Matrix math

[ericremoreynolds]

Hello Christoph,

From your source code it seems to me that there is no support for matrix algebra and calculus in the library, is this correct?

Introducing matrix algebra is a pain, I have found, because all of a sudden some product expressions are commutative and others aren't.

Regards,

Eric.

[cdrnet]

Indeed, there is no support for matrix expressions. There was in old Math.NET Classic, but not in Symbolics yet.

[MovGP0]

I would skip matrices completely and go for tensors (#14) instead.

This would make sense since scalars, vectors, and matrices are just a special kind of tensors.

[MovGP0]

the lack for matrices and tensors is annoying. it is currently not possible to solve system of equations symbolically:

let burger = symbol "burger"
let pommes = symbol "pommes"
let coke = symbol "coke"
let bill = symbol "bill"

let equations = [
        (2*coke) == 30.0
        (1*coke + 2*burger) == 20.0 // equals does not exist
        (1*burger + 4*pommes) == 9.0
        (burger + pommes * coke) == bill
    ]

linSolve equations bill // not working

the only way i could figure out was the numerical solution:

let M = matrix [[3.0; 0.0; 0.0]
                [1.0; 2.0; 0.0]
                [0.0; 1.0; 4.0]]

let R = vector [30.0; 20.0; 9.0]

let result = M.Solve(R)

let coke = result.[0]
let burger = result.[1]
let pommes = result.[2]

burger + pommes * coke // 15

maybe we could port Redberry (Sourcecode), since it has great support for tensors.

[ingted]

Quick way / ugly way to achieve vector/matrix support

[ingted]

Matrix multiplication supported with an ugly way

    let v = FloatingPoint.RealVector <| vector[1.0;2.0;3.0]

    let M = FloatingPoint.RealMatrix <|
            matrix [[3.0; 0.0; 0.0]
                        [1.0; 2.0; 0.0]
                        [0.0; 1.0; 4.0]]

    let symbols2 = dict[ "a", v; "m", M ]
    let a0 = SymbolicExpression(Infix.parseOrThrow("a * 2")).Evaluate(symbols2)
    printfn "%A" a0.RealVectorValue
    let a1 = SymbolicExpression(Infix.parseOrThrow("a + 1")).Evaluate(symbols2)
    printfn "%A" a1.RealVectorValue
    let a2 = SymbolicExpression(Infix.parseOrThrow("mat_by_row(a, a)")).Evaluate(symbols2)
    printfn "%A" a2.RealMatrixValue
    let a4 = SymbolicExpression(Infix.parseOrThrow("mat_multiply(m, mat_by_col(a, vec(1.0, 2.0, 3.0), a), a)")).Evaluate(symbols2)
    printfn "%A" a4

Result

seq [2.0; 4.0; 6.0]
seq [2.0; 3.0; 4.0]
DenseMatrix 2x3-Double
1  2  3
1  2  3

DenseMatrix 3x2-Double
1  1
2  2
3  3

RealVector (seq [9.0; 13.0; 61.0])