func RegularizerTest(t *testing.T, r Regularizer, name string, parameters []float64, trueLoss float64, trueDeriv []float64) {
// Test that Loss works
loss := r.Loss(parameters)
if math.Abs(loss-trueLoss) > 1e-14 {
t.Errorf("Loss doesn't match for case %v. Expected: %v, Found: %v", name, trueLoss, loss)
}
// Test that LossDeriv works
derivative := make([]float64, len(trueDeriv))
lossDeriv := r.LossDeriv(parameters, derivative)
if math.Abs(lossDeriv-trueLoss) > 1e-14 {
t.Errorf("Loss doesn't match from LossDeriv for case %v. Expected: %v, Found: %v", name, trueLoss, lossDeriv)
}
if !floats.EqualApprox(trueDeriv, derivative, 1e-14) {
t.Errorf("Derivative doesn't match from LossDeriv for case %v", name)
}
for i := range derivative {
derivative[i] = float64(i)
}
lossAddDeriv := r.LossAddDeriv(parameters, derivative)
if math.Abs(lossAddDeriv-trueLoss) > 1e-14 {
t.Errorf("Loss doesn't match from LossAddDeriv for case %v. Expected: %v, Found: %v", name, trueLoss, lossAddDeriv)
}
for i := range derivative {
derivative[i] -= float64(i)
}
if !floats.EqualApprox(trueDeriv, derivative, 1e-14) {
t.Errorf("Derivative doesn't match from LossAddDeriv for case %v", name)
}
}
func (s *S) TestVectorMul(c *check.C) {
for i, test := range []struct {
m int
n int
}{
{
m: 10,
n: 5,
},
{
m: 5,
n: 5,
},
{
m: 5,
n: 10,
},
} {
vData := make([]float64, test.n)
for i := range vData {
vData[i] = rand.Float64()
}
vDataCopy := make([]float64, test.n)
copy(vDataCopy, vData)
v := NewVector(test.n, vData)
aData := make([]float64, test.n*test.m)
for i := range aData {
aData[i] = rand.Float64()
}
a := NewDense(test.m, test.n, aData)
var v2 Vector
v2.MulVec(a, false, v)
var v2M Dense
v2M.Mul(a, v)
same := floats.EqualApprox(v2.mat.Data, v2M.mat.Data, 1e-14)
c.Check(same, check.Equals, true, check.Commentf("Test %d", i))
var aT Dense
aT.TCopy(a)
v2.MulVec(&aT, true, v)
same = floats.EqualApprox(v2.mat.Data, v2M.mat.Data, 1e-14)
c.Check(same, check.Equals, true, check.Commentf("Test %d", i))
/*
v.MulVec(&aT, true, v)
same = floats.EqualApprox(v.mat.Data, v2M.mat.Data, 1e-14)
c.Check(same, check.Equals, true, check.Commentf("Test %d", i))
*/
}
}
func TestLogSquared(t *testing.T) {
prediction := []float64{1, -2, 3}
truth := []float64{1.1, -2.2, 2.7}
trueloss := (math.Log(.1*.1+1) + math.Log(.2*.2+1) + math.Log(.3*.3+1)) / 3
derivative := []float64{0, 0, 0}
sq := LogSquared{}
loss := sq.Loss(prediction, truth)
if math.Abs(loss-trueloss) > TOL {
t.Errorf("loss doesn't match from Loss(). Expected %v, Found: %v", trueloss, loss)
}
loss = sq.LossDeriv(prediction, truth, derivative)
if math.Abs(loss-trueloss) > TOL {
t.Errorf("loss doesn't match from LossDeriv()")
}
derivative, fdDerivative := finiteDifferenceLosser(sq, prediction, truth)
if !floats.EqualApprox(derivative, fdDerivative, FDTol) {
t.Errorf("Derivative doesn't match. \n deriv: %v \n fdDeriv: %v ", derivative, fdDerivative)
}
err := common.InterfaceTestMarshalAndUnmarshal(sq)
if err != nil {
t.Errorf("Error marshaling and unmarshaling")
}
}
func TestRelativeLog(t *testing.T) {
tol := 1e-2
prediction := []float64{1, -2, 3}
truth := []float64{1.1, -2.2, 2.7}
trueloss := ((.1/(1.1+tol))*(.1/(1.1+tol)) + (.2/(2.2+tol))*(.2/(2.2+tol)) + (.3/(2.7+tol))*(.3/(2.7+tol))) / 3
trueloss = math.Log(trueloss + 1)
derivative := []float64{0, 0, 0}
sq := RelativeLog(tol)
loss := sq.Loss(prediction, truth)
if math.Abs(loss-trueloss) > TOL {
t.Errorf("loss doesn't match from Loss(). Expected %v, Found: %v", trueloss, loss)
}
loss = sq.LossDeriv(prediction, truth, derivative)
if math.Abs(loss-trueloss) > TOL {
t.Errorf("loss doesn't match from LossDeriv()")
}
derivative, fdDerivative := finiteDifferenceLosser(sq, prediction, truth)
if !floats.EqualApprox(derivative, fdDerivative, FDTol) {
t.Errorf("Derivative doesn't match. \n deriv: %v \n fdDeriv: %v ", derivative, fdDerivative)
}
err := common.InterfaceTestMarshalAndUnmarshal(sq)
if err != nil {
t.Errorf("Error marshaling and unmarshaling: " + err.Error())
}
}
func DrsclTest(t *testing.T, impl Drscler) {
for _, test := range []struct {
x []float64
a float64
}{
{
x: []float64{1, 2, 3, 4, 5},
a: 4,
},
{
x: []float64{1, 2, 3, 4, 5},
a: math.MaxFloat64,
},
{
x: []float64{1, 2, 3, 4, 5},
a: 1e-307,
},
} {
xcopy := make([]float64, len(test.x))
copy(xcopy, test.x)
// Cannot test the scaling directly because of floating point scaling issues
// (the purpose of Drscl). Instead, check that scaling and scaling back
// yeilds approximately x. If overflow or underflow occurs then the scaling
// won't match.
impl.Drscl(len(test.x), test.a, xcopy, 1)
if floats.Equal(xcopy, test.x) {
t.Errorf("x unchanged during call to drscl. a = %v, x = %v.", test.a, test.x)
}
impl.Drscl(len(test.x), 1/test.a, xcopy, 1)
if !floats.EqualApprox(xcopy, test.x, 1e-14) {
t.Errorf("x not equal after scaling and unscaling. a = %v, x = %v.", test.a, test.x)
}
}
}
func testDerivParam(t *testing.T, d derivParamTester) {
// Tests that the derivative matches for a number of different quantiles
// along the distribution.
nTest := 10
quantiles := make([]float64, nTest)
floats.Span(quantiles, 0.1, 0.9)
deriv := make([]float64, d.NumParameters())
fdDeriv := make([]float64, d.NumParameters())
initParams := d.parameters(nil)
init := make([]float64, d.NumParameters())
for i, v := range initParams {
init[i] = v.Value
}
for _, v := range quantiles {
d.setParameters(initParams)
x := d.Quantile(v)
d.DLogProbDParam(x, deriv)
f := func(p []float64) float64 {
params := d.parameters(nil)
for i, v := range p {
params[i].Value = v
}
d.setParameters(params)
return d.LogProb(x)
}
fd.Gradient(fdDeriv, f, init, nil)
if !floats.EqualApprox(deriv, fdDeriv, 1e-6) {
t.Fatal("Derivative mismatch. Want", fdDeriv, ", got", deriv, ".")
