func showLU(a *mat.DenseMatrix) {
fmt.Printf("\na:\n%v\n", a)
l, u, p := a.LU()
fmt.Printf("l:\n%v\n", l)
fmt.Printf("u:\n%v\n", u)
fmt.Printf("p:\n%v\n", p)
}
func demo(m *mat.DenseMatrix) {
fmt.Println("A:")
fmt.Println(m)
l, err := m.Cholesky()
if err != nil {
fmt.Println(err)
return
}
fmt.Println("L:")
fmt.Println(l)
}
func MatrixNormal(M, Omega, Sigma *mx.DenseMatrix) func() (X *mx.DenseMatrix) {
checkMatrixNormal(M, Omega, Sigma)
Mv := mx.Vectorize(M)
Cov := mx.Kronecker(Omega, Sigma)
normal := MVNormal(Mv, Cov)
return func() (X *mx.DenseMatrix) {
Xv := normal()
X = mx.Unvectorize(Xv, M.Rows(), M.Cols())
return
}
}
func getNextLocations(piece byte, allMoves *matrix.DenseMatrix, ellipse *matrix.DenseMatrix, baseNode *node.Node) []*node.Node {
result := make([]*node.Node, 0, 20)
x := baseNode.GetX()
y := baseNode.GetY()
next := baseNode.GetStep() + 1
// Start with the single move board
var singleMove *matrix.DenseMatrix
switch piece {
case Pawn:
singleMove = singlePawnMove
case Rook:
singleMove = singleRookMove
case Knight:
singleMove = singleKnightMove
case Bishop:
singleMove = singleBishopMove
case Queen:
singleMove = singleQueenMove
case King:
singleMove = singleKingMove
case Puppy:
singleMove = singlePuppyMove
}
singleMove = shiftMatrix(singleMove, x-8, y-8)
singleMove = singleMove.GetMatrix(7, 0, 8, 8)
// fmt.Println("(", x, ", ", y, ")")
// fmt.Println("Single Move: \n", singleMove)
// fmt.Println("\nAll Moves: \n", allMoves)
// fmt.Println("\nEllipse: ", ellipse)
for i := 0; i < 8; i++ {
for j := 0; j < 8; j++ {
// fmt.Println("(", i+1, ", ", 8-j, ") : single: ", singleMove.Get(j, i), "ellipse: ", ellipse.Get(j, i), "all: ", allMoves.Get(j, i))
if singleMove.Get(j, i) != 0 && ellipse.Get(j, i) != 0 && allMoves.Get(j, i) == float64(next) {
// fmt.Println("New Child Node: (", i+1, ", ", 8-j, ")")
var newNode *node.Node
newNode = new(node.Node)
newNode.SetX(i + 1)
newNode.SetY(8 - j)
newNode.SetStep(next)
baseNode.AddChild(newNode)
result = append(result, newNode)
}
}
}
return result
}
func Wishart(n int, V *m.DenseMatrix) func() *m.DenseMatrix {
p := V.Rows()
zeros := m.Zeros(p, 1)
rowGen := MVNormal(zeros, V)
return func() *m.DenseMatrix {
x := make([][]float64, n)
for i := 0; i < n; i++ {
x[i] = rowGen().Array()
}
X := m.MakeDenseMatrixStacked(x)
S, _ := X.Transpose().TimesDense(X)
return S
}
}
//Computes the Euclidean distance between two vectors.
func (KNN *KNNClassifier) ComputeDistance(vector *mat.DenseMatrix, testrow *mat.DenseMatrix) float64 {
var sum float64
difference, err := testrow.MinusDense(vector)
flat := difference.Array()
if err != nil {
fmt.Println(err)
}
for _, i := range flat {
squared := math.Pow(i, 2)
sum += squared
}
eucdistance := math.Sqrt(sum)
return eucdistance
}
func addMovesToBoard(current *matrix.DenseMatrix, newMoves *matrix.DenseMatrix, steps int) *matrix.DenseMatrix {
// fmt.Println("New Moves: \n", newMoves.String())
result := current
for i := 0; i < 15; i++ {
for j := 0; j < 15; j++ {
if newMoves.Get(i, j) != 0 && result.Get(i, j) == float64(0) {
// fmt.Println(" Adding ", steps, " to (", i, ", ", j, ")")
// if HoleBoard.Get(i, j) > 0 {
// result.Set(i, j, 500)
// } else {
result.Set(i, j, float64(steps))
// }
}
}
}
return result
}
func calculate_even_fib_until(limit int64) (m []float64) {
if limit <= 2 { // base case: This cannot be determined by the recurrence relation
m = []float64{2, 0}
return
}
done := false
var a, b, c *matrix.DenseMatrix
a = relation_mat // a holds older b before multiplication
b = relation_mat // b holds result of matrix multiplication
c = relation_mat // c holds matrix that is to be multiplied in current iteration
dict[float64(1)] = relation_mat
for !done {
a = b
b, _ = b.TimesDense(c)
t, _ := b.TimesDense(init_mat) // calculate resultant vector for a certain power of a matrix
if t.ColCopy(0)[1] < float64(limit) {
if pow[1] == -1 { // pow[1] = -1 means we are exponentiating the matrix (first mode).
