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) Double the number of sampled points on a Fourier series. |
reset(self, N) Reset this DST. |
transform(self, f) Compute `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) Compute the Fourier sum given the sine and cosine of the angle, using Clenshaw summation `sum(F[i] * sin((2*i+1) * x))` for `i in range(min(len(F), *N))`. |
integral(sinx, cosx, F, *N) Compute the integral of Fourier sum given the sine and cosine of the angle using Clenshaw summation `-sum(F[i] / (2*i+1) * cos((2*i+1) * x))` for `i in range(min(len(F), *N))`. |
integral2(sin1, cos1, sin2, cos2, F, *N) Compute the integral of Fourier sum given the sine and cosine of the angles at the end points using Clenshaw summation `integral(siny, cosy, F) - integral(sinx, cosx, F)`. |

Properties
| N Get this DST's size, number of points (`int`).
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 |
Compute the Fourier sum given the sine and cosine of the angle, using Clenshaw summation `sum(F[i] * sin((2*i+1) * x))` for `i in range(min(len(F), *N))`. 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 |
Compute the integral of Fourier sum given the sine and cosine of the angle using Clenshaw summation `-sum(F[i] / (2*i+1) * cos((2*i+1) * x))` for `i in range(min(len(F), *N))`. 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 intergral (`float`). See Also: Methods `AuxDST.evaluate` and `AuxDST.integral2`.

### integral2 (sin1, cos1, sin2, cos2, F, *N) Static Method |
Compute the integral of Fourier sum given the sine and cosine of the angles at the end points using Clenshaw summation `integral(siny, cosy, F) - integral(sinx, cosx, F)`. Arguments: `sin1` - The sin(sigma1) (`float`). `cos1` - The cos(sigma1) (`float`). `sin2` - The sin(sigma2) (`float`). `cos2` - The cos(sigma2) (`float`). `F` - The Fourier coefficients (`float`[]). `N` - Optional, (smaller) number of terms to evaluate (`int`). Returns: Precison Clenshaw intergral (`float`). See Also: Methods `AuxDST.evaluate` and `AuxDST.integral`.

### refine (self, f, F) |
Double the number of sampled points on a Fourier series. Arguments: `f` - Single-argument function (`callable(sigma)` with `sigma = PI_4 * j / N for j in range(1, N*2, 2)`. `F` - The initial Fourier series coefficients (`float`[:N]). Returns: Fourier series coefficients (`float`[:N*2]).

### reset (self, N) |
Reset this DST. Arguments: `N` - Size, number of points (`int`). Returns: The new size (`int`, non-negative).

### transform (self, f) |
Compute `N + 1` terms in the Fourier series. Arguments: `f` - Single-argument function (`callable(sigma)` with `sigma = PI_2 * i / N for i in range(1, N + 1)`. Returns: Fourier series coefficients (`float`[:N + 1]).

Property Details

### N Get this DST's size, number of points (`int`). 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.