`lib-math` 库参考

原文: https://finproducts.atlassian.net/wiki/spaces/JIDD3/pages/34793521509/FIN+5.3.1+lib-math 中文整理基于 FIN 5.3.1

导读： 数学函数库

以下为 API 参考，保留英文以便对照源码；目录已列出（英文标题便于检索）；概述已尽量中译。

目录（导读）

lib
meta
funcs
def
acos(val)
- supertypes
asin(val)
atan(val)
atan2(y, x)
bitAnd(a, b)
bitNot(a)
bitOr(a, b)
bitShiftl(a, b)
bitShiftr(a, b)
bitXor(a, b)
ceil(val)
cos(val)
cosh(val)
exp(val)
fitLinearRegression(grid, opts: null)
floor(val)
log10(val)
logE(val)
matrixAdd(a, b)
matrixDeterminant(m)
matrixFitLinearRegression(y, x)
matrixInverse(m)
matrixMult(a, b)
matrixSub(a, b)
matrixTranspose(m)
mean(val, acc)
meanBiasErr(val, acc, nDegrees: 0)
median(val, acc)
pi()
pow(val, exp)
quantile(percent, method: "linear")
random(range: null)
remainder(a, b)
rootMeanSquareErr(val, acc, nDegrees: 0)
round(val)
sin(val)
sinh(val)
sqrt(val)
standardDeviation(val, acc)
tan(val)
tanh(val)
toDegrees(val)
toMatrix(obj, opts: {})
toRadians(val)

概述（中译）

数学函数库

API 正文（英文）

funcs


acos	Return the arc cosine
asin	Return the arc sine
atan	Return the arc tangent
atan2	Converts rectangular coordinates (x, y) to polar (r, theta)
bitAnd	Bitwise and
bitNot	Bitwise not
bitOr	Bitwise or
bitShiftl	Bitwise left shift
bitShiftr	Bitwise right shift
bitXor	Bitwise xor
ceil	Return the smallest whole number greater than or equal to val
cos	Return the cosine of angle in radians
cosh	Return the hyperbolic cosine
exp	Return e raised to val
fitLinearRegression	Given a grid of x, y coordinates compute the best fit linear regression equation using the ordinary least squares method
floor	Return the largest whole number less than or equal to val
log10	Return base 10 logarithm of val
logE	Return natural logarithm to the base e of val
matrixAdd	Add two matrices together and return new matrix
matrixDeterminant	Return the determinant as a unitless Number for the given matrix which is any value accepted by `toMatrix()`
matrixFitLinearRegression	Given a matrix of y coordinates and a matrix of multiple x coordinates compute the best fit multiple linear regression equation using the ordinary least squares method
matrixInverse	Return the inverse of the given matrix which is any value accepted by `toMatrix()`
matrixMult	Multiply two matrices and return new matrix
matrixSub	Subtract two matrices and return new matrix
matrixTranspose	Transpose the given matrix which is any value accepted by `toMatrix()`
mean	Fold a sample of numbers into their standard average or arithmetic mean
meanBiasErr	Fold a sample of numbers into their MBE (mean bias error)
median	Fold a sample of numbers into their median value which is the middle value of the sorted samples
pi	Return constant for pi
pow	Return val raised to the specified power
quantile	Computes the pth quantile of a list of numbers, according to the specified interpolation method
random	Return random integer within given inclusive range
remainder	Return the remainder or modulo of division
rootMeanSquareErr	Fold a sample of numbers into their RMSE (root mean square error)
round	Returns the nearest whole number to val
sin	Return sine of angle in radians
sinh	Return hyperbolic sine
sqrt	Return square root of val
standardDeviation	Fold a series of numbers into the standard deviation of a sample
tan	Return tangent of angle in radians
tanh	Return hyperbolic tangent
toDegrees	Convert angle in radians to an angle in degrees
toMatrix	Convert a general grid to an optimized matrix grid
toRadians	Convert angle in degrees to an angle in radians

func:acos

acos(val)

