mammos_analysis.hysteresis#

Hysteresis analysis and postprocessing functions.

Functions

`extract_B_curve`(H, M, ...)	Compute the B–H curve from a hysteresis loop.
`extract_coercive_field`(H, M)	Extract the coercive field from a hysteresis loop.
`extract_maximum_energy_product`(H, B)	Determine the maximum energy product from a hysteresis loop.
`extract_remanent_magnetization`(H, M)	Extract the remanent magnetization from a hysteresis loop.
`extrinsic_properties`(H, M[, ...])	Compute extrinsic properties of a hysteresis loop.
`find_linear_segment`(H, M, margin[, method, ...])	Identify the largest field value over which the hysteresis loop is linear.

Classes

`ExtrinsicProperties`(Hc, Mr, BHmax)	Extrinsic properties extracted from a hysteresis loop.
`LinearSegmentProperties`(Mr, Hmax, gradient)	Linear segment properties extracted from a hysteresis loop.
`MaximumEnergyProductProperties`(Hd, Bd, BHmax)	Properties related to the maximum energy product in a hysteresis loop.

class mammos_analysis.hysteresis.ExtrinsicProperties(Hc, Mr, BHmax)#

Extrinsic properties extracted from a hysteresis loop.

Parameters:

Hc (Entity)
Mr (Entity)
BHmax (Entity)

BHmax: Entity#: Maximum energy product.

Hc: Entity#: Coercive field.

Mr: Entity#: Remanent magnetization.

class mammos_analysis.hysteresis.LinearSegmentProperties(Mr, Hmax, gradient, _H=None, _M=None)#

Linear segment properties extracted from a hysteresis loop.

Parameters:

Mr (Entity)
Hmax (Entity)
gradient (Quantity)
_H (Entity | None)
_M (Entity | None)

Hmax: Entity#: Maximum field strength in the linear segment.

Mr: Entity#: M(H=0) from linear segment fit.

gradient: Quantity#: Gradient of the linear segment.

plot(ax=None)#

Plot the spontaneous magnetization data-points.

Parameters:: ax (matplotlib.axes.Axes | None)
Return type:: matplotlib.axes.Axes

class mammos_analysis.hysteresis.MaximumEnergyProductProperties(Hd, Bd, BHmax)#

Properties related to the maximum energy product in a hysteresis loop.

Parameters:

Hd (Entity)
Bd (Entity)
BHmax (Entity)

BHmax: Entity#: Maximum energy product value.

Bd: Entity#: Flux density at which BHmax occurs.

Hd: Entity#: Field strength at which BHmax occurs.

mammos_analysis.hysteresis.extract_B_curve(H, M, demagnetization_coefficient)#

Compute the B–H curve from a hysteresis loop.

Parameters:

H (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – External magnetic field.
M (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – Spontaneous magnetization.
demagnetization_coefficient (float) – Demagnetization coefficient (0 to 1).

Returns:

Magnetic flux density as an Entity.

Raises:

ValueError – If the coefficient is out of range.

Return type:

me.Entity

Examples

>>> import mammos_analysis.hysteresis
>>> import mammos_entity as me
>>> H = me.H([0, 1e4, 2e4], unit="A/m")
>>> M = me.Ms([1e5, 2e5, 3e5], unit="A/m")
>>> mammos_analysis.hysteresis.extract_B_curve(H, M, 1/3)
MagneticFluxDensity(...)

mammos_analysis.hysteresis.extract_coercive_field(H, M)#

Extract the coercive field from a hysteresis loop.

Parameters:

H (Entity | Quantity | ndarray) – External magnetic field.
M (Entity | Quantity | ndarray) – Spontaneous magnetization.

Returns:

Coercive field in the same format as H.

Raises:

ValueError – If the coercive field cannot be calculated.

Return type:

Entity

mammos_analysis.hysteresis.extract_maximum_energy_product(H, B)#

Determine the maximum energy product from a hysteresis loop.

Parameters:

H (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – External magnetic field.
B (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – Magnetic flux density.

Returns:

Properties of the maximum energy product.