pow[0] = 2 * pow[0]
c = b
dict[pow[0]] = b
} else {
pow[0] = math.Ceil((pow[1] + pow[0]) / float64(2))
c = dict[math.Ceil((pow[1]-pow[0])/float64(2))]
}
} else {
if pow[1] == -1 {
pow[1] = pow[0]
pow[0] = pow[0] / 2
dict[pow[1]] = b
if pow[1]-pow[0] < 2 {
c = dict[float64(1)]
} else {
c = dict[math.Ceil((pow[1]-pow[0])/float64(2))]
}
b = a
} else {
pow[1] = math.Ceil((pow[1] + pow[0]) / float64(2))
c = dict[math.Ceil((pow[1]-pow[0])/float64(2))]
b = a
}
}
t, _ = b.TimesDense(init_mat)
if pow[1] != -1 && t.ColCopy(0)[1] < float64(limit) && t.ColCopy(0)[0] >= float64(limit) {
done = true
m = t.ColCopy(0)
}
}
return
}
func Wishart_PDF(n int, V *m.DenseMatrix) func(W *m.DenseMatrix) float64 {
p := V.Rows()
Vdet := V.Det()
Vinv, _ := V.Inverse()
normalization := pow(2, -0.5*float64(n*p)) *
pow(Vdet, -0.5*float64(n)) /
Γ(0.5*float64(n))
return func(W *m.DenseMatrix) float64 {
VinvW, _ := Vinv.Times(W)
return normalization * pow(W.Det(), 0.5*float64(n-p-1)) *
exp(-0.5*VinvW.Trace())
}
}
func Wishart_LnPDF(n int, V *m.DenseMatrix) func(W *m.DenseMatrix) float64 {
p := V.Rows()
Vdet := V.Det()
Vinv, _ := V.Inverse()
normalization := log(2)*(-0.5*float64(n*p)) +
log(Vdet)*(-0.5*float64(n)) -
LnΓ(0.5*float64(n))
return func(W *m.DenseMatrix) float64 {
VinvW, _ := Vinv.Times(W)
return normalization +
log(W.Det())*0.5*float64(n-p-1) -
0.5*VinvW.Trace()
}
}
func MatrixT(M, Omega, Sigma *mx.DenseMatrix, n int) func() (T *mx.DenseMatrix) {
checkMatrixT(M, Omega, Sigma, n)
fmt.Println("M:", M)
fmt.Println("Sigma:", Sigma)
fmt.Println("Omega:", Omega)
p := M.Rows()
m := M.Cols()
OmegaInv, err := Omega.Inverse()
if err != nil {
panic(err)
}
Sdist := Wishart(n+p-1, OmegaInv)
Xdist := MatrixNormal(mx.Zeros(p, m), mx.Eye(p), Sigma)
return func() (T *mx.DenseMatrix) {
S := Sdist()
Sinv, err := S.Inverse()
if err != nil {
panic(err)
}
Sinvc, err := Sinv.Cholesky()
if err != nil {
panic(err)
}
X := Xdist()
fmt.Println("Sinvc:", Sinvc)
fmt.Println("X:", X)
T, err = Sinvc.Transpose().TimesDense(X)
if err != nil {
panic(err)
}
err = T.AddDense(M)
if err != nil {
panic(err)
}
return
}
}
func (this *KnownVarianceLRPosterior) Remove(x, y *mx.DenseMatrix) {
xxt, _ := x.TimesDense(x.Transpose())
this.XXt.Subtract(xxt)
yxt, _ := y.TimesDense(x.Transpose())
this.YXt.Subtract(yxt)
}
func (this *KnownVarianceLRPosterior) Insert(x, y *mx.DenseMatrix) {
xxt, _ := x.TimesDense(x.Transpose())
this.XXt.Add(xxt)
yxt, _ := y.TimesDense(x.Transpose())
this.YXt.Add(yxt)
}
/*
M is r x c, o x i
Sigma is r x r, o x o
Phi is c x c, i x i
Sigma matches Y o x 1 output dimension
Phi matches X i x 1 input dimension
*/
func NewKnownVarianceLRPosterior(M, Sigma, Phi *mx.DenseMatrix) (this *KnownVarianceLRPosterior) {
