52 lines
1.6 KiB
Go
52 lines
1.6 KiB
Go
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package optim
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import (
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"math"
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"testing"
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"sourcedock.dev/petrbalvin/tensor/internal/core"
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)
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// A residual linear in the parameters makes one Gauss-Newton step the
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// exact answer: the normal equations solve to the least-squares
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// solution in a single iteration, so the fit's first step must land on
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// it. Every off-diagonal entry of the three-parameter normal matrix is
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// load-bearing there; a step computed from an asymmetric matrix lands
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// somewhere else.
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func TestLevenbergMarquardtSingleStepExactQuadratic(t *testing.T) {
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// A is 12x3, well conditioned, nothing symmetric in its columns.
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A := [][]float64{
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{1, 0.5, -0.25}, {2, -1, 0.75}, {-0.5, 1.5, 2}, {0.25, -0.75, 1},
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{1.5, 2, -1}, {-2, 0.25, 0.5}, {0.75, -2, 1.5}, {1, 1, 1},
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{-1, 0.5, 2}, {0.5, 2, -0.5}, {2, 1, -2}, {-0.25, -1.5, 0.25},
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}
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truth := []float64{1.5, -0.75, 2.25}
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y := make([]float64, len(A))
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for r := range A {
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y[r] = A[r][0]*truth[0] + A[r][1]*truth[1] + A[r][2]*truth[2]
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}
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residual := func(p *core.Array) (*core.Array, error) {
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pv := p.RawFloats()
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out := make([]float64, len(A))
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for r := range A {
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out[r] = A[r][0]*pv[0] + A[r][1]*pv[1] + A[r][2]*pv[2] - y[r]
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}
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return core.FromFloats(out, len(A))
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}
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p0, err := core.FromFloats([]float64{0, 0, 0}, 3)
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if err != nil {
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t.Fatal(err)
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}
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opts := LMOptions{MaxIterations: 8}
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pFit, _, err := LevenbergMarquardt(residual, p0, opts)
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if err != nil {
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t.Fatal(err)
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}
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got := pFit.RawFloats()
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for k := range truth {
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if math.Abs(got[k]-truth[k]) > 1e-9 {
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t.Fatalf("parameter %d: the fit answered %g, the exact single step is %g", k, got[k], truth[k])
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}
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}
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}
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