Raises:

ValueError – If inputs are not monotonic or B decreases with H.

Return type:

MaximumEnergyProductProperties

mammos_analysis.hysteresis.extract_remanent_magnetization(H, M)#

Extract the remanent magnetization from a hysteresis loop.

Parameters:

H (Entity | Quantity | ndarray) – External magnetic field.
M (Entity | Quantity | ndarray) – Spontaneous magnetization.

Returns:

Remanent magnetization in the same format as M.

Raises:

ValueError – If the field does not cross zero or calculation fails.

Return type:

Entity

mammos_analysis.hysteresis.extrinsic_properties(H, M, demagnetization_coefficient=None)#

Compute extrinsic properties of a hysteresis loop.

Parameters:

H (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – External magnetic field.
M (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – Spontaneous magnetization.
demagnetization_coefficient (float | None) – Demagnetization coefficient for BHmax.

Returns:

ExtrinsicProperties containing Hc, Mr, and BHmax.

Raises:

ValueError – If Hc or Mr calculation fails.

Return type:

ExtrinsicProperties

mammos_analysis.hysteresis.find_linear_segment(H, M, margin, method='maxdev', min_points=5)#

Identify the largest field value over which the hysteresis loop is linear.

There are two possible criteria, selected by the method argument:

Max‐Deviation Criterion (method=”maxdev”): Require that every data point in the segment satisfies

\[\max_{\,i_0 \le i \le i_{\max}}\;\bigl|\,M_i - (m\,H_i + b)\bigr| \;\le\; \delta,\]

where:
- \(\{(H_i, M_i)\}\) are the data points,
- \(m\) is the fitted slope,
- \(b\) is the fitted intercept (value of \(M\) at \(H=0\)),
- \(\delta\) is the user‐supplied margin (in the same units as \(M\)).
This guarantees each point lies within \(\pm \delta\).
RMS Criterion (method=”rms”): Require that the root‐mean‐square error over the segment satisfies

\[\mathrm{RMSE} \;=\; \sqrt{\frac{1}{n}\sum_{\,i=i_0}^{\,i_{\max}} \bigl(M_i - (m\,H_i + b)\bigr)^2} \;\le\; \delta,\]

where \(n = i_{\max} - i_0 + 1\). Occasional points may exceed \(\delta\) provided the overall RMS error remains within \(\delta\).

Parameters:

H (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – Applied magnetic field values. Must be monotonic.
M (mammos_entity.Entity | mammos_units.Quantity | np.ndarray) – Magnetization values corresponding to H.
margin (mammos_entity.Entity | mammos_units.Quantity | numbers.Number) – Allowed deviation \(\delta\).
method (str) – Which deviation test to use: - “maxdev” (default): per‐point maximum deviation, - “rms”: root‐mean‐square deviation.
min_points (int) – Minimum number of points required to attempt any fit.

Returns:

Mr: fitted intercept \(b\) (magnetization at \(H=0\)),
Hmax: largest field value up to which data remain “linear” under the chosen criterion,
gradient: fitted slope \(m\) (dimensionless).

Return type:

LinearSegmentProperties containing

Notes

Growing‐Window Fit We attempt to extend the segment one index at a time:

\[\{\,i_0,\,i_0+1,\,\dots,\,i\,\}.\]

For each candidate endpoint \(i\), we fit a line \(\hat{M}(H) = m\,H + b\) via np.polyfit(H[i_0:i+1], M[i_0:i+1], 1). Then we compute either:

Max‐Deviation: \(\max_{j=i_0}^i\,\bigl|M_j - (m\,H_j + b)\bigr| \le \delta,\) or
RMS:

\[\mathrm{RMSE} \;=\; \sqrt{\frac{1}{\,i - i_0 + 1\,} \sum_{j=i_0}^{i} \bigl(M_j - (m\,H_j + b)\bigr)^2} \;\le\; \delta.\]

As soon as adding \(i+1\) would violate the chosen inequality, we stop and take \(i_{\max} = i\). We then refit \((m,b)\) on \(\{i_0,\dots,i_{\max}\}\) to produce the final slope/intercept returned.