}
}
}
func TestPrivatePredictsMatch(t *testing.T) {
for i, test := range netIniters {
for j := 0; j < nRandSamp; j++ {
n := testNets[i]
input := make([]float64, test.inputDim)
floats.Fill(rand.NormFloat64, input)
outputSimple := make([]float64, test.outputDim)
floats.Fill(rand.NormFloat64, outputSimple)
outputCache := make([]float64, test.outputDim)
floats.Fill(rand.NormFloat64, outputCache)
// predict using uncached method
tmp1, tmp2 := newPredictMemory(n.neurons)
predict(input, n.neurons, n.parameters, tmp1, tmp2, outputSimple)
// predict using cached method
combinations := newPerNeuronMemory(n.neurons)
outputs := newPerNeuronMemory(n.neurons)
cachePredict(input, n.neurons, n.parameters, combinations, outputs, outputCache)
if !floats.EqualApprox(outputSimple, outputCache, 1e-14) {
t.Errorf("test %v: output mismatch between simple and cached predict. Simple: %v, Cached: %v", test.name, outputSimple, outputCache)
break
}
}
}
}
func DspmvTest(t *testing.T, blasser Dspmver) {
for i, test := range []struct {
ul blas.Uplo
n int
a [][]float64
x []float64
y []float64
alpha float64
beta float64
ans []float64
}{
{
ul: blas.Upper,
n: 3,
a: [][]float64{
{5, 6, 7},
{0, 8, 10},
{0, 0, 13},
},
x: []float64{3, 4, 5},
y: []float64{6, 7, 8},
alpha: 2.1,
beta: -3,
ans: []float64{137.4, 189, 240.6},
},
{
ul: blas.Lower,
n: 3,
a: [][]float64{
{5, 0, 0},
{6, 8, 0},
{7, 10, 13},
},
x: []float64{3, 4, 5},
y: []float64{6, 7, 8},
alpha: 2.1,
beta: -3,
ans: []float64{137.4, 189, 240.6},
},
} {
incTest := func(incX, incY, extra int) {
x := makeIncremented(test.x, incX, extra)
y := makeIncremented(test.y, incY, extra)
aFlat := flattenTriangular(test.a, test.ul)
ans := makeIncremented(test.ans, incY, extra)
blasser.Dspmv(test.ul, test.n, test.alpha, aFlat, x, incX, test.beta, y, incY)
if !floats.EqualApprox(ans, y, 1e-14) {
t.Errorf("Case %v, incX=%v, incY=%v: Want %v, got %v.", i, incX, incY, ans, y)
}
}
incTest(1, 1, 0)
incTest(2, 3, 0)
incTest(3, 2, 0)
incTest(-3, 2, 0)
incTest(-2, 4, 0)
incTest(2, -1, 0)
incTest(-3, -4, 3)
}
}
func Dlasv2Test(t *testing.T, impl Dlasv2er) {
rnd := rand.New(rand.NewSource(1))
for i := 0; i < 100; i++ {
f := rnd.NormFloat64()
g := rnd.NormFloat64()
h := rnd.NormFloat64()
ssmin, ssmax, snr, csr, snl, csl := impl.Dlasv2(f, g, h)
// tmp =
// [ csl snl] [f g]
// [-snl csl] [0 h]
tmp11 := csl * f
tmp12 := csl*g + snl*h
tmp21 := -snl * f
tmp22 := -snl*g + csl*h
// lhs =
// [tmp11 tmp12] [csr -snr]
// [tmp21 tmp22] [snr csr]
ans11 := tmp11*csr + tmp12*snr
ans12 := tmp11*-snr + tmp12*csr
ans21 := tmp21*csr + tmp22*snr
ans22 := tmp21*-snr + tmp22*csr
lhs := []float64{ans11, ans12, ans21, ans22}
rhs := []float64{ssmax, 0, 0, ssmin}
if !floats.EqualApprox(rhs, lhs, 1e-12) {
t.Errorf("SVD mismatch. f = %v, g = %v, h = %v.\nLHS: %v\nRHS: %v", f, g, h, lhs, rhs)
}
}
}
func testDpotf2(t *testing.T, impl Dpotf2er, testPos bool, a, ans [][]float64, stride int, ul blas.Uplo) {
aFlat := flattenTri(a, stride, ul)
ansFlat := flattenTri(ans, stride, ul)
pos := impl.Dpotf2(ul, len(a[0]), aFlat, stride)
if pos != testPos {
t.Errorf("Positive definite mismatch: Want %v, Got %v", testPos, pos)
return
}
if testPos && !floats.EqualApprox(ansFlat, aFlat, 1e-14) {
t.Errorf("Result mismatch: Want %v, Got %v", ansFlat, aFlat)
}
}
func TestNormRand(t *testing.T) {
for _, test := range []struct {
mean []float64
cov []float64
}{
{
mean: []float64{0, 0},
cov: []float64{
1, 0,
0, 1,
},
},
{
mean: []float64{0, 0},
cov: []float64{
1, 0.9,
0.9, 1,
},
},
{
mean: []float64{6, 7},
cov: []float64{
5, 0.9,
0.9, 2,
},
},
} {
dim := len(test.mean)
cov := mat64.NewSymDense(dim, test.cov)
n, ok := NewNormal(test.mean, cov, nil)
if !ok {
t.Errorf("bad covariance matrix")
}
nSamples := 1000000
samps := mat64.NewDense(nSamples, dim, nil)
for i := 0; i < nSamples; i++ {
n.Rand(samps.RawRowView(i))
}
estMean := make([]float64, dim)
for i := range estMean {
estMean[i] = stat.Mean(mat64.Col(nil, i, samps), nil)
}
if !floats.EqualApprox(estMean, test.mean, 1e-2) {
t.Errorf("Mean mismatch: want: %v, got %v", test.mean, estMean)
}
estCov := stat.CovarianceMatrix(nil, samps, nil)
if !mat64.EqualApprox(estCov, cov, 1e-2) {
t.Errorf("Cov mismatch: want: %v, got %v", cov, estCov)
}
}
}
func testLinear(t *testing.T, kind linearTest) {
u := &Linear{}
data := flatten(kind.data)
err := u.SetScale(data)
if err != nil {
if kind.eqDim != true {
t.Errorf("Error where there shouldn't be for case " + kind.name + ": " + err.Error())
}
}
if !floats.EqualApprox(u.Min, kind.min, 1e-14) {
t.Errorf("Min doesn't match for case " + kind.name)
}
if !floats.EqualApprox(u.Max, kind.max, 1e-14) {
t.Errorf("Max doesn't match for case " + kind.name)
}
scaledData := flatten(kind.scaledData)
testScaling(t, u, data, scaledData, kind.name)
u2 := &Linear{}
testGob(u, u2, t)
}
func denseEqualApprox(a *Dense, acomp matComp, tol float64) bool {
ar2, ac2 := a.Dims()
if ar2 != acomp.r {
return false
}
if ac2 != acomp.c {
return false
}
if !floats.EqualApprox(a.mat.Data, acomp.data, tol) {
return false
}
return true
}
func testNormal(t *testing.T, kind normalTest) {
u := &Normal{}
data := flatten(kind.data)
err := u.SetScale(data)
if err != nil {
if kind.eqDim != true {
t.Errorf("Error where there shouldn't be for case " + kind.name + ": " + err.Error())
}
}
if !floats.EqualApprox(u.Mu, kind.mu, 1e-14) {
t.Errorf("Mu doesn't match for case "+kind.name+". Expected: %v, Found: %v", kind.mu, u.Mu)
}
if !floats.EqualApprox(u.Sigma, kind.sigma, 1e-14) {
t.Errorf("Sigma doesn't match for case "+kind.name+". Expected: %v, Found: %v", kind.sigma, u.Sigma)
}
scaledData := flatten(kind.scaledData)
testScaling(t, u, data, scaledData, kind.name)
