Package pygeodesy :: Module fmath |
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# Module fmath

Precision mathematical functions, utilities and constants.

Version: 19.02.21

Classes
| Fsum Precision floating point summation similar to standard Python function `math.fsum`.

Functions
hypot(x, y) Return the Euclidean distance, sqrt(x*x + y*y). |
acos1(x) Return math.acos(max(-1, min(1, x))). |
cbrt(x) Compute the cubic root x**(1/3). |
cbrt2(x) Compute the cubic root squared x**(2/3). |
favg(v1, v2, f=0.5) Return the weighted average of two values. |
fdot(a, *b) Return the precision dot product sum(a[i] * b[i] for i=0..len(a)). |
fdot3(a, b, c, start=0) Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)). |
fhorner(x, *cs) Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) using the Horner form. |
fmean(xs) Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs). |
fpolynomial(x, *cs) Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)). |
fpowers(x, n, alts=0) Return a series of powers [x**i for i=1..n]. |
fprod(iterable, start=1.0) Iterable product, like `numpy.prod`. |
value |
freduce(function, sequence, initial=...) Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. |
fStr(floats, prec=6, sep=`'``,` `'`, fmt=`'``%.*f``'`, ints=False) Convert floats to string, optionally with trailing zero decimals stripped. |
fStrzs(fstr) Strip trailing zero decimals from a float string. |
fsum_(*args) Precision floating point sum of the positional argument vulues. |
fsum(iterable) Return an accurate floating point sum of values in the iterable. |
hypot1(x) Compute the norm sqrt(1 + x**2). |
hypot3(x, y, z) Compute the norm sqrt(x**2 + y**2 + z**2). |
isfinite(obj) Check for `Inf` and `NaN` values. |
isint(obj, both=False) Check for integer type or integer value. |
isscalar(obj) Check for scalar types. |
len2(seq) Make built-in function `len` work for generators, iterators, etc. |
map1(func, *args) Apply each argument to a single-argument function and return a tuple of results. |
map2(func, *args) Apply arguments to a function and return a tuple of results. |
scalar(value, low=2.22044604925e-16, high=1.0, name=`'``scalar``'`) Validate a scalar. |
sqrt3(x) Compute the square root cubed sqrt(x)**3 or sqrt(x**3). |

Variables
| __all__ = `_ALL_LAZY.fmath`
| EPS = `2.22044604925e-16` Approximate epsilon (`float`)
| EPS1 = `1.0` 1 - EPS (`float`), about 0.9999999999999998

Function Details

### cbrt(x) |
Compute the cubic root x**(1/3). Parameters: `x` - Value (`scalar`). Returns: Cubic root (`float`).

### cbrt2(x) |
Compute the cubic root squared x**(2/3). Parameters: `x` - Value (`scalar`). Returns: Cubic root squared (`float`). See Also: Function sqrt3.

### favg(v1, v2, f=0.5) |
Return the weighted average of two values. Parameters: `v1` - One value (`scalar`). `v2` - Other value (`scalar`). `f` - Optional fraction (`float`). Returns: v1 + f * (v2 - v1) (`float`).

### fdot(a, *b) |
Return the precision dot product sum(a[i] * b[i] for i=0..len(a)). Parameters: `a` - List, sequence, tuple, etc. (scalars). `b` - All positional arguments (scalars). Returns: Dot product (`float`). Raises: `ValueError` - Unequal `len`(a) and `len`(b).

### fdot3(a, b, c, start=0) |
Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)). Parameters: `a` - List, sequence, tuple, etc. (`scalar`[]). `b` - List, sequence, tuple, etc. (`scalar`[]). `c` - List, sequence, tuple, etc. (`scalar`[]). `start` - Optional bias (`scalar`). Returns: Dot product (`float`). Raises: `ValueError` - Unequal `len`(a), `len`(b) and/or `len`(c).

### fhorner(x, *cs) |
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) using the Horner form. Parameters: `x` - Polynomial argument (`scalar`). `cs` - Polynomial coeffients (`scalar`[]). Returns: Horner value (`float`). Raises: `TypeError` - Non-scalar x. `ValueError` - No cs coefficients or x is not finite. See Also: Function fpolynomial.

### fmean(xs) |
Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs). Parameters: `xs` - Values (scalars). Returns: Mean value (`float`). Raises: `ValueError` - No xs values.

### fpolynomial(x, *cs) |
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)). Parameters: `x` - Polynomial argument (`scalar`). `cs` - Polynomial coeffients (`scalar`[]). Returns: Polynomial value (`float`). Raises: `TypeError` - Non-scalar x. `ValueError` - No cs coefficients or x is not finite. See Also: Function fhorner.

