gavo.utils.mathtricks module

Math-related helper functions.

gavo.utils.mathtricks.cartToSpher(unitvector)

returns spherical coordinates for a 3-unit vector.

We do not check if unitvector actually is a unit vector. The returned angles are in rad.

gavo.utils.mathtricks.ceilInt(flt: float) → float

returns the smallest integer largest than flt, except if flt is a special float, in which case flt is returned.

gavo.utils.mathtricks.findMinimum(f: Callable[[float], float], left: float, right: float, minInterval: float = 3e-08) → float

returns an estimate for the minimum of the single-argument function f on (left,right).

minInterval is a fourth of the smallest test interval considered.

For constant functions, a value close to left will be returned.

This function should only be used on functions having exactly one minimum in the interval.

gavo.utils.mathtricks.floorInt(flt: float) → float

returns the largest integer smaller than flt, except if flt is a special float, in which case flt is returned.

gavo.utils.mathtricks.getHexToBin() → Dict[str, str]

returns a dictionary mapping hex chars to their binary expansions.

gavo.utils.mathtricks.getRotX(angle)

returns a 3-rotation matrix for rotating angle radians around x.

gavo.utils.mathtricks.getRotY(angle)

returns a 3-rotation matrix for rotating angle radians around y.

gavo.utils.mathtricks.getRotZ(angle)

returns a 3-rotation matrix for rotating angle radians around z.

gavo.utils.mathtricks.nprepr(npobj: Union[int, float, float64, ndarray[Any, dtype[ScalarType]]])

formats a simple numpy array of value avoiding excessive digits.

This, realistically, is mainly for doctests.

gavo.utils.mathtricks.roundO2M(num: float) → int

returns a plausible rounding of num.

This will round up the last couple of digits. For now, this will only do cardinals. >>> roundO2M(0) 0 >>> roundO2M(2.5) 2 >>> roundO2M(15) 20 >>> roundO2M(9900) 10000 >>> roundO2M(8321) 8400 >>> roundO2M(3.2349302e9) 3300000000

gavo.utils.mathtricks.spherToCart(theta: Union[int, float, float64], phi: Union[int, float, float64]) → ndarray[Any, dtype[ScalarType]]

returns a 3-cartesian unit vector pointing to longitude theta, latitude phi.

The angles are in rad.

>>> print(spherToCart(0,0))
[1. 0. 0.]
>>> nprepr(spherToCart(0, 90*DEG))
'[6.123e-17 0 1]'
>>> nprepr(spherToCart(90*DEG, 90*DEG))
'[3.749e-33 6.123e-17 1]'
>>> nprepr(spherToCart(90*DEG, 0))
'[6.123e-17 1 0]'
>>> nprepr(spherToCart(180*DEG, -45*DEG))
'[-0.7071 8.66e-17 -0.7071]'

gavo.utils.mathtricks.toBinary(anInt: int, desiredLength: Optional[int] = None) → str

returns anInt as a string with its binary digits, MSB first.

If desiredLength is given and the binary expansion is shorter, the value will be padded with zeros.

>>> toBinary(349)
'101011101'
>>> toBinary(349, 10)
'0101011101'