Spline (hwx.common.math)#

class Spline(x, y=None, unitSystem=None, xunits='time', yunits='length')#

Bases: list

A two element list of (x, y) values.

Spline has methods to convert to/from units, add/insert/delete rows, interpolate, get the derivative and read/write CSV files.

The length of x should be the same as y and at least 4. Also, x should be increasing i.e. x[i] < x[i+1].

Attribute Table#
Name	Type
`x`	`property`
`y`	`property`

Method Table#
Name	Description
`addInterpolated` (self, row)	Adds a linear interpolated value after the specified row.
`appendInterpolated` (self)	Appends a linear interpolated value.
`copy` (self, **kwds)	Return a copy of self.
`deleteRows` (self, *deleteRows)	Removes the specified rows.
`derivative` (self, order=1, npts=None, type=’akima’, scaled=True)	Computes the derivative.
`fromBaseUnits` (self)	Makes the Spline values work like other Double values.
`getFormattedStrings` (self, format=5)	Returns the values suitable for display in the gui fields or table cells.
`getXFromY` (self, y)	Returns a computed x value from the specified y value.
`insertInterpolated` (self, row)	Adds a linear interpolated value before the specified row.
`interpolate` (self, npts=None, type=’akima’, order=0, x=None)	Recalculates x and y by interpolation.
`isValid` (self)	Determines if self can be interpolated and if the derivative can be computed.
`prependInterpolated` (self)	Adds a linear interpolated value in the beginning.
`readCsv` (self, fname, validationMethod=None)	Reads a csv file to populate the x/y values.
`reflect` (self)	Reflects the data across X and Y.
`removeNegativeX` (self)	Removes x, y pairs with negative x values.
`scalex` (self, factor)	Mulitplies the x values by a scale factor.
`scaley` (self, factor)	Mulitplies the y values by a scale factor.
`setComponent` (self, row, col, value)	Sets a single value.
`setValues` (self, x, y=None)	Sets the list of x and y values.
`shiftx` (self, offset)	Shifts the x values by an offset.
`shifty` (self, offset)	Shifts the y values by an offset.
`toBaseUnits` (self)	Makes the Spline values work like other Double values.
`writeCsv` (self, fname=None)	Writes x/y values to a csv file.

Example

Define and use Splines.#

import math
import matplotlib.pyplot as plt
from hwx.common.math import Spline

knots = 10
knot_vector = [1.0 * i for i in list(range(knots))]
p = [math.exp(-i) / 3 for i in knot_vector]

s = Spline(knot_vector, p)
fig, ax = plt.subplots()

plt.scatter(s.x, s.y)
plt.title('Spilne')

fig.tight_layout()
show(fig)

exception SplineValueError#

Bases: ValueError

Exceptions for Spline objects.

property x#: The x values.

property y#: The y values.

setValues(x, y=None)#

Sets the list of x and y values.

Parameters:

x (list) – The list of x values.
y (list) – The list of y values.

Returns:

A reference to the instance Spline object on which it was called.

Return type:

Spline

copy(**kwds)#

Return a copy of self.

It is updated with kwds if specified to support derived classes.

isValid()#

Determines if self can be interpolated and if the derivative can be computed.

Returns:: True if it is valid, False otherwise.
Return type:: bool

fromBaseUnits()#: Makes the Spline values work like other Double values.

toBaseUnits()#: Makes the Spline values work like other Double values.

getFormattedStrings(format=5)#

Returns the values suitable for display in the gui fields or table cells.

Parameters:: format (int | str) – The format of the values as strings.
Returns:: The x, y values.
Return type:: list[list[float], list[float]]

setComponent(row, col, value)#

Sets a single value.

Parameters:

row (int) – The row value to set.
col (int) – The column value to set.
value (float) – The value to set.

Raises:

SplineValueError – If value is not numeric.

Returns:

A reference to the instance Spline object on which it was called.

Return type:

Spline

deleteRows(*deleteRows)#

Removes the specified rows.

Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

prependInterpolated()#

Adds a linear interpolated value in the beginning.

Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

appendInterpolated()#

Appends a linear interpolated value.

Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

addInterpolated(row)#

Adds a linear interpolated value after the specified row.

Parameters:: row (int) – The row where to add the value after.
Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

insertInterpolated(row)#

Adds a linear interpolated value before the specified row.

Parameters:: row (int) – The row where to add the value before.
Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

writeCsv(fname=None)#

Writes x/y values to a csv file.

Parameters:: fname (str) – The path to the csv file.

readCsv(fname, validationMethod=None)#

Reads a csv file to populate the x/y values.

Parameters:

fname (str) – The path to the csv file.
validationMethod (func) – A function used to validate the csv reading.

Returns:

A reference to the instance Spline object on which it was called.

Return type:

Spline

scalex(factor)#

Mulitplies the x values by a scale factor.

Parameters:: factor (float) – The factor to multiply the values with.
Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

scaley(factor)#

Mulitplies the y values by a scale factor.

Parameters:: factor (float) – The factor to multiply the values with.
Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

shiftx(offset)#

Shifts the x values by an offset.

Parameters:: offset (float) – The offset to shift the values with.
Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

shifty(offset)#

Shifts the y values by an offset.

Parameters:: offset (float) – The offset to shift the values with.
Returns:: A reference to the instance Spline object on which it was called.
Return type:: Spline

interpolate(npts=None, type='akima', order=0, x=None)#

Recalculates x and y by interpolation.

This is used to get equally spaced values of x, kind can be “akima” or any scipy.interpolate.inter1d.

If x is specified, returns the computed y value.

Parameters:

npts (int) – Number of samples to generate, if x is None.
type (str) – The type of interpolation. Possible choices are “akima”, “linear”, “cubic”, “zero”, “natural”. If none of these is given then “splev” is used.
order (int) – The order of interpolation.
x (float) – The x value used to return the interpolated y.

Returns:

A reference to the instance Spline object on which it was called.

Return type:

Spline

getXFromY(y)#

Returns a computed x value from the specified y value.

This uses linear interpolation since we can not assume the y values are monotonically increasing.

Parameters:: y (float) – The y value.
Returns:: The x value.
Return type:: float

derivative(order=1, npts=None, type='akima', scaled=True)#

Computes the derivative.

Scale the derivative so it is not too big but can still be viewed.

Parameters:

order (int) – Order of the derivative.
npts (int) – Number of points to interpolate.
type (str) – Type of Interpolation.
scaled (bool | float) – The factor to scale y values.

Returns:

A reference to the instance Spline object on which it was called.

Return type:

Spline

reflect()#: Reflects the data across X and Y.

removeNegativeX()#: Removes x, y pairs with negative x values.