Return the arc cosine.

meta


def	func:acos
is	func
lib	lib:math
name	acos

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:asin

asin(val)

Return the arc sine.

meta


def	func:asin
is	func
lib	lib:math
name	asin

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:atan

atan(val)

Return the arc tangent.

meta


def	func:atan
is	func
lib	lib:math
name	atan

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:atan2

atan2(y, x)

Converts rectangular coordinates (x, y) to polar (r, theta).

meta


def	func:atan2
is	func
lib	lib:math
name	atan2

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:bitAnd

bitAnd(a, b)

Bitwise and: a & b

meta


def	func:bitAnd
is	func
lib	lib:math
name	bitAnd

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:bitNot

bitNot(a)

Bitwise not: ~a

meta


def	func:bitNot
is	func
lib	lib:math
name	bitNot

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:bitOr

bitOr(a, b)

Bitwise or: a | b

meta


def	func:bitOr
is	func
lib	lib:math
name	bitOr

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:bitShiftl

bitShiftl(a, b)

Bitwise left shift: a << b

meta


def	func:bitShiftl
is	func
lib	lib:math
name	bitShiftl

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:bitShiftr

bitShiftr(a, b)

Bitwise right shift: a >> b

meta


def	func:bitShiftr
is	func
lib	lib:math
name	bitShiftr

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:bitXor

bitXor(a, b)

Bitwise xor: a ^ b

meta


def	func:bitXor
is	func
lib	lib:math
name	bitXor

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:ceil

ceil(val)

Return the smallest whole number greater than or equal to val. Result has same unit as val.

meta


def	func:ceil
is	func
lib	lib:math
name	ceil

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:cos

cos(val)

Return the cosine of angle in radians.

meta


def	func:cos
is	func
lib	lib:math
name	cos

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:cosh

cosh(val)

Return the hyperbolic cosine.

meta


def	func:cosh
is	func
lib	lib:math
name	cosh

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:exp

exp(val)

Return e raised to val.

meta


def	func:exp
is	func
lib	lib:math
name	exp

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

func:fitLinearRegression

fitLinearRegression(grid, opts: null)

Given a grid of x, y coordinates compute the best fit linear regression equation using the ordinary least squares method. The first column of the grid is used for x and the second column is y. Any rows without a Number for both x and y are skipped. Any special Numbers (infinity/NaN) are skipped.

Options:

x: column name to use for x if not first column
y: column name to use for y if not second column

The resulting linear equation is:

yᵢ = mxᵢ + b

The equation is returned as a dictionary with these keys:

m: slope of the best fit regression line
b: intercept of the best fit regression line
r2: R² coefficient of determination as a number between 1.0 (perfect correlation) and 0.0 (no correlation)
xmin: minimum value of x variable in sample data
xmax: maximum value of x variable in sample data
ymin: minimum value of y variable in sample data
ymax: maximum value of y variable in sample data

Also see matrixFitLinearRegression() to compute a multiple linear regression.

Example:

data: [{x:1, y:2},
       {x:2, y:4},
       {x:4, y:4},
       {x:6, y:5}].toGrid
 fitLinearRegression(data)

 >>> {m:0.4915, b: 2.1525, r2: 0.7502}

meta


def	func:fitLinearRegression
is	func
lib	lib:math
name	fitLinearRegression

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:floor

floor(val)

Return the largest whole number less than or equal to val. Result has same unit as val.

meta


def	func:floor
is	func
lib	lib:math
name	floor

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:log10

log10(val)

Return base 10 logarithm of val.

meta


def	func:log10
is	func
lib	lib:math
name	log10

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:logE

logE(val)

Return natural logarithm to the base e of val.

meta


def	func:logE
is	func
lib	lib:math
name	logE

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:matrixAdd

matrixAdd(a, b)

Add two matrices together and return new matrix. The parameters may be any value supported toMatrix(). Matrices must have the same dimensions.

meta


def	func:matrixAdd
is	func
lib	lib:math
name	matrixAdd

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:matrixDeterminant

matrixDeterminant(m)

Return the determinant as a unitless Number for the given matrix which is any value accepted by toMatrix(). The matrix must be square.

meta


def	func:matrixDeterminant
is	func
lib	lib:math
name	matrixDeterminant

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:matrixFitLinearRegression

matrixFitLinearRegression(y, x)

Given a matrix of y coordinates and a matrix of multiple x coordinates compute the best fit multiple linear regression equation using the ordinary least squares method. Both y and x may be any value accepted by toMatrix().

