mathFunctions (skrf.mathFunctions)

Provides commonly used mathematical functions.

Mathematical Constants

Some convenient constants are defined in the skrf.constants module.

Complex Component Conversion

complex_2_reim(z)	Return real and imaginary parts of a complex number.
complex_2_magnitude(z)	Return the magnitude of the complex argument.
complex_2_db(z)	Return the magnitude in dB of a complex number (as \(20\log_{10}(|z|)\))..
complex_2_db10(z)	Return the magnitude in dB of a complex number (as \(10\log_{10}(|z|)\)).
complex_2_radian(z)	Return the angle complex argument in radian.
complex_2_degree(z)	Returns the angle complex argument in degree.
complex_2_magnitude(z)	Return the magnitude of the complex argument.
complex_2_quadrature(z)	Take a complex number and returns quadrature, which is (length, arc-length from real axis)

Phase Unwrapping

unwrap_rad(phi)	Unwraps a phase given in radians.
sqrt_phase_unwrap(z)	Take the square root of a complex number with unwrapped phase.

Unit Conversion

radian_2_degree(rad)	Convert angles from radians to degrees.
degree_2_radian(deg)	Convert angles from degrees to radians.
np_2_db(x)	Converts a value in Nepers (Np) to decibel (dB).
db_2_np(db)	Converts a value in decibel (dB) to neper (Np).

Scalar-Complex Conversion

These conversions are useful for wrapping other functions that don’t support complex numbers.

complex2Scalar(z)	Serialize a list/array of complex numbers
scalar2Complex(s)	Unserialize a list/array of real and imag numbers into a complex array.

Special Functions

dirac_delta(x)	Calculate Dirac function.
neuman(x)	Calculate Neumans number.
null(A[, eps])	Calculate the null space of matrix A.
cross_ratio(a, b, c, d)	Calculate the cross ratio of a quadruple of distinct points on the real line.

Various Utility Functions

psd2TimeDomain(f, y[, windowType])	Convert a one sided complex spectrum into a real time-signal.
rational_interp(x, y[, d, epsilon, axis, ...])	Interpolates function using rational polynomials of degree d.
ifft(x)	Transforms S-parameters to time-domain bandpass.
irfft(x[, n])	Transforms S-parameters to time-domain, assuming complex conjugates for values corresponding to negative frequencies.
is_square(mat)	Tests whether mat is a square matrix.
is_symmetric(mat[, tol])	Tests mat for symmetry.
is_Hermitian(mat[, tol])	Tests whether mat is Hermitian.
is_positive_definite(mat[, tol])	Tests mat for positive definiteness.
is_positive_semidefinite(mat[, tol])	Tests mat for positive semidefiniteness.
get_Hermitian_transpose(mat)	Returns the conjugate transpose of mat.