ + [ 0, -(Rc * Rd + ((Ag + 1) * Rc + (Ag + 1) * Rd) * Ri - Rc * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), -(Rb * Rd + ((Ag + 1) * Rb - Ag * Rd) * Ri - (Rb + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro), (((Ag + 1) * Rb + Ag * Rc) * Ri - (Rb + Rc + Ri) * Ro) / ((Rb + Rc) * Rd + ((Ag + 1) * Rb + (Ag + 1) * Rc + Rd) * Ri - (Rb + Rc + Ri) * Ro) ], [ -(Rb * Rc * Rd - Rb * Rc * Ro + ((Ag + 1) * Rb * Rc + Rb * Rd) * Ri) / (Rb * Rc * Rd + ((Ag + 1) * Rb * Rc + (Ag + 1) * Rb * Rd) * Ri - (Rb * Rc + (Rb + Rc) * Rd + (Rc + Rd) * Ri) * Ro), -(Rb * Rb * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rd) * Ri * Ri + (Rb * Rb * Rc - (Rc + Rd) * Ri * Ri + (Rb * Rb - Rc * Rc) * Rd - (Rc * Rc + 2 * Rc * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rb * Rc * Rd + (Ag + 1) * Rb * Rb * Rd * Rd) * Ri - (2 * Rb * Rb * Rc * Rd + (Rb * Rb - Rc * Rc) * Rd * Rd - ((Ag + 1) * Rc * Rc + (Ag + 2) * Rc * Rd + Rd * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rb * Rc - 2 * Rc * Rd * Rd + (2 * (Ag + 1) * Rb * Rb - (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (Rb * Rb * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + Ag * Rb * Rd * Rd + ((2 * Ag * Ag + 3 * Ag + 1) * Rb * Rb + (Ag * Ag + Ag) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + 2 * (Rb * Rb + Rb * Rc) * Rd + (Rb * Rc + 2 * Rb * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rb * Rc * Rd + ((2 * Ag + 1) * Rb * Rb + Ag * Rb * Rc) * Rd * Rd) * Ri - (2 * Rb * Rb * Rc * Rd + 2 * (Rb * Rb + Rb * Rc) * Rd * Rd + ((Ag + 1) * Rb * Rc + (2 * Ag + 1) * Rb * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * Rb * Rd * Rd + ((4 * Ag + 3) * Rb * Rb + 3 * (Ag + 1) * Rb * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (((Ag - 1) * Rb * Rb * Rc + Ag * Rb * Rc * Rc) * Rd * Ri + ((Ag * Ag - 1) * Rb * Rb * Rc + (Ag * Ag + Ag) * Rb * Rc * Rc - ((Ag + 1) * Rb * Rb - Ag * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + Rb * Rc * Ri) * Ro * Ro - (((Ag - 1) * Rb * Rc - Rb * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * Ag * Rb * Rb * Rc + (2 * Ag + 1) * Rb * Rc * Rc - Rb * Rb * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) ], [ -((Ag + 1) * Rb * Rc * Ri + Rb * Rc * Rd - (Rb * Rc + Rc * Ri) * Ro) / (Rb * Rc * Rd + ((Ag + 1) * Rb * Rc + (Ag + 1) * Rb * Rd) * Ri - (Rb * Rc + (Rb + Rc) * Rd + (Rc + Rd) * Ri) * Ro), (Rb * Rc * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rd) * Ri * Ri + (Rb * Rc * Rc + 2 * (Rb * Rc + Rc * Rc) * Rd + (Rc * Rc + 2 * Rc * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rc * Rc * Rd + (Ag + 1) * Rb * Rc * Rd * Rd) * Ri - (2 * Rb * Rc * Rc * Rd + 2 * (Rb * Rc + Rc * Rc) * Rd * Rd + ((Ag + 1) * Rc * Rc + (Ag + 1) * Rc * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rc * Rc + 2 * Rc * Rd * Rd + (3 * (Ag + 1) * Rb * Rc + (2 * Ag + 3) * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), -(Rb * Rc * Rc * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc - (Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rd - (Ag + 1) * Rb * Rd * Rd) * Ri * Ri + (Rb * Rc * Rc - Rd * Ri * Ri - (Rb * Rb - Rc * Rc) * Rd + (Rc * Rc - 2 * Rb * Rd) * Ri) * Ro * Ro + (2 * (Ag + 1) * Rb * Rc * Rc * Rd - (Ag + 1) * Rb * Rb * Rd * Rd) * Ri - (2 * Rb * Rc * Rc * Rd - (Rb * Rb - Rc * Rc) * Rd * Rd + ((Ag + 1) * Rc * Rc - 2 * (Ag + 1) * Rb * Rd - Rd * Rd) * Ri * Ri + (2 * (Ag + 1) * Rb * Rc * Rc - 2 * Rb * Rd * Rd - (2 * (Ag + 1) * Rb * Rb - (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (((Ag + 1) * Rb * Rb * Rc + (Ag + 2) * Rb * Rc * Rc) * Rd * Ri + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 3 * Ag + 2) * Rb * Rc * Rc + 2 * (Ag + 1) * Rb * Rc * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + Rc * Ri * Ri + (2 * Rb * Rc + Rc * Rc) * Ri) * Ro * Ro - ((2 * (Ag + 1) * Rb * Rc + (Ag + 2) * Rc * Rc + 2 * Rc * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + (2 * Ag + 3) * Rb * Rc * Rc + (3 * Rb * Rc + 2 * Rc * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) ], [ ((Ag + 1) * Rb * Rd * Ri - ((Rb + Rc) * Rd + Rd * Ri) * Ro) / (Rb * Rc * Rd + ((Ag + 1) * Rb * Rc + (Ag + 1) * Rb * Rd) * Ri - (Rb * Rc + (Rb + Rc) * Rd + (Rc + Rd) * Ri) * Ro), -((Ag + 1) * Rb * Rc * Rd * Rd * Ri + ((Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rd + (Ag * Ag + 2 * Ag + 1) * Rb * Rd * Rd) * Ri * Ri - (Rc * Rd * Ri + (Rb * Rc + Rc * Rc) * Rd) * Ro * Ro + ((Rb * Rc + Rc * Rc) * Rd * Rd - ((Ag + 1) * Rc * Rd + (Ag + 1) * Rd * Rd) * Ri * Ri + ((Ag + 1) * Rc * Rc * Rd - ((Ag + 1) * Rb + Ag * Rc) * Rd * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), (((Ag + 1) * Rb * Rb + 2 * (Ag + 1) * Rb * Rc) * Rd * Rd * Ri + ((Ag * Ag + 3 * Ag + 2) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + 2 * (Ag * Ag + 2 * Ag + 1) * Rb * Rc) * Rd) * Ri * Ri + ((2 * Rb + Rc) * Rd * Ri + Rd * Ri * Ri + (Rb * Rb + Rb * Rc) * Rd) * Ro * Ro - ((Rb * Rb + Rb * Rc) * Rd * Rd + ((Ag + 2) * Rd * Rd + 2 * ((Ag + 1) * Rb + (Ag + 1) * Rc) * Rd) * Ri * Ri + (((Ag + 3) * Rb + (Ag + 2) * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 1) * Rb * Rc) * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro), -(((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd * Ri + (Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd - ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc - (Ag + 1) * Rb * Rd * Rd) * Ri * Ri - (Rb * Rb * Rc + Rb * Rc * Rc + Rc * Ri * Ri + (2 * Rb * Rc + Rc * Rc) * Ri) * Ro * Ro - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd - (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc - Rd * Rd) * Ri * Ri - 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc - (Rb + Rc) * Rd * Rd) * Ri) * Ro) / ((Rb * Rb * Rc + Rb * Rc * Rc) * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb * Rc + (Ag * Ag + 2 * Ag + 1) * Rb * Rc * Rc + (Ag + 1) * Rb * Rd * Rd + ((Ag * Ag + 2 * Ag + 1) * Rb * Rb + (Ag * Ag + 3 * Ag + 2) * Rb * Rc) * Rd) * Ri * Ri + (Rb * Rb * Rc + Rb * Rc * Rc + (Rc + Rd) * Ri * Ri + (Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd + (2 * Rb * Rc + Rc * Rc + 2 * (Rb + Rc) * Rd) * Ri) * Ro * Ro + (((Ag + 1) * Rb * Rb + (Ag + 2) * Rb * Rc) * Rd * Rd + 2 * ((Ag + 1) * Rb * Rb * Rc + (Ag + 1) * Rb * Rc * Rc) * Rd) * Ri - ((Rb * Rb + 2 * Rb * Rc + Rc * Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rc + (Ag + 1) * Rc * Rc + (2 * (Ag + 1) * Rb + (Ag + 2) * Rc) * Rd + Rd * Rd) * Ri * Ri + 2 * (Rb * Rb * Rc + Rb * Rc * Rc) * Rd + (2 * (Ag + 1) * Rb * Rb * Rc + 2 * (Ag + 1) * Rb * Rc * Rc + 2 * (Rb + Rc) * Rd * Rd + (2 * (Ag + 1) * Rb * Rb + 3 * (Ag + 2) * Rb * Rc + (Ag + 2) * Rc * Rc) * Rd) * Ri) * Ro) ] ]) diff --git a/pywdf/examples/voltage_divider.py b/pywdf/examples/voltage_divider.py new file mode 100644 index 0000000..6af0fa8 --- /dev/null +++ b/pywdf/examples/voltage_divider.py @@ -0,0 +1,64 @@ +import sys +import os + +sys.path.append(os.path.abspath(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))) + +from core.wdf import * +from core.circuit import Circuit + +import matplotlib.pyplot as plt + + +class VoltageDivider(Circuit): + def __init__(self, fs: int, R1_val: float, R2_val: float) -> None: + self.fs = fs + + self.R1 = Resistor(R1_val) + self.R2 = Resistor(R2_val) + + self.S1 = SeriesAdaptor(self.R1, self.R2) + + self.I1 = PolarityInverter(self.S1) + self.Vs = IdealVoltageSource(self.I1) + + super().