The resulting linear equation for r X coordinates is:

yᵢ = bias + b₁xᵢ₁ + b₂xᵢ₂ +...+ bᵣxᵢᵣ

The equation is returned as a grid. The grid meta:

bias: bias or zero coefficient which is independent of any of the x factors
r2: R² coefficient of determination as a number between 1.0 (perfect correlation) and 0.0 (no correlation)
r: the square root of R², referred to as the correlation coefficient
rowCount: the number of rows of data used in the correlation For each X factor there is a row with the following tags:
b: the correlation coefficient for the given X factor

meta


def	func:matrixFitLinearRegression
is	func
lib	lib:math
name	matrixFitLinearRegression

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:matrixInverse

matrixInverse(m)

Return the inverse of the given matrix which is any value accepted by toMatrix().

meta


def	func:matrixInverse
is	func
lib	lib:math
name	matrixInverse

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:matrixMult

matrixMult(a, b)

Multiply two matrices and return new matrix. The parameters may be any value supported toMatrix(). Matrix a column count must match matrix b row count.

meta


def	func:matrixMult
is	func
lib	lib:math
name	matrixMult

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:matrixSub

matrixSub(a, b)

Subtract two matrices and return new matrix. The parameters may be any value supported toMatrix(). Matrices must have the same dimensions.

meta


def	func:matrixSub
is	func
lib	lib:math
name	matrixSub

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:matrixTranspose

matrixTranspose(m)

Transpose the given matrix which is any value accepted by toMatrix().

meta


def	func:matrixTranspose
is	func
lib	lib:math
name	matrixTranspose

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:mean

mean(val, acc)

Fold a sample of numbers into their standard average or arithmetic mean. This function is the same as core::avg. Nulls values are ignored. Return null if no values.

Example:

[2, 4, 5, 3].fold(mean)

meta


def	func:mean
disKey	ui::mean
foldOn	Number
is	func
lib	lib:math
name	mean

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:meanBiasErr

meanBiasErr(val, acc, nDegrees: 0)

Fold a sample of numbers into their MBE (mean bias error). The MBE function determines the MBE between a sample set and its mean:

MBE = Σ(xᵢ - median) / (n - nDegrees)

Examples:

samples.fold(meanBiasErr)         // unbiased zero degrees of freedom
samples.fold(meanBiasErr(_,_,1))  // 1 degree of freedom

meta


def	func:meanBiasErr
disKey	ui::meanBiasErr
foldOn	Number
is	func
lib	lib:math
name	meanBiasErr

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:median

median(val, acc)

Fold a sample of numbers into their median value which is the middle value of the sorted samples. If there are an even number of sample, then the median is the mean of the middle two. Null values are ignored. Return null if no values.

Example:

[2, 4, 5, 3, 1].fold(median)

meta


def	func:median
disKey	ui::median
foldOn	Number
is	func
lib	lib:math
name	median

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:pi

pi()

Return constant for pi: 3.141592653589793

meta


def	func:pi
is	func
lib	lib:math
name	pi

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:pow

pow(val, exp)

Return val raised to the specified power.

meta


def	func:pow
is	func
lib	lib:math
name	pow

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:quantile

quantile(percent, method: "linear")

Computes the p*th* quantile of a list of numbers, according to the specified interpolation method. The value p must be a number between 0.0 to 1.0.

linear (default): Interpolates proportionally between the two closest values
nearest: Rounds to the nearest data point
lower: Rounds to the nearest lower data point
higher: Rounds to the nearest higher data point
midpoint: Averages two nearest values