u2 := &Normal{}
testGob(u, u2, t)
}
func DorgqlTest(t *testing.T, impl Dorgqler) {
rnd := rand.New(rand.NewSource(1))
for _, test := range []struct {
m, n, k, lda int
}{
{5, 4, 3, 0},
{100, 100, 100, 0},
{200, 100, 50, 0},
{200, 200, 50, 0},
} {
m := test.m
n := test.n
k := test.k
lda := test.lda
if lda == 0 {
lda = n
}
a := make([]float64, m*lda)
for i := range a {
a[i] = rnd.NormFloat64()
}
tau := nanSlice(min(m, n))
work := nanSlice(max(m, n))
impl.Dgeql2(m, n, a, lda, tau, work)
aCopy := make([]float64, len(a))
copy(aCopy, a)
impl.Dorg2l(m, n, k, a, lda, tau, work)
ans := make([]float64, len(a))
copy(ans, a)
impl.Dorgql(m, n, k, a, lda, tau, work, -1)
work = make([]float64, int(work[0]))
copy(a, aCopy)
impl.Dorgql(m, n, k, a, lda, tau, work, len(work))
if !floats.EqualApprox(a, ans, 1e-8) {
t.Errorf("Answer mismatch. m = %v, n = %v, k = %v", m, n, k)
}
}
}
// TestDeriv uses finite difference to test that the prediction from Deriv
// is correct, and tests that computing the loss in parallel works properly
// Only does finite difference for the first nTest to save time
func TestDeriv(t *testing.T, trainable DerivTester, inputs, trueOutputs common.RowMatrix, name string) {
// Set the parameters to something random
trainable.RandomizeParameters()
// Compute the loss and derivative
losser := loss.SquaredDistance{}
regularizer := regularize.TwoNorm{}
batchGrad := train.NewBatchGradBased(trainable, true, inputs, trueOutputs, losser, regularizer)
derivative := make([]float64, trainable.NumParameters())
parameters := trainable.Parameters(nil)
// Don't need to check loss, because if predict is right and losser is right then loss must be correct
_ = batchGrad.ObjGrad(parameters, derivative)
fdDerivative := make([]float64, trainable.NumParameters())
wg := &sync.WaitGroup{}
wg.Add(trainable.NumParameters())
for i := 0; i < trainable.NumParameters(); i++ {
go func(i int) {
newParameters := make([]float64, trainable.NumParameters())
tmpDerivative := make([]float64, trainable.NumParameters())
copy(newParameters, parameters)
newParameters[i] += fdStep
loss1 := batchGrad.ObjGrad(newParameters, tmpDerivative)
newParameters[i] -= 2 * fdStep
loss2 := batchGrad.ObjGrad(newParameters, tmpDerivative)
newParameters[i] += fdStep
fdDerivative[i] = (loss1 - loss2) / (2 * fdStep)
wg.Done()
}(i)
}
wg.Wait()
if !floats.EqualApprox(derivative, fdDerivative, 1e-6) {
t.Errorf("%v: deriv doesn't match: Finite Difference: %v, Analytic: %v", name, fdDerivative, derivative)
}
}
func TestPredictFeaturized(t *testing.T) {
for _, test := range []struct {
z []float64
featureWeights [][]float64
output []float64
Name string
}{
{
Name: "General",
z: []float64{1, 2, 3},
featureWeights: [][]float64{
{3, 4},
{1, 2},
{0.5, 0.4},
},
output: []float64{6.5, 9.2},
},
} {
zCopy := make([]float64, len(test.z))
copy(zCopy, test.z)
fwMat := flatten(test.featureWeights)
fwMatCopy := &mat64.Dense{}
fwMatCopy.Clone(fwMat)
output := make([]float64, len(test.output))
predictFeaturized(zCopy, fwMat, output)
// Test that z wasn't changed
if !floats.Equal(test.z, zCopy) {
t.Errorf("z changed during call")
}
if !floats.EqualApprox(output, test.output, 1e-14) {
t.Errorf("output doesn't match for test %v. Expected %v, found %v", test.Name, test.output, output)
}
}
}
func TestManhattanDistance(t *testing.T) {
prediction := []float64{1, 2, 3}
truth := []float64{1.1, 2.2, 2.7}
trueloss := (.1 + .2 + .3) / 3
derivative := []float64{0, 0, 0}
sq := ManhattanDistance{}
loss := sq.Loss(prediction, truth)
if math.Abs(loss-trueloss) > TOL {
t.Errorf("loss doesn't match from Loss()")
}
loss = sq.LossDeriv(prediction, truth, derivative)
if math.Abs(loss-trueloss) > TOL {
t.Errorf("loss doesn't match from LossDeriv()")
}
derivative, fdDerivative := finiteDifferenceLosser(sq, prediction, truth)
if !floats.EqualApprox(derivative, fdDerivative, FDTol) {
t.Errorf("Derivative doesn't match. \n deriv: %v \n fdDeriv: %v ", derivative, fdDerivative)
}
err := common.InterfaceTestMarshalAndUnmarshal(sq)
if err != nil {
t.Errorf("Error marshaling and unmarshaling")
}
truth = []float64{1, 2, 3}
loss = sq.LossDeriv(prediction, truth, derivative)
if loss != 0 {
t.Errorf("Non-zero loss for equal pred and truth")
}
for _, val := range derivative {
if val != 0 {
t.Errorf("Non-zero derivative for equal pred and truth")
}
}
}
func DormbrTest(t *testing.T, impl Dormbrer) {
rnd := rand.New(rand.NewSource(1))
bi := blas64.Implementation()
for _, vect := range []lapack.DecompUpdate{lapack.ApplyQ, lapack.ApplyP} {
for _, side := range []blas.Side{blas.Left, blas.Right} {
for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
for _, test := range []struct {
m, n, k, lda, ldc int
}{
{3, 4, 5, 0, 0},
{3, 5, 4, 0, 0},
{4, 3, 5, 0, 0},
{4, 5, 3, 0, 0},
{5, 3, 4, 0, 0},
{5, 4, 3, 0, 0},
{3, 4, 5, 10, 12},
{3, 5, 4, 10, 12},
{4, 3, 5, 10, 12},
{4, 5, 3, 10, 12},
{5, 3, 4, 10, 12},
{5, 4, 3, 10, 12},
} {
m := test.m
n := test.n
k := test.k
ldc := test.ldc
if ldc == 0 {
ldc = n
}
nq := n
if side == blas.Left {
nq = m
}
// Compute a decomposition.
var ma, na int
var a []float64
if vect == lapack.ApplyQ {
ma = nq
na = k
} else {
ma = k
na = nq
}
lda := test.lda
if lda == 0 {
lda = na
}
a = make([]float64, ma*lda)
for i := range a {
a[i] = rnd.NormFloat64()
}
nTau := min(nq, k)
tauP := make([]float64, nTau)
tauQ := make([]float64, nTau)
d := make([]float64, nTau)
e := make([]float64, nTau)
lwork := -1
work := make([]float64, 1)
impl.Dgebrd(ma, na, a, lda, d, e, tauQ, tauP, work, lwork)
work = make([]float64, int(work[0]))
lwork = len(work)
impl.Dgebrd(ma, na, a, lda, d, e, tauQ, tauP, work, lwork)
// Apply and compare update.