__init__(self.Vs, self.Vs, self.R1) + + def set_R1(self,new_R): + self.R1.set_resistance(new_R) + + def set_R2(self,new_R): + self.R2.set_resistance(new_R) + + + def process_sample(self, sample: float) -> float: + # return super().process_sample(sample) + self.R1.wave_to_voltage() + self.C1.wave_to_voltage() + pass + +if __name__ == '__main__': + + vd = VoltageDivider(44100, 1e4, 1e4) + + vd.plot_freqz() + + vs = np.arange(0.0, 6.0, 0.01) + + y = vd.process_i_v_signals(vs) + + v, _, i = zip(*y) + + _, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6.5)) + ax.plot(v, label="voltage across", alpha=0.75) + ax.set_xlabel("sample") + ax.set_ylabel("v[n]") + color = 'tab:blue' + ax2 = ax.twinx() + ax2.set_ylabel('i[n]', color=color) + ax2.tick_params(axis='y', labelcolor=color) + ax2.plot(i, color=color, label="current through output", alpha=0.75) + + ax.set_title(loc="left", label="v[n] voltage across and i[n] current through resistor R1 ") + ax.grid(True) + ax.legend() + + plt.savefig("voltage_divider.png") + plt.show() \ No newline at end of file diff --git a/pywdf/figures/diode_clipper_transient.png b/pywdf/figures/diode_clipper_transient.png new file mode 100644 index 0000000..a7b7744 Binary files /dev/null and b/pywdf/figures/diode_clipper_transient.png differ diff --git a/pywdf/figures/diode_clipper_transient_anal.png b/pywdf/figures/diode_clipper_transient_anal.png deleted file mode 100644 index 1ea2f65..0000000 Binary files a/pywdf/figures/diode_clipper_transient_anal.png and /dev/null differ diff --git a/pywdf/figures/hat_res_IR.png b/pywdf/figures/hat_res_IR.png index e3fc69f..a5e2ecb 100644 Binary files a/pywdf/figures/hat_res_IR.png and b/pywdf/figures/hat_res_IR.png differ diff --git a/pywdf/figures/mk2_sef_lpf_knob.png b/pywdf/figures/mk2_sef_lpf_knob.png index 92aa1e0..c7fee95 100644 Binary files a/pywdf/figures/mk2_sef_lpf_knob.png and b/pywdf/figures/mk2_sef_lpf_knob.png differ diff --git a/pywdf/figures/voltage_divider_IR.png b/pywdf/figures/voltage_divider_IR.png new file mode 100644 index 0000000..e1971ef Binary files /dev/null and b/pywdf/figures/voltage_divider_IR.png differ diff --git a/pywdf/figures/voltage_divider_transient.png b/pywdf/figures/voltage_divider_transient.png new file mode 100644 index 0000000..bc0cad9 Binary files /dev/null and b/pywdf/figures/voltage_divider_transient.png differ diff --git a/test.py b/test.py index 2fffbee..7ce0b40 100644 --- a/test.py +++ b/test.py @@ -1,14 +1,25 @@ -from pywdf import RCA_MK2_SEF, TR_808_HatResonator, DiodeClipper +from pywdf import RCA_MK2_SEF, TR_808_HatResonator, DiodeClipper, VoltageDivider, Chua -# sweep positions of RCA mk2 SEF low pass filter knob and plot frequency responses -mk2_sef = RCA_MK2_SEF(44100, 0, 3000) -positions = range(0,11) -mk2_sef.plot_freqz_list(positions, mk2_sef.set_lowpass_knob_position, param_label = 'lpf knob pos', outpath='pywdf/figures/mk2_sef_lpf_knob.png') +#### analyze transient response of Diode Clipper to AC signal +dc = Chua(44100, cutoff= 