Usage:

[1,2,3].fold(quantile(p, method))

Examples:

[10,10,10,25,100].fold(quantile(0.7 )) => 22 //default to linear
[10,10,10,25,100].fold(quantile(0.7, "nearest")) => 25
[10,10,10,25,100].fold(quantile(0.7, "lower")) => 10
[10,10,10,25,100].fold(quantile(0.7, "higher")) => 25
[10,10,10,25,100].fold(quantile(0.7, "linear")) => 22 //same as no arg
[10,10,10,25,100].fold(quantile(0.7, "midpoint")) => 17.5

Detailed Logic:

p: percentile (decimal 0-1)
n: list size
rank: p * (n-1) // this is the index of the percentile in your list
// if rank is an integer, return list[rank]
// if rank is not an integer, interpolate via one of the above methods (illustrated below in examples)

[1,2,3,4,5].percentile(0.5) => 3 // rank=2 is an int so we can index[2] directly

[10,10,10, 25, 100].percentile(0.7, method)
  rank = (0.7 * 4) => 2.8

  //adjust rank based on method
  nearest =  index[3]                // => 25
  lower =    index[2]                // => 10
  higher =   index[3]                // => 25

  //or interpolate for these methods

  //takes the 2 closest indices and calculates midpoint
  midpoint = (25-10)/2 + 10          // => 17.5

  //takes the 2 closest indices and calculates weighted average
  linear =   (0.2 * 10) + (0.8 * 25) // => 22

meta


def	func:quantile
is	func
lib	lib:math
name	quantile

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:random

random(range: null)

Return random integer within given inclusive range. If range is null, then full range of representative integers is assumed.

Examples:

random()       // random num with no range
random(0..100) // random num between 0 and 100

meta


def	func:random
is	func
lib	lib:math
name	random

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:remainder

remainder(a, b)

Return the remainder or modulo of division: a % b. Result has same unit as a.

meta


def	func:remainder
is	func
lib	lib:math
name	remainder

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:rootMeanSquareErr

rootMeanSquareErr(val, acc, nDegrees: 0)

Fold a sample of numbers into their RMSE (root mean square error). The RMSE function determines the RMSE between a sample set and its mean using the n-degrees of freedom RMSE:

RMBE = sqrt( Σ(xᵢ - median)² ) / (n - nDegrees)

Examples:

samples.fold(rootMeanSquareErr)         // unbiased zero degrees of freedom
samples.fold(rootMeanSquareErr(_,_,1))  // 1 degree of freedom

meta


def	func:rootMeanSquareErr
disKey	ui::rootMeanSquareErr
foldOn	Number
is	func
lib	lib:math
name	rootMeanSquareErr

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:round

round(val)

Returns the nearest whole number to val. Result has same unit as val.

meta


def	func:round
is	func
lib	lib:math
name	round

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:sin

sin(val)

Return sine of angle in radians.

meta


def	func:sin
is	func
lib	lib:math
name	sin

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:sinh

sinh(val)

Return hyperbolic sine.

meta


def	func:sinh
is	func
lib	lib:math
name	sinh

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:sqrt

sqrt(val)

Return square root of val.

meta


def	func:sqrt
is	func
lib	lib:math
name	sqrt

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:standardDeviation

standardDeviation(val, acc)

Fold a series of numbers into the standard deviation of a sample:

s = sqrt(Σ (xᵢ - mean)² / (n-1))

Example:

[4, 2, 5, 8, 6].fold(standardDeviation)

meta


def	func:standardDeviation
disKey	ui::standardDeviation
foldOn	Number
is	func
lib	lib:math
name	standardDeviation

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:tan

tan(val)

Return tangent of angle in radians.

meta


def	func:tan
is	func
lib	lib:math
name	tan

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:tanh

tanh(val)

Return hyperbolic tangent.

meta


def	func:tanh
is	func
lib	lib:math
name	tanh

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:toDegrees

toDegrees(val)

Convert angle in radians to an angle in degrees.

meta


def	func:toDegrees
is	func
lib	lib:math
name	toDegrees

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:toMatrix

toMatrix(obj, opts: {})

Convert a general grid to an optimized matrix grid. Matrixs are two dimensional grids of Numbers. Columns are named "v0", "v1", "v2", etc. Grid meta is preserved, but not column meta. Numbers in the resulting matrix are unitless; any units passed in are stripped.