c := make([]float64, m*ldc)
for i := range c {
c[i] = rnd.NormFloat64()
}
cCopy := make([]float64, len(c))
copy(cCopy, c)
if vect == lapack.ApplyQ {
impl.Dormbr(vect, side, trans, m, n, k, a, lda, tauQ, c, ldc, work, lwork)
} else {
impl.Dormbr(vect, side, trans, m, n, k, a, lda, tauP, c, ldc, work, lwork)
}
// Check that the multiplication was correct.
cOrig := blas64.General{
Rows: m,
Cols: n,
Stride: ldc,
Data: make([]float64, len(cCopy)),
}
copy(cOrig.Data, cCopy)
cAns := blas64.General{
Rows: m,
Cols: n,
Stride: ldc,
Data: make([]float64, len(cCopy)),
}
copy(cAns.Data, cCopy)
nb := min(ma, na)
var mulMat blas64.General
if vect == lapack.ApplyQ {
mulMat = constructQPBidiagonal(lapack.ApplyQ, ma, na, nb, a, lda, tauQ)
} else {
mulMat = constructQPBidiagonal(lapack.ApplyP, ma, na, nb, a, lda, tauP)
}
mulTrans := trans
if side == blas.Left {
bi.Dgemm(mulTrans, blas.NoTrans, m, n, m, 1, mulMat.Data, mulMat.Stride, cOrig.Data, cOrig.Stride, 0, cAns.Data, cAns.Stride)
} else {
bi.Dgemm(blas.NoTrans, mulTrans, m, n, n, 1, cOrig.Data, cOrig.Stride, mulMat.Data, mulMat.Stride, 0, cAns.Data, cAns.Stride)
}
if !floats.EqualApprox(cAns.Data, c, 1e-8) {
isApplyQ := vect == lapack.ApplyQ
isLeft := side == blas.Left
isTrans := trans == blas.Trans
t.Errorf("C mismatch. isApplyQ: %v, isLeft: %v, isTrans: %v, m = %v, n = %v, k = %v, lda = %v, ldc = %v",
isApplyQ, isLeft, isTrans, m, n, k, lda, ldc)
}
}
}
}
}
}
// testFunction checks that the function can evaluate itself (and its gradient)
// correctly.
func testFunction(f function, ftests []funcTest, t *testing.T) {
// Make a copy of tests because we may append to the slice.
tests := make([]funcTest, len(ftests))
copy(tests, ftests)
// Get information about the function.
fMinima, isMinimumer := f.(minimumer)
fGradient, isGradient := f.(gradient)
// If the function is a Minimumer, append its minima to the tests.
if isMinimumer {
for _, minimum := range fMinima.Minima() {
// Allocate gradient only if the function can evaluate it.
var grad []float64
if isGradient {
grad = make([]float64, len(minimum.X))
}
tests = append(tests, funcTest{
X: minimum.X,
F: minimum.F,
Gradient: grad,
})
}
}
for i, test := range tests {
F := f.Func(test.X)
// Check that the function value is as expected.
if math.Abs(F-test.F) > defaultTol {
t.Errorf("Test #%d: function value given by Func is incorrect. Want: %v, Got: %v",
i, test.F, F)
}
if test.Gradient == nil {
continue
}
// Evaluate the finite difference gradient.
fdGrad := fd.Gradient(nil, f.Func, test.X, nil)
// Check that the finite difference and expected gradients match.
if !floats.EqualApprox(fdGrad, test.Gradient, defaultFDGradTol) {
dist := floats.Distance(fdGrad, test.Gradient, math.Inf(1))
t.Errorf("Test #%d: numerical and expected gradients do not match. |fdGrad - WantGrad|_∞ = %v",
i, dist)
}
// If the function is a Gradient, check that it computes the gradient correctly.
if isGradient {
grad := make([]float64, len(test.Gradient))
fGradient.Grad(grad, test.X)
if !floats.EqualApprox(grad, test.Gradient, defaultGradTol) {
dist := floats.Distance(grad, test.Gradient, math.Inf(1))
t.Errorf("Test #%d: gradient given by Grad is incorrect. |grad - WantGrad|_∞ = %v",
i, dist)
}
}
}
}
func DsymmTest(t *testing.T, blasser Dsymmer) {
for i, test := range []struct {
m int
n int
side blas.Side
ul blas.Uplo
a [][]float64
b [][]float64
c [][]float64
alpha float64
beta float64
ans [][]float64
}{
{
side: blas.Left,
ul: blas.Upper,
m: 3,
n: 4,
a: [][]float64{
{2, 3, 4},
{0, 6, 7},
{0, 0, 10},
},
b: [][]float64{
{2, 3, 4, 8},
{5, 6, 7, 15},
{8, 9, 10, 20},
},
c: [][]float64{
{8, 12, 2, 1},
{9, 12, 9, 9},
{12, 1, -1, 5},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{126, 156, 144, 285},
{211, 252, 275, 535},
{282, 291, 327, 689},
},
},
{
side: blas.Left,
ul: blas.Upper,
m: 4,
n: 3,
a: [][]float64{
{2, 3, 4, 8},
{0, 6, 7, 9},
{0, 0, 10, 10},
{0, 0, 0, 11},
},
b: [][]float64{
{2, 3, 4},
{5, 6, 7},
{8, 9, 10},
{2, 1, 1},
},
c: [][]float64{
{8, 12, 2},
{9, 12, 9},
{12, 1, -1},
{1, 9, 5},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{158, 172, 160},
{247, 270, 293},
{322, 311, 347},
{329, 385, 427},
},
},
{
side: blas.Left,
ul: blas.Lower,
m: 3,
n: 4,
a: [][]float64{
{2, 0, 0},
{3, 6, 0},
{4, 7, 10},
},
b: [][]float64{
{2, 3, 4, 8},
{5, 6, 7, 15},
{8, 9, 10, 20},
},
c: [][]float64{
{8, 12, 2, 1},
{9, 12, 9, 9},
{12, 1, -1, 5},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{126, 156, 144, 285},
{211, 252, 275, 535},
{282, 291, 327, 689},
},
},
{
side: blas.Left,
ul: blas.Lower,
m: 4,
n: 3,
a: [][]float64{
{2, 0, 0, 0},
{3, 6, 0, 0},
{4, 7, 10, 0},
{8, 9, 10, 11},
},
b: [][]float64{
{2, 3, 4},
{5, 6, 7},
{8, 9, 10},
{2, 1, 1},
},
c: [][]float64{
{8, 12, 2},
{9, 12, 9},
{12, 1, -1},
{1, 9, 5},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{158, 172, 160},