1000, input_gain_db = 5) +dc.i_v_analysis(outpath='pywdf/figures/chua_circuit_transient.png') -# visualize impulse response of TR-808 hat resonator -hr = TR_808_HatResonator(44100, 1000, .5) -hr.plot_impulse_response(outpath='pywdf/figures/hat_res_IR.png') +# dc = DiodeClipper(44100, cutoff= 1000, input_gain_db = 5) +# dc.i_v_analysis(outpath='pywdf/figures/diode_clipper_transient_anal.png') +# dc.AC_transient_analysis(outpath='pywdf/figures/diode_clipper_transient_anal.png') -# analyze transient response of Diode Clipper to AC signal -dc = DiodeClipper(44100, cutoff= 1000, input_gain_db = 5) -dc.AC_transient_analysis(outpath='pywdf/figures/diode_clipper_transient_anal.png') +#### sweep positions of RCA mk2 SEF low pass filter knob and plot frequency responses +# mk2_sef = RCA_MK2_SEF(44100, 0, 3000) +# positions = range(0,11) +# mk2_sef.plot_freqz_list(positions, mk2_sef.set_lowpass_knob_position, param_label = 'lpf knob pos', outpath='pywdf/figures/mk2_sef_lpf_knob.png') + +#### visualize impulse response of TR-808 hat resonator +# hr = TR_808_HatResonator(44100, 1000, .5) +# hr.plot_impulse_response(outpath='pywdf/figures/hat_res_IR.png') + + +#### plot voltage and current waveforms for voltage divider +# vd = VoltageDivider(44100, 1e5, 1e10) +# vd.plot_freqz(outpath='pywdf/figures/voltage_divider_freqz.png') +# vd.AC_transient_analysis(outpath='pywdf/figures/voltage_divider_transient_anal.png') +# vd.plot_impulse_response(outpath='pywdf/figures/voltage_divider_IR.png') diff --git a/tests/chua_ac_analysis.png b/tests/chua_ac_analysis.png new file mode 100644 index 0000000..61cb8bc Binary files /dev/null and b/tests/chua_ac_analysis.png differ diff --git a/tests/chua_impulse_response.png b/tests/chua_impulse_response.png new file mode 100644 index 0000000..55bb72c Binary files /dev/null and b/tests/chua_impulse_response.png differ diff --git a/tests/data/rk4_example1_results.csv b/tests/data/rk4_example1_results.csv new file mode 100644 index 0000000..d072e99 --- /dev/null +++ b/tests/data/rk4_example1_results.csv @@ -0,0 +1,22 @@ +time,y_numerical,y_analytical,error +0.000000000000000000e+00,1.000000000000000000e+00,1.000000000000000000e+00,0.000000000000000000e+00 +1.000000000000000056e-01,8.187333333333333130e-01,8.187307530779818210e-01,2.580255351491977933e-06 +2.000000000000000111e-01,6.703242711111110363e-01,6.703200460356393275e-01,4.225075471708805708e-06 +3.000000000000000444e-01,5.488168249010370037e-01,5.488116360940263894e-01,5.188807010614304716e-06 +4.000000000000000222e-01,4.493346284406423696e-01,4.493289641172215632e-01,5.664323420806471887e-06 +5.000000000000000000e-01,3.678852381253019388e-01,3.678794411714423340e-01,5.796953859604769832e-06 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x^2 - 2 = 0) +def f1(x): + return x**2 - 2 + +def df1(x): + return 2*x + +print("Example 1: Finding square root of 2") +root1, iterations1 = newton_raphson(f1, df1, x0=1.0) +print(f"Root: {root1:.10f}") +print(f"Iterations: {iterations1}") +print(f"Verification: {root1}^2 = {root1**2:.10f}") +print() + +# Example 2: Find root of x^3 - x - 1 = 0 +def f2(x): + return x**3 - x - 1 + +def df2(x): + return 3*x**2 - 1 + +print("Example 2: Finding root of x^3 - x - 1 = 0") +root2, iterations2 = newton_raphson(f2, df2, x0=1.5) +print(f"Root: {root2:.10f}") +print(f"Iterations: {iterations2}") +print(f"Verification: f({root2:.6f}) = {f2(root2):.2e}") +print() + +# Example 