twpasolver.mathutils module#

Utility functions for mathematical expressions and RF equations.

This module provides a set of utility functions optimized with Numba for high performance. These functions include matrix multiplications, conversions between different parameter representations, and solutions for coupled mode equations used in RF engineering.

twpasolver.mathutils.matmul_2x2(matrices_a: ndarray[Any, dtype[complex128]], matrices_b: ndarray[Any, dtype[complex128]]) → ndarray[Any, dtype[complex128]][source]#

Fast multiplication between arrays of 2x2 matrices.

Parameters:

  • matrices_a (ComplexArray) – Array of 2x2 complex matrices.

  • matrices_b (ComplexArray) – Array of 2x2 complex matrices.

Returns:

Resultant array of 2x2 complex matrices after multiplication.

Return type:

ComplexArray

twpasolver.mathutils.matpow_2x2(matrices_a: ndarray[Any, dtype[complex128]], exponent: int) → ndarray[Any, dtype[complex128]][source]#

Fast exponentiation of arrays of 2x2 matrices using recursion.

Parameters:

  • matrices_a (ComplexArray) – Array of 2x2 complex matrices.

  • exponent (int) – Exponent to which matrices are to be raised.

Returns:

Resultant array of 2x2 complex matrices after exponentiation.

Return type:

ComplexArray

twpasolver.mathutils.a2s(abcd: ndarray[Any, dtype[complex128]], Z0: complex | float) → ndarray[Any, dtype[complex128]][source]#

Convert arrays of ABCD matrices to arrays of S-parameters.

Parameters:

  • abcd (ComplexArray) – Array of 2x2 ABCD matrices.

  • Z0 (complex | float) – Reference impedance.

Returns:

Array of 2x2 S-parameter matrices.

Return type:

ComplexArray

twpasolver.mathutils.s2a(spar: ndarray[Any, dtype[complex128]], Z0: complex | float) → ndarray[Any, dtype[complex128]][source]#

Convert arrays of S-parameters to arrays of ABCD matrices.

Parameters:

  • spar (ComplexArray) – Array of 2x2 S-parameter matrices.

  • Z0 (complex | float) – Reference impedance.

Returns:

Array of 2x2 ABCD matrices.

Return type:

ComplexArray

twpasolver.mathutils.a2z(abcd: ndarray[Any, dtype[complex128]]) → ndarray[Any, dtype[complex128]][source]#

Convert arrays of ABCD matrices to arrays of Z-parameters.

Parameters:

abcd (ComplexArray) – Array of 2x2 ABCD matrices.

Returns:

Array of 2x2 Z-parameter matrices.

Return type:

ComplexArray

twpasolver.mathutils.z2a(z_mat: ndarray[Any, dtype[complex128]]) → ndarray[Any, dtype[complex128]][source]#

Convert arrays of Z-parameters to arrays of ABCD matrices.

Parameters:

z_mat (ComplexArray) – Array of 2x2 Z-parameter matrices.

Returns:

Array of 2x2 ABCD matrices.

Return type:

ComplexArray

twpasolver.mathutils.to_dB(values: ndarray[Any, dtype[float64]] | ndarray[Any, dtype[complex128]]) → ndarray[Any, dtype[float64]][source]#

Convert arrays of values to dB.

Parameters:

values (FloatArray | ComplexArray) – Array of values to be converted to dB.

Returns:

Array of values in dB.

Return type:

FloatArray

twpasolver.mathutils.dBm_to_I(power: float, Z0: float = 50) → float[source]#

Convert power from dBm to current in amperes.

Parameters:

  • power (float) – Power in dBm.

  • Z0 (float, optional) – Reference impedance, default is 50 ohms.

Returns:

Current amplitude in amperes.

Return type:

float

twpasolver.mathutils.I_to_dBm(curr: float, Z0: float = 50) → float[source]#

Convert current in amperes to power in dBm.

Parameters:

  • curr (float) – Current amplitude in amperes.

  • Z0 (float, optional) – Reference impedance, default is 50 ohms.

Returns:

Power in dBm.

Return type:

float

twpasolver.mathutils.compute_phase_matching(freqs: ndarray[Any, dtype[float64]], pump_freqs: ndarray[Any, dtype[float64]], k_signal_array: ndarray[Any, dtype[float64]], k_pump_array: ndarray[Any, dtype[float64]], chi: float, gamma_pump_array: ndarray[Any, dtype[complex128]]) → Tuple[ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]]][source]#

Compute phase matching profiles and triplets for given frequencies.

Parameters:

  • freqs (FloatArray) – Array of signal frequencies.

  • pump_freqs (FloatArray) – Array of pump frequencies.

  • k_signal_array (FloatArray) – Array of signal wave numbers.

  • k_pump_array (FloatArray) – Array of pump wave numbers.

  • chi (float) – Nonlinear coefficient.

  • gamma_pump_array (ComplexArray) – Array of pump reflection coefficients.

Returns:

Phase matching profile, frequency triplets, and wave number triplets.

Return type:

Tuple[FloatArray, FloatArray, FloatArray]