{247, 270, 293},
{322, 311, 347},
{329, 385, 427},
},
},
{
side: blas.Right,
ul: blas.Upper,
m: 3,
n: 4,
a: [][]float64{
{2, 0, 0, 0},
{3, 6, 0, 0},
{4, 7, 10, 0},
{3, 4, 5, 6},
},
b: [][]float64{
{2, 3, 4, 9},
{5, 6, 7, -3},
{8, 9, 10, -2},
},
c: [][]float64{
{8, 12, 2, 10},
{9, 12, 9, 10},
{12, 1, -1, 10},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{32, 72, 86, 138},
{47, 108, 167, -6},
{68, 111, 197, 6},
},
},
{
side: blas.Right,
ul: blas.Upper,
m: 4,
n: 3,
a: [][]float64{
{2, 0, 0},
{3, 6, 0},
{4, 7, 10},
},
b: [][]float64{
{2, 3, 4},
{5, 6, 7},
{8, 9, 10},
{2, 1, 1},
},
c: [][]float64{
{8, 12, 2},
{9, 12, 9},
{12, 1, -1},
{1, 9, 5},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{32, 72, 86},
{47, 108, 167},
{68, 111, 197},
{11, 39, 35},
},
},
{
side: blas.Right,
ul: blas.Lower,
m: 3,
n: 4,
a: [][]float64{
{2, 0, 0, 0},
{3, 6, 0, 0},
{4, 7, 10, 0},
{3, 4, 5, 6},
},
b: [][]float64{
{2, 3, 4, 2},
{5, 6, 7, 1},
{8, 9, 10, 1},
},
c: [][]float64{
{8, 12, 2, 1},
{9, 12, 9, 9},
{12, 1, -1, 5},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{94, 156, 164, 103},
{145, 244, 301, 187},
{208, 307, 397, 247},
},
},
{
side: blas.Right,
ul: blas.Lower,
m: 4,
n: 3,
a: [][]float64{
{2, 0, 0},
{3, 6, 0},
{4, 7, 10},
},
b: [][]float64{
{2, 3, 4},
{5, 6, 7},
{8, 9, 10},
{2, 1, 1},
},
c: [][]float64{
{8, 12, 2},
{9, 12, 9},
{12, 1, -1},
{1, 9, 5},
},
alpha: 2,
beta: 3,
ans: [][]float64{
{82, 140, 144},
{139, 236, 291},
{202, 299, 387},
{25, 65, 65},
},
},
} {
aFlat := flatten(test.a)
bFlat := flatten(test.b)
cFlat := flatten(test.c)
ansFlat := flatten(test.ans)
blasser.Dsymm(test.side, test.ul, test.m, test.n, test.alpha, aFlat, len(test.a[0]), bFlat, test.n, test.beta, cFlat, test.n)
if !floats.EqualApprox(cFlat, ansFlat, 1e-14) {
t.Errorf("Case %v: Want %v, got %v.", i, ansFlat, cFlat)
}
}
}
func Dspr2Test(t *testing.T, blasser Dspr2er) {
for i, test := range []struct {
n int
a [][]float64
ul blas.Uplo
x []float64
y []float64
alpha float64
ans [][]float64
}{
{
n: 3,
a: [][]float64{
{7, 2, 4},
{0, 3, 5},
{0, 0, 6},
},
x: []float64{2, 3, 4},
y: []float64{5, 6, 7},
alpha: 2,
ul: blas.Upper,
ans: [][]float64{
{47, 56, 72},
{0, 75, 95},
{0, 0, 118},
},
},
{
n: 3,
a: [][]float64{
{7, 0, 0},
{2, 3, 0},
{4, 5, 6},
},
x: []float64{2, 3, 4},
y: []float64{5, 6, 7},
alpha: 2,
ul: blas.Lower,
ans: [][]float64{
{47, 0, 0},
{56, 75, 0},
{72, 95, 118},
},
},
} {
incTest := func(incX, incY, extra int) {
aFlat := flattenTriangular(test.a, test.ul)
x := makeIncremented(test.x, incX, extra)
y := makeIncremented(test.y, incY, extra)
blasser.Dspr2(test.ul, test.n, test.alpha, x, incX, y, incY, aFlat)
ansFlat := flattenTriangular(test.ans, test.ul)
if !floats.EqualApprox(aFlat, ansFlat, 1e-14) {
t.Errorf("Case %v, incX = %v, incY = %v. Want %v, got %v.", i, incX, incY, ansFlat, aFlat)
}
}
incTest(1, 1, 0)
incTest(-2, 1, 0)
incTest(-2, 3, 0)
incTest(2, -3, 0)
incTest(3, -2, 0)
incTest(-3, -4, 0)
}
}
func DlarfbTest(t *testing.T, impl Dlarfber) {
rnd := rand.New(rand.NewSource(1))
for _, store := range []lapack.StoreV{lapack.ColumnWise, lapack.RowWise} {
for _, direct := range []lapack.Direct{lapack.Forward, lapack.Backward} {
for _, side := range []blas.Side{blas.Left, blas.Right} {
for _, trans := range []blas.Transpose{blas.Trans, blas.NoTrans} {
for cas, test := range []struct {
ma, na, cdim, lda, ldt, ldc int
}{
{6, 6, 6, 0, 0, 0},
{6, 8, 10, 0, 0, 0},
{6, 10, 8, 0, 0, 0},
{8, 6, 10, 0, 0, 0},
{8, 10, 6, 0, 0, 0},
{10, 6, 8, 0, 0, 0},
{10, 8, 6, 0, 0, 0},
{6, 6, 6, 12, 15, 30},
{6, 8, 10, 12, 15, 30},
{6, 10, 8, 12, 15, 30},
{8, 6, 10, 12, 15, 30},
{8, 10, 6, 12, 15, 30},
{10, 6, 8, 12, 15, 30},
{10, 8, 6, 12, 15, 30},
{6, 6, 6, 15, 12, 30},
{6, 8, 10, 15, 12, 30},
{6, 10, 8, 15, 12, 30},
{8, 6, 10, 15, 12, 30},
{8, 10, 6, 15, 12, 30},
{10, 6, 8, 15, 12, 30},
{10, 8, 6, 15, 12, 30},
} {
// Generate a matrix for QR
ma := test.ma
na := test.na
lda := test.lda
if lda == 0 {
lda = na
}
a := make([]float64, ma*lda)
for i := 0; i < ma; i++ {
for j := 0; j < lda; j++ {
a[i*lda+j] = rnd.Float64()
}
}
k := min(ma, na)
// H is always ma x ma
var m, n, rowsWork int
switch {
default:
panic("not implemented")
case side == blas.Left:
m = test.ma
n = test.cdim
rowsWork = n
case side == blas.Right:
m = test.cdim
n = test.ma
rowsWork = m
}
// Use dgeqr2 to find the v vectors
tau := make([]float64, na)
work := make([]float64, na)
impl.Dgeqr2(ma, k, a, lda, tau, work)
// Correct the v vectors based on the direct and store
vMatTmp := extractVMat(ma, na, a, lda, lapack.Forward, lapack.ColumnWise)
vMat := constructVMat(vMatTmp, store, direct)
v := vMat.Data
ldv := vMat.Stride
// Use dlarft to find the t vector
ldt := test.ldt
if ldt == 0 {
ldt = k
}
tm := make([]float64, k*ldt)
impl.Dlarft(direct, store, ma, k, v, ldv, tau, tm, ldt)
