I'm having trouble with the QuadraticMinimizer- every time I execute it I get errors that are non-sensical. I've looked at the scaladoc and the code and I am just not sure what I am doing incorrectly.
I have the following code:
val lBounds:DenseVector[Double] = DenseVector(Array(Double.NegativeInfinity, 5.0, 0.1, 50.0, 50.0))
val uBounds:DenseVector[Double] = DenseVector(Array(Double.PositiveInfinity, 500.0, 100.0, 99000.0, 99000.0))
val inputMatrix:DenseMatrix[Double] = breeze.linalg.csvread(file=new java.io.File(getClass.getResource("/input/zip06latlong.csv").toURI), skipLines=1)
val y = inputMatrix(::, 0).toDenseVector
val X = inputMatrix(::, Seq(1,2,3,4,5)).copy.toDenseMatrix
val T = X.toDenseMatrix.t
val gram = (T * X)
val b:Transpose[DenseVector[Double]] = y.t * X
println(gram)
println(b.inner)
breeze.linalg.csvwrite(new java.io.File("grammatrix.csv"), gram)
val minimizer:QuadraticMinimizer = new QuadraticMinimizer(rank(gram), ProjectBox(lBounds,uBounds))
val coeffs = minimizer.minimize(gram, b.inner)
println(coeffs)
here's what the gram looks like:
279.0 628207.0 1461245.0 1024.0 729.5
628207.0 1.569309427E9 3.414471724E9 2449533.0 1755536.5
1461245.0 3.414471724E9 1.2324155401E10 5511816.0 3846583.0
1024.0 2449533.0 5511816.0 3980.0 2786.0
729.5 1755536.5 3846583.0 2786.0 2092.75
and the b vector is:
2.917264069193999E8, 7.294450468242601E11, 1.585917338779061E12, 1.131888709844E9, 8.260072757806E8
when I execute the code I get:
DenseVector(-12171.118011368422, -424.79971124882286, -9.565028484748783, 49.3827769217138, 49.536905925364195)
Which is below the lower bounds specified.
Could you please add the H (gram matrix) and y (linear term) as well so that I can test it out ? Also the initialize pattern is for advanced users (like Spark ALS for which I wrote the solver) but you can use the simple pattern as follows (I used your bounds):
val lb = DenseVector(Array(Double.NegativeInfinity, 5.0, 0.1, 50.0, 50.0))
val ub = DenseVector(Array(Double.PositiveInfinity, 500.0, 100.0, 99000.0, 99000.0))
val n = 5
val ata = new DenseMatrix[Double](5, 5,
Array(4.377, -3.531, -1.306, -0.139, 3.418,
-3.531, 4.344, 0.934, 0.305, -2.140,
-1.306, 0.934, 2.644, -0.203, -0.170,
-0.139, 0.305, -0.203, 5.883, 1.428,
3.418, -2.140, -0.170, 1.428, 4.684))
val atb = DenseVector(-1.632, 2.115, 1.094, -1.025, -0.636)
val qpSolverBounds = new QuadraticMinimizer(n, ProjectBox(lb, ub))
val result = qpSolverBounds.minimize(ata, atb)
println(s"Bounds test $result")
I am getting result as DenseVector(-33.02749751949581, 5.0, 0.1, 50.0, 50.0) which does not look non-sensical.
Please don't change the default maxIter since this control is given for flows where absolute convergence is not necessary. Let the solver choose the maxIter.