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PyGeodesy
Package pygeodesy :: Package auxilats :: Module auxDST :: Class AuxDST
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Class AuxDST

object --+
         |
        AuxDST

Discrete Sine Transforms (DST) for Auxiliary latitudes.

See Also: Karney's C++ class DST.

Instance Methods
 
__init__(self, N)
New AuxDST instance.
 
refine(self, f, F, *sentinel)
Refine the Fourier series by doubling the sampled points.
 
reset(self, N)
Reset this DST.
 
transform(self, f)
Determine [N + 1] terms in the Fourier series.

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Static Methods
 
evaluate(sinx, cosx, F, *N)
Evaluate the Fourier sum given the sine and cosine of the angle, using precision Clenshaw summation.
 
integral(sinx, cosx, F, *N)
Evaluate the integral of Fourier sum given the sine and cosine of the angle, using precision Clenshaw summation.
 
integral2(sinx, cosx, siny, cosy, F, *N)
Compute the definite integral of Fourier sum given the sine and cosine of the angles at the end points, using precision Clenshaw summation.
Properties
  N

Inherited from object: __class__

Method Details

__init__ (self, N)
(Constructor)

 

New AuxDST instance.

Arguments:
  • N - Size, number of points (int).
Overrides: object.__init__

evaluate (sinx, cosx, F, *N)
Static Method

 

Evaluate the Fourier sum given the sine and cosine of the angle, using precision Clenshaw summation.

Arguments:
  • sinx - The sin(sigma) (float).
  • cosx - The cos(sigma) (float).
  • F - The Fourier coefficients (float[]).
  • N - Optional, (smaller) number of terms to evaluate (int).
Returns:
Precison Clenshaw sum (float).

See Also: Methods AuxDST.integral and AuxDST.integral2.

integral (sinx, cosx, F, *N)
Static Method

 

Evaluate the integral of Fourier sum given the sine and cosine of the angle, using precision Clenshaw summation.

Arguments:
  • sinx - The sin(sigma) (float).
  • cosx - The cos(sigma) (float).
  • F - The Fourier coefficients (float[]).
  • N - Optional, len(F) or a (smaller) number of terms to evaluate (int).
Returns:
Precison Clenshaw intergral (float).

See Also: Methods AuxDST.evaluate and AuxDST.integral2.

integral2 (sinx, cosx, siny, cosy, F, *N)
Static Method

 

Compute the definite integral of Fourier sum given the sine and cosine of the angles at the end points, using precision Clenshaw summation.

Arguments:
  • sinx - The sin(sigma1) (float).
  • cosx - The cos(sigma1) (float).
  • siny - The sin(sigma2) (float).
  • cosy - The cos(sigma2) (float).
  • F - The Fourier coefficients (float[]).
  • N - Optional, len(F) or a (smaller) number of terms to evaluate (int).
Returns:
Precison Clenshaw integral (float).

See Also: Methods AuxDST.evaluate and AuxDST.integral.

refine (self, f, F, *sentinel)

 

Refine the Fourier series by doubling the sampled points.

Arguments:
  • f - Single-argument callable (f(sigma)).
  • F - Initial Fourier series coefficients (float[:N]).
  • sentinel - Optional coefficient(s) to append (float(s)).
Returns:
Fourier series coefficients (float[:N*2]).

Note: Any initial F[N:] sentinel coefficients are ignored.

reset (self, N)

 

Reset this DST.

Arguments:
  • N - Size, number of points (int).
Returns:
The new size (int, non-negative).

transform (self, f)

 

Determine [N + 1] terms in the Fourier series.

Arguments:
  • f - Single-argument callable (f(sigma)).
Returns:
Fourier series coefficients (float[:N+1], leading 0).

Property Details

N

Get method:
N(self) - Get this DST's size, number of points (int).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

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