// Generate c matrix
ldc := test.ldc
if ldc == 0 {
ldc = n
}
c := make([]float64, m*ldc)
for i := 0; i < m; i++ {
for j := 0; j < ldc; j++ {
c[i*ldc+j] = rnd.Float64()
}
}
cCopy := make([]float64, len(c))
copy(cCopy, c)
ldwork := k
work = make([]float64, rowsWork*k)
// Call Dlarfb with this information
impl.Dlarfb(side, trans, direct, store, m, n, k, v, ldv, tm, ldt, c, ldc, work, ldwork)
h := constructH(tau, vMat, store, direct)
cMat := blas64.General{
Rows: m,
Cols: n,
Stride: ldc,
Data: make([]float64, m*ldc),
}
copy(cMat.Data, cCopy)
ans := blas64.General{
Rows: m,
Cols: n,
Stride: ldc,
Data: make([]float64, m*ldc),
}
copy(ans.Data, cMat.Data)
switch {
default:
panic("not implemented")
case side == blas.Left && trans == blas.NoTrans:
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, h, cMat, 0, ans)
case side == blas.Left && trans == blas.Trans:
blas64.Gemm(blas.Trans, blas.NoTrans, 1, h, cMat, 0, ans)
case side == blas.Right && trans == blas.NoTrans:
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, cMat, h, 0, ans)
case side == blas.Right && trans == blas.Trans:
blas64.Gemm(blas.NoTrans, blas.Trans, 1, cMat, h, 0, ans)
}
if !floats.EqualApprox(ans.Data, c, 1e-14) {
t.Errorf("Cas %v mismatch. Want %v, got %v.", cas, ans.Data, c)
}
}
}
}
}
}
}
func Dgelq2Test(t *testing.T, impl Dgelq2er) {
for c, test := range []struct {
m, n, lda int
}{
{1, 1, 0},
{2, 2, 0},
{3, 2, 0},
{2, 3, 0},
{1, 12, 0},
{2, 6, 0},
{3, 4, 0},
{4, 3, 0},
{6, 2, 0},
{1, 12, 0},
{1, 1, 20},
{2, 2, 20},
{3, 2, 20},
{2, 3, 20},
{1, 12, 20},
{2, 6, 20},
{3, 4, 20},
{4, 3, 20},
{6, 2, 20},
{1, 12, 20},
} {
n := test.n
m := test.m
lda := test.lda
if lda == 0 {
lda = test.n
}
k := min(m, n)
tau := make([]float64, k)
for i := range tau {
tau[i] = rand.Float64()
}
work := make([]float64, m)
for i := range work {
work[i] = rand.Float64()
}
a := make([]float64, m*lda)
for i := 0; i < m*lda; i++ {
a[i] = rand.Float64()
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
impl.Dgelq2(m, n, a, lda, tau, work)
Q := constructQ("LQ", m, n, a, lda, tau)
// Check that Q is orthonormal
for i := 0; i < Q.Rows; i++ {
nrm := blas64.Nrm2(Q.Cols, blas64.Vector{Inc: 1, Data: Q.Data[i*Q.Stride:]})
if math.Abs(nrm-1) > 1e-14 {
t.Errorf("Q not normal. Norm is %v", nrm)
}
for j := 0; j < i; j++ {
dot := blas64.Dot(Q.Rows,
blas64.Vector{Inc: 1, Data: Q.Data[i*Q.Stride:]},
blas64.Vector{Inc: 1, Data: Q.Data[j*Q.Stride:]},
)
if math.Abs(dot) > 1e-14 {
t.Errorf("Q not orthogonal. Dot is %v", dot)
}
}
}
L := blas64.General{
Rows: m,
Cols: n,
Stride: n,
Data: make([]float64, m*n),
}
for i := 0; i < m; i++ {
for j := 0; j <= min(i, n-1); j++ {
L.Data[i*L.Stride+j] = a[i*lda+j]
}
}
ans := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, m*lda),
}
copy(ans.Data, aCopy)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, L, Q, 0, ans)
if !floats.EqualApprox(aCopy, ans.Data, 1e-14) {
t.Errorf("Case %v, LQ mismatch. Want %v, got %v.", c, aCopy, ans.Data)
}
}
}
// checkPLU checks that the PLU factorization contained in factorize matches
// the original matrix contained in original.
func checkPLU(t *testing.T, ok bool, m, n, lda int, ipiv []int, factorized, original []float64, tol float64, print bool) {
var hasZeroDiagonal bool
for i := 0; i < min(m, n); i++ {
if factorized[i*lda+i] == 0 {
hasZeroDiagonal = true
break
}
}
if hasZeroDiagonal && ok {
t.Error("Has a zero diagonal but returned ok")
}
if !hasZeroDiagonal && !ok {
t.Error("Non-zero diagonal but returned !ok")
}
// Check that the LU decomposition is correct.
mn := min(m, n)
l := make([]float64, m*mn)
ldl := mn
u := make([]float64, mn*n)
ldu := n
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
v := factorized[i*lda+j]
switch {
case i == j:
l[i*ldl+i] = 1
u[i*ldu+i] = v
case i > j:
l[i*ldl+j] = v
case i < j:
u[i*ldu+j] = v
}
}
}
LU := blas64.General{
Rows: m,
Cols: n,
Stride: n,
Data: make([]float64, m*n),
}
U := blas64.General{
Rows: mn,
Cols: n,
Stride: ldu,
Data: u,
}
L := blas64.General{
Rows: m,
Cols: mn,
Stride: ldl,
Data: l,
}
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, L, U, 0, LU)
p := make([]float64, m*m)
ldp := m
for i := 0; i < m; i++ {
p[i*ldp+i] = 1
}
for i := len(ipiv) - 1; i >= 0; i-- {
v := ipiv[i]
blas64.Swap(m, blas64.Vector{1, p[i*ldp:]}, blas64.Vector{1, p[v*ldp:]})
}
P := blas64.General{
Rows: m,
Cols: m,
Stride: m,
Data: p,
}
aComp := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, m*lda),
}
copy(aComp.Data, factorized)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, P, LU, 0, aComp)
if !floats.EqualApprox(aComp.Data, original, tol) {
if print {
t.Errorf("PLU multiplication does not match original matrix.\nWant: %v\nGot: %v", original, aComp.Data)
return
}
t.Error("PLU multiplication does not match original matrix.")
