Linear regression.

The type is

linear :: [(Double, Double)] -> V2

but overloaded to work with boxed and unboxed Vectors.

>>> let input1 = [(0, 1), (1, 3), (2, 5)]
>>> PP $ linear input1
V2 2.0000 1.00000

>>> let input2 = [(0.1, 1.2), (1.3, 3.1), (1.9, 4.9), (3.0, 7.1), (4.1, 9.0)]
>>> PP $ linear input2
V2 2.0063 0.88685

Like linear but also return parameters' standard errors.

To get confidence intervals you should multiply the errors by quantile (studentT (n - 2)) ci' from statistics package or similar. For big n using value 1 gives 68% interval and using value 2 gives 95% confidence interval. See https://en.wikipedia.org/wiki/Student%27s_t-distribution#Table_of_selected_values (quantile calculates one-sided values, you need two-sided, thus adjust ci value).

The first input is perfect fit:

>>> PP $ linearWithErrors input1
(V2 2.0000 1.00000, V2 0.00000 0.00000)

The second input is quite good:

>>> PP $ linearWithErrors input2
(V2 2.0063 0.88685, V2 0.09550 0.23826)

But the third input isn't so much, standard error of a slope argument is 20%.

>>> let input3 = [(0, 2), (1, 3), (2, 6), (3, 11)]
>>> PP $ linearWithErrors input3
(V2 3.0000 1.00000, V2 0.63246 1.1832)

Since: 0.1.1

Quadratic regression.

The type is

quadratic :: [(Double, Double)] -> V3

but overloaded to work with boxed and unboxed Vectors.

>>> let input1 = [(0, 1), (1, 3), (2, 5)]
>>> quadratic input1
V3 0.0 2.0 1.0

>>> let input2 = [(0.1, 1.2), (1.3, 3.1), (1.9, 4.9), (3.0, 7.1), (4.1, 9.0)]
>>> PP $ quadratic input2
V3 (-0.00589) 2.0313 0.87155

>>> let input3 = [(0, 2), (1, 3), (2, 6), (3, 11)]
>>> PP $ quadratic input3
V3 1.00000 0.00000 2.0000

Like quadratic but also return parameters' standard errors.

>>> PP $ quadraticWithErrors input2
(V3 (-0.00589) 2.0313 0.87155, V3 0.09281 0.41070 0.37841)

>>> PP $ quadraticWithErrors input3
(V3 1.00000 0.00000 2.0000, V3 0.00000 0.00000 0.00000)

Since: 0.1.1

Do both linear and quadratic regression in one data scan.

>>> PP $ quadraticAndLinear input2
(V3 (-0.00589) 2.0313 0.87155, V2 2.0063 0.88685)

Like quadraticAndLinear but also return parameters' standard errors

>>> PP $ quadraticAndLinearWithErrors input2
((V3 (-0.00589) 2.0313 0.87155, V2 2.0063 0.88685), (V3 0.09281 0.41070 0.37841, V2 0.09550 0.23826))

Since: 0.1.1

Addition

Identity

Multiplication of different things.

Determinant

Inverse

Solve linear equation.

>>> zerosLin (V2 1 2)
-2.0

Solve quadratic equation.

>>> zerosQuad (V3 2 0 (-1))
Right (-0.7071067811865476,0.7071067811865476)

>>> zerosQuad (V3 2 0 1)
Left ((-0.0) :+ (-0.7071067811865476),(-0.0) :+ 0.7071067811865476)

Double root is not treated separately:

>>> zerosQuad (V3 1 0 0)
Right (-0.0,0.0)

>>> zerosQuad (V3 1 (-2) 1)
Right (1.0,1.0)

Find an optima point.

>>> optimaQuad (V3 1 (-2) 0)
1.0

compare to

>>> zerosQuad (V3 1 (-2) 0)
Right (0.0,2.0)

2d vector. Strict pair of Doubles.

Also used to represent linear polynomial: V2 a b \(= a x + b\).

2×2 matrix.

3d vector. Strict triple of Doubles.

Also used to represent quadratic polynomial: V3 a b c \(= a x^2 + b x + c\).

3×3 matrix.

Like Foldable but with element in the class definition.

Class witnessing that dp has a pair of Doubles.