The following options are supported:

nullVal (Number): replace null values in the grid with this value
naVal (Number): replace NA values in the grid with this value

toMatrix(grid, {nullVal: 0, naVal: 0})

To create a sparse or initialized matrix you can pass a Dict with the the following tags (all required)

toMatrix({rows:10, cols: 1000, init: 0})

meta


def	func:toMatrix
is	func
lib	lib:math
name	toMatrix

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

def

func:toRadians

toRadians(val)

Convert angle in degrees to an angle in radians.

meta


def	func:toRadians
is	func
lib	lib:math
name	toRadians

supertypes


feature	Feature namespace of definitions formatted as `feature:name`
func	Axon function

lib-math 库参考 ​

目录（导读） ​

概述（中译） ​

API 正文（英文） ​

funcs ​

func:acos ​

acos(val) ​

func:asin ​

asin(val) ​

func:atan ​

atan(val) ​

func:atan2 ​

atan2(y, x) ​

func:bitAnd ​

bitAnd(a, b) ​

func:bitNot ​

bitNot(a) ​

func:bitOr ​

bitOr(a, b) ​

func:bitShiftl ​

bitShiftl(a, b) ​

func:bitShiftr ​

bitShiftr(a, b) ​

func:bitXor ​

bitXor(a, b) ​

func:ceil ​

ceil(val) ​

func:cos ​

cos(val) ​

func:cosh ​

cosh(val) ​

func:exp ​

exp(val) ​

func:fitLinearRegression ​

fitLinearRegression(grid, opts: null) ​

func:floor ​

floor(val) ​

func:log10 ​

log10(val) ​

func:logE ​

logE(val) ​

func:matrixAdd ​

matrixAdd(a, b) ​

func:matrixDeterminant ​

matrixDeterminant(m) ​

func:matrixFitLinearRegression ​

matrixFitLinearRegression(y, x) ​

func:matrixInverse ​

matrixInverse(m) ​

func:matrixMult ​

matrixMult(a, b) ​

func:matrixSub ​

matrixSub(a, b) ​

func:matrixTranspose ​

matrixTranspose(m) ​

func:mean ​

mean(val, acc) ​

func:meanBiasErr ​

meanBiasErr(val, acc, nDegrees: 0) ​

`lib-math` 库参考

目录（导读）

概述（中译）

API 正文（英文）

funcs

func:acos

acos(val)

func:asin

asin(val)

func:atan

atan(val)

func:atan2

atan2(y, x)

func:bitAnd

bitAnd(a, b)

func:bitNot

bitNot(a)

func:bitOr

bitOr(a, b)

func:bitShiftl

bitShiftl(a, b)

func:bitShiftr

bitShiftr(a, b)

func:bitXor

bitXor(a, b)

func:ceil

ceil(val)

func:cos

cos(val)

func:cosh

cosh(val)

func:exp

exp(val)

func:fitLinearRegression

fitLinearRegression(grid, opts: null)

func:floor

floor(val)

func:log10

log10(val)

func:logE

logE(val)

func:matrixAdd

matrixAdd(a, b)

func:matrixDeterminant

matrixDeterminant(m)

func:matrixFitLinearRegression

matrixFitLinearRegression(y, x)

func:matrixInverse

matrixInverse(m)

func:matrixMult

matrixMult(a, b)

func:matrixSub

matrixSub(a, b)

func:matrixTranspose

matrixTranspose(m)

func:mean

mean(val, acc)

func:meanBiasErr

meanBiasErr(val, acc, nDegrees: 0)