}
}
// TestPredict tests that predict returns the expected value, and that calling predict in parallel
// also works
func TestPredictAndBatch(t *testing.T, p Predictor, inputs, trueOutputs common.RowMatrix, name string) {
nSamples, inputDim := inputs.Dims()
if inputDim != p.InputDim() {
panic("input Dim doesn't match predictor input dim")
}
nOutSamples, outputDim := trueOutputs.Dims()
if outputDim != p.OutputDim() {
panic("outpuDim doesn't match predictor outputDim")
}
if nOutSamples != nSamples {
panic("inputs and outputs have different number of rows")
}
// First, test sequentially
for i := 0; i < nSamples; i++ {
trueOut := make([]float64, outputDim)
for j := 0; j < outputDim; j++ {
trueOut[j] = trueOutputs.At(i, j)
}
// Predict with nil
input := make([]float64, inputDim)
inputCpy := make([]float64, inputDim)
for j := 0; j < inputDim; j++ {
input[j] = inputs.At(i, j)
inputCpy[j] = inputs.At(i, j)
}
out1, err := p.Predict(input, nil)
if err != nil {
t.Errorf(name + ": Error predicting with nil output")
return
}
if !floats.Equal(input, inputCpy) {
t.Errorf("%v: input changed with nil input for row %v", name, i)
break
}
out2 := make([]float64, outputDim)
for j := 0; j < outputDim; j++ {
out2[j] = rand.NormFloat64()
}
_, err = p.Predict(input, out2)
if err != nil {
t.Errorf("%v: error predicting with non-nil input for row %v", name, i)
break
}
if !floats.Equal(input, inputCpy) {
t.Errorf("%v: input changed with non-nil input for row %v", name, i)
break
}
if !floats.Equal(out1, out2) {
t.Errorf(name + ": different answers with nil and non-nil predict ")
break
}
if !floats.EqualApprox(out1, trueOut, 1e-14) {
t.Errorf("%v: predicted output doesn't match for row %v. Expected %v, found %v", name, i, trueOut, out1)
break
}
}
// Check that predict errors with bad sized arguments
badOuput := make([]float64, outputDim+1)
input := make([]float64, inputDim)
for i := 0; i < inputDim; i++ {
input[i] = inputs.At(0, i)
}
output := make([]float64, outputDim)
for i := 0; i < outputDim; i++ {
output[i] = trueOutputs.At(0, i)
}
_, err := p.Predict(input, badOuput)
if err == nil {
t.Errorf("Predict did not throw an error with an output too large")
}
if outputDim > 1 {
badOuput := make([]float64, outputDim-1)
_, err := p.Predict(input, badOuput)
if err == nil {
t.Errorf("Predict did not throw an error with an output too small")
}
}
badInput := make([]float64, inputDim+1)
_, err = p.Predict(badInput, output)
if err == nil {
t.Errorf("Predict did not err when input is too large")
}
if inputDim > 1 {
badInput := make([]float64, inputDim-1)
_, err = p.Predict(badInput, output)
if err == nil {
t.Errorf("Predict did not err when input is too small")
}
}
// Now, test batch
// With non-nil
inputCpy := &mat64.Dense{}
inputCpy.Clone(inputs)
predOutput, err := p.PredictBatch(inputs, nil)
if err != nil {
t.Errorf("Error batch predicting: %v", err)
}
if !inputCpy.Equals(inputs) {
t.Errorf("Inputs changed during call to PredictBatch")
}
predOutputRows, predOutputCols := predOutput.Dims()
if predOutputRows != nSamples || predOutputCols != outputDim {
t.Errorf("Dimension mismatch after predictbatch with nil input")
}
outputs := mat64.NewDense(nSamples, outputDim, nil)
_, err = p.PredictBatch(inputs, outputs)
pd := predOutput.(*mat64.Dense)
if !pd.Equals(outputs) {
t.Errorf("Different outputs from predict batch with nil and non-nil")
}
badInputs := mat64.NewDense(nSamples, inputDim+1, nil)
_, err = p.PredictBatch(badInputs, outputs)
if err == nil {
t.Error("PredictBatch did not err when input dim too large")
}
badInputs = mat64.NewDense(nSamples+1, inputDim, nil)
_, err = p.PredictBatch(badInputs, outputs)
if err == nil {
t.Errorf("PredictBatch did not err with row mismatch")
}
badOuputs := mat64.NewDense(nSamples, outputDim+1, nil)
_, err = p.PredictBatch(inputs, badOuputs)
if err == nil {
t.Errorf("PredictBatch did not err with output dim too large")
}
}
// TestLinearsolveAndDeriv compares the optimal weights found from gradient-based optimization with those found
// from computing a linear solve
func TestLinearsolveAndDeriv(t *testing.T, linear train.LinearTrainable, inputs, trueOutputs common.RowMatrix, name string) {
// Compare with no weights
rows, cols := trueOutputs.Dims()
predOutLinear := mat64.NewDense(rows, cols, nil)
parametersLinearSolve := train.LinearSolve(linear, nil, inputs, trueOutputs, nil, nil)
linear.SetParameters(parametersLinearSolve)
linear.Predictor().PredictBatch(inputs, predOutLinear)
//fmt.Println("Pred out linear", predOutLinear)
linear.RandomizeParameters()
parameters := linear.Parameters(nil)
batch := train.NewBatchGradBased(linear, true, inputs, trueOutputs, nil, loss.SquaredDistance{}, regularize.None{})
problem := batch
settings := multivariate.DefaultSettings()
settings.GradAbsTol = 1e-11
//settings. = 0
result, err := multivariate.OptimizeGrad(problem, parameters, settings, nil)
if err != nil {
t.Errorf("Error training: %v", err)
}
parametersDeriv := result.Loc
deriv := make([]float64, linear.NumParameters())
loss1 := batch.ObjGrad(parametersDeriv, deriv)
linear.SetParameters(parametersDeriv)
predOutDeriv := mat64.NewDense(rows, cols, nil)
linear.Predictor().PredictBatch(inputs, predOutDeriv)
linear.RandomizeParameters()
init2 := linear.Parameters(nil)
batch2 := train.NewBatchGradBased(linear, true, inputs, trueOutputs, nil, loss.SquaredDistance{}, regularize.None{})
problem2 := batch2
result2, err := multivariate.OptimizeGrad(problem2, init2, settings, nil)
parametersDeriv2 := result2.Loc
//fmt.Println("starting deriv2 loss")
deriv2 := make([]float64, linear.NumParameters())
loss2 := batch2.ObjGrad(parametersDeriv2, deriv2)
//fmt.Println("starting derivlin loss")
derivlinear := make([]float64, linear.NumParameters())
lossLin := batch2.ObjGrad(parametersLinearSolve, derivlinear)
_ = loss1
_ = loss2
_ = lossLin
/*
fmt.Println("param deriv 1 =", parametersDeriv)
fmt.Println("param deriv2 =", parametersDeriv2)
fmt.Println("linear params =", parametersLinearSolve)
fmt.Println("deriv1 loss =", loss1)
fmt.Println("deriv2 loss =", loss2)
fmt.Println("lin loss =", lossLin)
fmt.Println("deriv =", deriv)
fmt.Println("deriv2 =", deriv2)
fmt.Println("linderiv =", derivlinear)
//fmt.Println("Pred out deriv", predOutDeriv)
*/
/*
for i := 0; i < rows; i++ {
fmt.Println(predOutLinear.RowView(i), predOutBatch.RowView(i))
}
*/
if !floats.EqualApprox(parametersLinearSolve, parametersDeriv, 1e-8) {
t.Errorf("Parameters don't match for gradient based and linear solve.")
//for i := range parametersDeriv {
// fmt.Printf("index %v: Deriv = %v, linsolve = %v, diff = %v\n", i, parametersDeriv[i], parametersLinearSolve[i], parametersDeriv[i]-parametersLinearSolve[i])
//}
}
}
func DlarfTest(t *testing.T, impl Dlarfer) {
for i, test := range []struct {
m, n, ldc int
incv, lastv int
lastr, lastc int
tau float64
}{
{
m: 3,
n: 2,
ldc: 2,
incv: 4,
lastv: 1,
lastr: 2,
lastc: 1,
tau: 2,
},
{
m: 2,
n: 3,
ldc: 3,
incv: 4,
lastv: 1,
lastr: 1,
lastc: 2,
tau: 2,
},
{
m: 2,
n: 3,
ldc: 3,
incv: 4,
lastv: 1,
lastr: 0,
lastc: 1,
tau: 2,
},
{
m: 2,
n: 3,
ldc: 3,
incv: 4,
lastv: 0,
lastr: 0,
lastc: 1,
tau: 2,
},
{
m: 10,
n: 10,
ldc: 10,
incv: 4,
lastv: 6,
lastr: 9,
lastc: 8,
tau: 2,
},
} {
// Construct a random matrix.
c := make([]float64, test.ldc*test.m)
for i := 0; i <= test.lastr; i++ {
for j := 0; j <= test.lastc; j++ {
c[i*test.ldc+j] = rand.Float64()
}
}
cCopy := make([]float64, len(c))
copy(cCopy, c)
cCopy2 := make([]float64, len(c))
copy(cCopy2, c)
// Test with side right.
sz := max(test.m, test.n) // so v works for both right and left side.