### fpowers(x, n, alts=0) |
Return a series of powers [x**i for i=1..n]. Parameters: `x` - Value (`scalar`). `n` - Highest exponent (`int`). `alts` - Only alternating powers, starting with this exponent (`int`). Returns: Powers of x (`float`[]). Raises: `TypeError` - Non-scalar x or n not `int`. `ValueError` - Non-positive n or x is not finite.

### fprod(iterable, start=1.0) |
Iterable product, like `numpy.prod`. Parameters: `iterable` - Values to be multiplied (`scalar`[]). `start` - Initial product, also the value returned for an empty iterable (`scalar`). Returns: The product (`float`). See Also: NumPy.prod.

### freduce(function, sequence, initial=...) |
Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates ((((1+2)+3)+4)+5). If initial is present, it is placed before the items of the sequence in the calculation, and serves as a default when the sequence is empty. Returns: value

### fStr(floats, prec=6, sep=`'``,` `'`, fmt=`'``%.*f``'`, ints=False) |
Convert floats to string, optionally with trailing zero decimals stripped. Parameters: `floats` - List, sequence, tuple, etc. (scalars). `prec` - Optional precision, number of decimal digits (0..9). Trailing zero decimals are stripped for prec values of 1 and above, but kept for negative prec values. `sep` - Optional, separator to join (string). `fmt` - Optional, float format (string). `ints` - Optionally, remove decimal dot (`bool`). Returns: The floats as 'f, f, ... f' (string).

### fStrzs(fstr) |
Strip trailing zero decimals from a float string. Parameters: `fstr` - Float (string). Returns: Float (string).

### fsum_(*args) |
Precision floating point sum of the positional argument vulues. Parameters: `args` - Values to be added (`scalar`[]). Returns: Accurate fsum (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `TypeError` - Non-scalar arg value. `ValueError` - Invalid or infinite arg value.

### fsum(iterable) |
Return an accurate floating point sum of values in the iterable. Assumes IEEE-754 floating point arithmetic.

### hypot1(x) |
Compute the norm sqrt(1 + x**2). Parameters: `x` - Argument (`scalar`). Returns: Norm (`float`).

### hypot3(x, y, z) |
Compute the norm sqrt(x**2 + y**2 + z**2). Parameters: `x` - X argument (`scalar`). `y` - Y argument (`scalar`). `z` - Z argument (`scalar`). Returns: Norm (`float`).

### isfinite(obj) |
Check for `Inf` and `NaN` values. Parameters: `obj` - Value (`scalar`). Returns: `False` if obj is `Inf` or `NaN`, `True` otherwise. Raises: `TypeError` - Non-scalar obj.

### isint(obj, both=False) |
Check for integer type or integer value. Parameters: `obj` - The object (any `type`). `both` - Optionally, check both type and value (`bool`). Returns: `True` if obj is `int`, `False` otherwise.

### isscalar(obj) |
Check for scalar types. Parameters: `obj` - The object (any `type`). Returns: `True` if obj is `scalar`, `False` otherwise.

### len2(seq) |
Make built-in function `len` work for generators, iterators, etc. since those can only be started exactly once. Parameters: `seq` - Generator, iterator, list, range, tuple, etc. Returns: 2-Tuple (number, ...) of items (`int`, `list` or `range` or `tuple`).

### map1(func, *args) |
Apply each argument to a single-argument function and return a tuple of results. Parameters: `func` - Function to apply (callable). `args` - Arguments to apply (any positional). Returns: Function results (`tuple`).

### map2(func, *args) |
Apply arguments to a function and return a tuple of results. Unlike Python 2's built-in `map`, Python 3+ `map` returns a `map` object, an iterator-like object which generates the results only once. Converting the `map` object to a tuple maintains Python 2 behavior. Parameters: `func` - Function to apply (callable). `args` - Arguments to apply (list, tuple, ...). Returns: N-Tuple of function results (`tuple`).

### scalar(value, low=2.22044604925e-16, high=1.0, name=`'``scalar``'`) |
Validate a scalar. Parameters: `value` - The value (`scalar`). `low` - Optional lower bound (`scalar`). `high` - Optional upper bound (`scalar`). `name` - Optional name of value (`str`). Returns: New value (`type` of low). Raises: `TypeError` - Non-scalar value. `ValueError` - Out-of-bounds value.

### sqrt3(x) |
Compute the square root cubed sqrt(x)**3 or sqrt(x**3). Parameters: `x` - Value (`scalar`). Returns: Cubed square root (`float`). Raises: `ValueError` - Negative x. See Also: Function cbrt2.