/** This class tests QR decomposition and least-squares routines in
    Matrix.frink.

    This tests the solution of a system of equations represented by matrices
    A * X = B

    where A and B are given and X is solved for.
*/

use Matrix.frink

A = new Matrix[[[2, 3],
                [5, 7]]]

B = new Matrix[[[12],
                [29]]]

println["Original matrix is:\n" + A.formatMatrix[]]
sol = A.leastSquares[B].roundToInt[]
println[]
println["Least-squares solution is:"]
println[sol.formatMatrix[]]

reverse = A.multiply[sol]
println["Verifying solution:"]
println[formatTable[[[reverse.formatMatrix[], "=", B.formatMatrix[]]]]]


A = new Matrix[[[1, 2],
                [1, 3]]]

B = new Matrix[[[1],
                [2]]]

println["\n\n"]
println["Original matrix is:\n" + A.formatMatrix[]]
[Q, R] = A.QRDecompose[]
println["Q and R are:"]
println[formatTable[[[Q.formatMatrix[], "*", R.formatMatrix[]]]]]
println["Testing decomposition.  This should equal original matrix: "]
println[Q.multiply[R].roundToInt[].formatMatrix[]]

sol = A.leastSquares[B].roundToInt[]
println[]
println["Least-squares solution is:"]
println[sol.formatMatrix[]]

reverse = A.multiply[sol]
println["Verifying solution:"]
println[formatTable[[[reverse.formatMatrix[], "=", B.formatMatrix[]]]]]


/*
// Symbolic test.  Produces big symbolic results!
symbolicMode[true]
A = new Matrix[[[f1_1, f2_1],
                [f2_1, f2_2]]]

B = new Matrix[[[y1],
                [y2]]]

println["\n\n"]
println["Original matrix is:\n" + A.formatMatrix[]]
sol = A.leastSquares[B]
println[]
println["Least-squares solution is:"]
println[sol.formatMatrix[]]

reverse = A.multiply[sol]
println["Verifying solution:"]
println[formatTable[[[reverse.formatMatrix[], "=", B.formatMatrix[]]]]]
*/