v := make([]float64, test.incv*sz+1)
// Fill with nonzero entries up until lastv.
for i := 0; i <= test.lastv; i++ {
v[i*test.incv] = rand.Float64()
}
// Construct h explicitly to compare.
h := make([]float64, test.n*test.n)
for i := 0; i < test.n; i++ {
h[i*test.n+i] = 1
}
hMat := blas64.General{
Rows: test.n,
Cols: test.n,
Stride: test.n,
Data: h,
}
vVec := blas64.Vector{
Inc: test.incv,
Data: v,
}
blas64.Ger(-test.tau, vVec, vVec, hMat)
// Apply multiplication (2nd copy is to avoid aliasing).
cMat := blas64.General{
Rows: test.m,
Cols: test.n,
Stride: test.ldc,
Data: cCopy,
}
cMat2 := blas64.General{
Rows: test.m,
Cols: test.n,
Stride: test.ldc,
Data: cCopy2,
}
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, cMat2, hMat, 0, cMat)
// cMat now stores the true answer. Compare with the function call.
work := make([]float64, sz)
impl.Dlarf(blas.Right, test.m, test.n, v, test.incv, test.tau, c, test.ldc, work)
if !floats.EqualApprox(c, cMat.Data, 1e-14) {
t.Errorf("Dlarf mismatch right, case %v. Want %v, got %v", i, cMat.Data, c)
}
// Test on the left side.
copy(c, cCopy2)
copy(cCopy, c)
// Construct h.
h = make([]float64, test.m*test.m)
for i := 0; i < test.m; i++ {
h[i*test.m+i] = 1
}
hMat = blas64.General{
Rows: test.m,
Cols: test.m,
Stride: test.m,
Data: h,
}
blas64.Ger(-test.tau, vVec, vVec, hMat)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hMat, cMat2, 0, cMat)
impl.Dlarf(blas.Left, test.m, test.n, v, test.incv, test.tau, c, test.ldc, work)
if !floats.EqualApprox(c, cMat.Data, 1e-14) {
t.Errorf("Dlarf mismatch left, case %v. Want %v, got %v", i, cMat.Data, c)
}
}
}
func DgeqrfTest(t *testing.T, impl Dgeqrfer) {
for c, test := range []struct {
m, n, lda int
}{
{10, 5, 0},
{5, 10, 0},
{10, 10, 0},
{300, 5, 0},
{3, 500, 0},
{200, 200, 0},
{300, 200, 0},
{204, 300, 0},
{1, 3000, 0},
{3000, 1, 0},
{10, 5, 20},
{5, 10, 20},
{10, 10, 20},
{300, 5, 400},
{3, 500, 600},
{200, 200, 300},
{300, 200, 300},
{204, 300, 400},
{1, 3000, 4000},
{3000, 1, 4000},
} {
m := test.m
n := test.n
lda := test.lda
if lda == 0 {
lda = test.n
}
a := make([]float64, m*lda)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
a[i*lda+j] = rand.Float64()
}
}
tau := make([]float64, n)
for i := 0; i < n; i++ {
tau[i] = rand.Float64()
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
ans := make([]float64, len(a))
copy(ans, a)
work := make([]float64, n)
// Compute unblocked QR.
impl.Dgeqr2(m, n, ans, lda, tau, work)
// Compute blocked QR with small work.
impl.Dgeqrf(m, n, a, lda, tau, work, len(work))
if !floats.EqualApprox(ans, a, 1e-14) {
t.Errorf("Case %v, mismatch small work.", c)
}
// Try the full length of work.
impl.Dgeqrf(m, n, a, lda, tau, work, -1)
lwork := int(work[0])
work = make([]float64, lwork)
copy(a, aCopy)
impl.Dgeqrf(m, n, a, lda, tau, work, lwork)
if !floats.EqualApprox(ans, a, 1e-12) {
t.Errorf("Case %v, mismatch large work.", c)
}
// Try a slightly smaller version of work to test blocking.
work = work[1:]
lwork--
copy(a, aCopy)
impl.Dgeqrf(m, n, a, lda, tau, work, lwork)
if !floats.EqualApprox(ans, a, 1e-12) {
t.Errorf("Case %v, mismatch large work.", c)
}
}
}
func TestGradient(t *testing.T) {
for i, test := range []struct {
nDim int
tol float64
method Method
}{
{
nDim: 2,
tol: 2e-4,
method: Forward,
},
{
nDim: 2,
tol: 1e-6,
method: Central,
},
{
nDim: 40,
tol: 2e-4,
method: Forward,
},
{
nDim: 40,
tol: 1e-6,
method: Central,
},
} {
x := make([]float64, test.nDim)
for i := range x {
x[i] = rand.Float64()
}
xcopy := make([]float64, len(x))
copy(xcopy, x)
r := Rosenbrock{len(x)}
trueGradient := make([]float64, len(x))
r.FDf(x, trueGradient)
settings := DefaultSettings()
settings.Method = test.method
// try with gradient nil
gradient := Gradient(nil, r.F, x, settings)
if !floats.EqualApprox(gradient, trueGradient, test.tol) {
t.Errorf("Case %v: gradient mismatch in serial with nil. Want: %v, Got: %v.", i, trueGradient, gradient)
}
if !floats.Equal(x, xcopy) {
t.Errorf("Case %v: x modified during call to gradient in serial with nil.", i)
}
for i := range gradient {
gradient[i] = rand.Float64()
}
Gradient(gradient, r.F, x, settings)
if !floats.EqualApprox(gradient, trueGradient, test.tol) {
t.Errorf("Case %v: gradient mismatch in serial. Want: %v, Got: %v.", i, trueGradient, gradient)
}
if !floats.Equal(x, xcopy) {
t.Errorf("Case %v: x modified during call to gradient in serial with non-nil.", i)
}
// Try with known value
for i := range gradient {
gradient[i] = rand.Float64()
}
settings.OriginKnown = true
settings.OriginValue = r.F(x)
Gradient(gradient, r.F, x, settings)
if !floats.EqualApprox(gradient, trueGradient, test.tol) {
t.Errorf("Case %v: gradient mismatch with known origin in serial. Want: %v, Got: %v.", i, trueGradient, gradient)
}
// Concurrently
for i := range gradient {
gradient[i] = rand.Float64()
}
settings.Concurrent = true
settings.OriginKnown = false
settings.Workers = 1000
Gradient(gradient, r.F, x, settings)
if !floats.EqualApprox(gradient, trueGradient, test.tol) {
t.Errorf("Case %v: gradient mismatch with unknown origin in parallel. Want: %v, Got: %v.", i, trueGradient, gradient)
}
if !floats.Equal(x, xcopy) {
t.Errorf("Case %v: x modified during call to gradient in parallel", i)
}
// Concurrently with origin known
for i := range gradient {
gradient[i] = rand.Float64()
}
settings.OriginKnown = true
Gradient(gradient, r.F, x, settings)
if !floats.EqualApprox(gradient, trueGradient, test.tol) {
t.Errorf("Case %v: gradient mismatch with known origin in parallel. Want: %v, Got: %v.", i, trueGradient, gradient)
}
// With default settings
for i := range gradient {
gradient[i] = rand.Float64()
}
settings = nil
Gradient(gradient, r.F, x, settings)
if !floats.EqualApprox(gradient, trueGradient, test.tol) {
t.Errorf("Case %v: gradient mismatch with default settings. Want: %v, Got: %v.", i, trueGradient, gradient)
}
}
}