3: Find root of cos(x) - x = 0 +def f3(x): + return math.cos(x) - x + +def df3(x): + return -math.sin(x) - 1 + +print("Example 3: Finding root of cos(x) - x = 0") +root3, iterations3 = newton_raphson(f3, df3, x0=0.5) +print(f"Root: {root3:.10f}") +print(f"Iterations: {iterations3}") +print(f"Verification: cos({root3:.6f}) - {root3:.6f} = {f3(root3):.2e}") +print() + +# Example with plotting (optional visualization) +try: + import matplotlib.pyplot as plt + import numpy as np + + def plot_newton_raphson_steps(f, df, x0, num_steps=5): + """Visualize the Newton-Raphson iteration steps""" + x_vals = [x0] + x = x0 + + # Perform iterations and collect x values + for _ in range(num_steps): + x = x - f(x) / df(x) + x_vals.append(x) + + # Create plot + x_plot = np.linspace(min(x_vals) - 1, max(x_vals) + 1, 1000) + y_plot = [f(xi) for xi in x_plot] + + plt.figure(figsize=(10, 6)) + plt.plot(x_plot, y_plot, 'b-', label='f(x) = x² - 2') + plt.axhline(y=0, color='k', linestyle='-', alpha=0.3) + plt.axvline(x=0, color='k', linestyle='-', alpha=0.3) + + # Plot iteration steps + colors = ['red', 'orange', 'green', 'purple', 'brown'] + for i in range(min(len(x_vals)-1, len(colors))): + x_curr = x_vals[i] + # Tangent line + slope = df(x_curr) + y_tangent = slope * (x_plot - x_curr) + f(x_curr) + plt.plot(x_plot, y_tangent, '--', color=colors[i], alpha=0.7, + label=f'Iteration {i+1}') + # Mark the point + plt.plot(x_curr, f(x_curr), 'o', color=colors[i], markersize=8) + plt.plot(x_vals[i+1], 0, 's', color=colors[i], markersize=6) + + plt.xlabel('x') + plt.ylabel('f(x)') + plt.title('Newton-Raphson Method Visualization') + plt.legend() + plt.grid(True, alpha=0.3) + + # Save plot to file + plt.savefig('newton_raphson_visualization.png', dpi=300, bbox_inches='tight') + print("Visualization saved to 'newton_raphson_visualization.png'") + plt.show() + + print("Plotting Newton-Raphson steps for x² - 2 = 0...") + plot_newton_raphson_steps(f1, df1, 1.0) + print("Plotted Newton-Raphson steps for x² - 2 = 0...") + +except ImportError: + print("Matplotlib not available for plotting visualization") \ No newline at end of file diff --git a/tests/test_runge_kutta.py b/tests/test_runge_kutta.py new file mode 100644 index 0000000..caa9104 --- /dev/null +++ b/tests/test_runge_kutta.py @@ -0,0 +1,155 @@ +import math +import numpy as np +import matplotlib.pyplot as plt + +from pywdf.core.solver.runge_kutta import rk4_solve + +# Example 1: Simple exponential decay dy/dt = -2y, y(0) = 1 +def example1(): + def f(t, y): + return -2 * y + + # Analytical solution: y = e^(-2t) + def analytical(t): + return np.exp(-2 * t) + + t_span = (0, 2) + y0 = 1 + h = 0.1 + + t_num, y_num = rk4_solve(f, t_span, y0, h) + + t_exact = np.linspace(0, 2, 100) + y_exact = analytical(t_exact) + + plt.figure(figsize=(10, 6)) + plt.plot(t_exact, y_exact, 'b-', label='Analytical solution', linewidth=2) + plt.plot(t_num, y_num, 'ro-', label='RK4 numerical solution', markersize=4) + plt.xlabel('Time t') + plt.ylabel('y(t)') + plt.title('Example 1: dy/dt = -2y, y(0) = 1') + plt.legend() + plt.grid(True, alpha=0.3) + + # Save plot to file + plt.savefig('tests/rk4_example1_plot.png', dpi=300, bbox_inches='tight') + plt.show() + + # Calculate error + y_exact_at_points = analytical(t_num) + error = np.abs(y_num - y_exact_at_points) + print(f"Maximum error: {np.max(error):.2e}") + + # Save numerical results to CSV file + results_data = np.column_stack((t_num, y_num, y_exact_at_points, error)) + np.savetxt('tests/rk4_example1_results.csv', results_data, + delimiter=',', + header='time,y_numerical,y_analytical,error', + comments='') + print("Results saved to 'rk4_example1_results.csv'") + +# Example 2: Harmonic oscillator d²y/dt² + y = 0 +# Convert to system: dy/dt = v, dv/dt = -y +def example2(): + def f(t, state): + y, v = state + dydt = v + dvdt = -y + return np.array([dydt, dvdt]) + + # Initial conditions: y(0) = 1, v(0) = 0 + # Analytical solution: y = cos(t), v = -sin(t) + def analytical(t): + y = np.cos(t) + v = -np.sin(t) + return y, v + + t_span = (0, 4*np.pi) + y0 = np.array([1, 0]) # [position, velocity] + h = 0.01 + + t_num, state_num = rk4_solve(f, t_span, y0, h) + y_num = state_num[:, 0] # position + v_num = state_num[:, 1] # velocity + + t_exact = np.linspace(0, 4*np.pi, 1000) + y_exact, v_exact = analytical(t_exact) + + plt.figure(figsize=(12, 8)) + + # Position plot + plt.subplot(2, 2, 1) + plt.plot(t_exact, y_exact, 'b-', label='Analytical', linewidth=2) + plt.plot(t_num[::10], y_num[::10], 'ro', label='RK4', markersize=3) + plt.xlabel('Time t') + plt.ylabel('Position y(t)') + plt.title('Harmonic Oscillator - Position') + plt.legend() + plt.grid(True, alpha=0.3) + + # Velocity plot + plt.subplot(2, 2, 2) + plt.plot(t_exact, v_exact, 'g-', label='Analytical', linewidth=2) + plt.plot(t_num[::10], v_num[::10], 'ro', label='RK4', markersize=3) + plt.xlabel('Time t') + plt.ylabel('Velocity v(t)') + plt.title('Harmonic Oscillator - Velocity') + plt.legend() + plt.grid(True, alpha=0.3) + + # Phase portrait + plt.subplot(2, 2, 3) + plt.plot(y_exact, v_exact, 'b-', label='Analytical', linewidth=2) + plt.plot(y_num, v_num, 'r--', label='RK4', linewidth=1) + plt.xlabel('Position y') + plt.ylabel('Velocity v') + plt.title('Phase Portrait') + plt.legend() + plt.grid(True, alpha=0.3) + plt.axis('equal') + + # Energy conservation check + energy_num = 0.5 * (y_num**2 + v_num**2) + plt.subplot(2, 2, 4) + plt.plot(t_num, energy_num, 'r-', linewidth=2) + plt.axhline(y=0.5, color='b', linestyle='--', label='Theoretical energy = 0.5') + plt.xlabel('Time t') + plt.ylabel('Total Energy') + plt.title('Energy Conservation') + plt.legend() + plt.grid(True, alpha=0.3) + + plt.tight_layout() + + # Save plot to file + plt.savefig('tests/rk4_example2_plot.png', dpi=300, bbox_inches='tight') + plt.show() + + # Save numerical results to CSV file + y_exact_at_points, v_exact_at_points = analytical(t_num) + position_error = np.abs(y_num - y_exact_at_points) + velocity_error = np.abs(v_num - v_exact_at_points) + + results_data = np.column_stack((t_num, y_num, v_num, + y_exact_at_points, v_exact_at_points, + position_error, velocity_error, energy_num)) + np.savetxt('tests/rk4_example2_results.csv', results_data, + delimiter=',', + header='time,position_num,velocity_num,position_exact,velocity_exact,position_error,velocity_error,energy', + comments='') + + print(f"Maximum position error: {np.max(position_error):.2e}") + print(f"Maximum velocity error: {np.max(velocity_error):.2e}") + print(f"Energy drift: {np.max(energy_num) - np.min(energy_num):.2e}") + print("Results saved to 'rk4_example2_results.csv'") + + +if __name__ == "__main__": + print("RK4 Method Examples") + print("=" * 50) + + print("\nExample 1: Exponential decay") + example1() + + print("\nExample 2: Harmonic oscillator") + example2() \ No newline at end of file