Curves module

Curves.

physicslab.curves.black_body_radiation(frequency, T)

UNIT = W/sr/m^2/Hz

To express the law per unit wavelength, input frequency = c / wavelength (UNIT = W/sr/m^3).

Parameters

• frequency (numpy.ndarray) –

• T (float) – Temperature

Returns

Spectral radiance

Return type

numpy.ndarray

physicslab.curves.gaussian_curve(x, expected_value, variance, amplitude=None, zero=0)

Gauss curve function of given parameters.

Parameters

• x (numpy.ndarray) – Free variable

• expected_value (float) – Center

• variance (float) – Variance (not FWHM)

• amplitude (float, optional) – Amplitude (value at maximum relative to the baseline). None normalize as probability, defaults to None

• zero (int) – Baseline, defaults to 0

Returns

Gaussian curve values

Return type

numpy.ndarray

physicslab.curves.gaussian_curve_FWHM(variance)

Find FWHM from variance of a Gaussian curve.

Parameters

variance (float) – Variance

Returns

Full Width at Half Maximum

Return type

float

physicslab.curves.spontaneous_magnetization(T, M0, TC, a, b, zero)

An empirical interpolation of the low temperature and the critical temperature regimes.

Parameters

• T (numpy.ndarray) – Temperature

• M0 (float) – Spontaneous magnetization at absolute zero

• TC (float) – Curie temperature

• a (float) – Magnetization stays close to M0 at higher temperatures

• b (float) – Critical exponent. Magnetization stays close to zero lower below TC

• zero (float) – Baseline

Returns

Magnetization

Return type

numpy.ndarray

physicslab.curves.magnetic_hysteresis_branch(H, saturation, remanence, coercivity, rising_branch=True)

One branch of magnetic hysteresis loop.

Parameters

• H (numpy.ndarray) – external magnetic field strength.

• saturation (float) – \(max(B)\)

• remanence (float) – \(B(H=0)\)

• coercivity (float) – \(H(B=0)\)

• rising_branch (bool, optional) – Rising (True) or falling (False) branch, defaults to True

Raises

• ValueError – If saturation is negative or zero

• ValueError – If remanence is negative

• ValueError – If coercivity is negative

• ValueError – If remanence is greater than saturation

Returns

Resulting magnetic field induction \(B\)

Return type

numpy.ndarray

physicslab.curves.magnetic_hysteresis_loop(H, saturation, remanence, coercivity)

Magnetic hysteresis loop.

If more control is needed, use magnetic_hysteresis_branch(). To check whether the data starts with rising or falling part, first and middle element are compared.

Parameters

• H (numpy.ndarray) – external magnetic field strength. The array is split in half for individual branches.

• saturation (float) – \(max(B)\)

• remanence (float) – \(B(H=0)\)

• coercivity (float) – \(H(B=0)\)

Returns

Resulting magnetic field induction \(B\)

Return type

numpy.ndarray

class physicslab.curves.Line(constant=0, slope=0)

Represents a line function: \(y=a_0+a_1x\).

Call the instance to enumerate it at the given x. You can do arithmetic with Line, find zeros, etc.

Parameters

• constant (int, optional) – Constant term (\(a_0\)), defaults to 0

• slope (int, optional) – Linear term (\(a_1\)), defaults to 0

__call__(x)

Find function values of self.

Parameters

x (numpy.ndarray) – Free variable

Returns

Function value

Return type

numpy.ndarray

zero()

Find free variable (x) value which evaluates to zero.

Raises

ValueError – If slope is zero.

root()

Alias for zero().

invert()

Return inverse function of self.

Returns

Inverted function

Return type

Line

static Intersection(line1, line2)

Find intersection coordinates of the two given Line.

Parameters

• line1 (Line) – First line

• line2 (Line) – Second line

Returns

Coordinates of the intersection of the two lines

Return type

tuple