if M.Rows() != Sigma.Rows() {
panic("M.Rows != Sigma.Rows")
}
if M.Cols() != Phi.Cols() {
panic("M.Cols != Phi.Cols")
}
if Sigma.Rows() != Sigma.Cols() {
panic("Sigma is not square")
}
if Phi.Rows() != Phi.Cols() {
panic("Phi is not square")
}
this = &KnownVarianceLRPosterior{
M: M,
Sigma: Sigma,
Phi: Phi,
XXt: mx.Zeros(Phi.Cols(), Phi.Cols()),
YXt: mx.Zeros(Sigma.Cols(), Phi.Cols()),
}
return
}
/*
If Y ~ N(AX, Sigma, I)
and A ~ N(M, Sigma, Phi)
this returns a sampler for P(A|X,Y,Sigma,M,Phi)
*/
func KnownVariancePosterior(Y, X, Sigma, M, Phi *mx.DenseMatrix) func() (A *mx.DenseMatrix) {
o := Y.Rows()
i := X.Rows()
n := Y.Cols()
if n != X.Cols() {
panic("X and Y don't have the same number of columns")
}
if o != M.Rows() {
panic("Y.Rows != M.Rows")
}
if i != M.Cols() {
panic("Y.Rows != M.Cols")
}
if o != Sigma.Rows() {
panic("Y.Rows != Sigma.Rows")
}
if Sigma.Cols() != Sigma.Rows() {
panic("Sigma is not square")
}
if i != Phi.Rows() {
panic("X.Rows != Phi.Rows")
}
if Phi.Cols() != Phi.Rows() {
panic("Phi is not square")
}
Xt := X.Transpose()
PhiInv, err := Phi.Inverse()
if err != nil {
panic(err)
}
XXt, err := X.TimesDense(Xt)
if err != nil {
panic(err)
}
XXtpPhiInv, err := XXt.PlusDense(PhiInv)
if err != nil {
panic(err)
}
Omega, err := XXtpPhiInv.Inverse()
if err != nil {
panic(err)
}
YXtpMPhiInv, err := Y.TimesDense(Xt)
if err != nil {
panic(err)
}
MPhiInv, err := M.TimesDense(PhiInv)
if err != nil {
panic(err)
}
err = YXtpMPhiInv.AddDense(MPhiInv)
if err != nil {
panic(err)
}
Mxy, err := YXtpMPhiInv.TimesDense(Omega)
if err != nil {
panic(err)
}
if false {
fmt.Printf("Mxy:\n%v\n", Mxy)
fmt.Printf("Sigma:\n%v\n", Sigma)
fmt.Printf("Omega:\n%v\n", Omega)
}
return dst.MatrixNormal(Mxy, Sigma, Omega)
}
func MatrixTLnPDF(M, Omega, Sigma *mx.DenseMatrix, n int) func(T *mx.DenseMatrix) (ll float64) {
checkMatrixT(M, Omega, Sigma, n)
nf := float64(n)
p := M.Rows()
pf := float64(p)
m := M.Cols()
mf := float64(m)
var norm float64 = 0
norm += logΓpr(p, 0.5*(nf+mf+pf-1), 0.5*(nf+pf-1))
norm += pow(π, -0.5*mf*pf)
norm += pow(Omega.Det(), -0.5*mf)
norm += pow(Sigma.Det(), -0.5*pf)
SigmaInv, err := Sigma.Inverse()
if err != nil {
panic(err)
}
OmegaInv, err := Omega.Inverse()
if err != nil {
panic(err)
}
return func(T *mx.DenseMatrix) (ll float64) {
ll = norm
diff, err := T.MinusDense(M)
if err != nil {
panic(err)
}
inner := OmegaInv.Copy()
inner, _ = inner.TimesDense(diff)
inner, _ = inner.TimesDense(SigmaInv)
inner, _ = inner.TimesDense(diff.Transpose())
ll += log(inner.Det()) * -0.5 * (nf + mf + pf - 1)
return
}
}
func GenerateMoveBoard(piece byte, x int, y int) *matrix.DenseMatrix {
var singleMove *matrix.DenseMatrix
var result *matrix.DenseMatrix
// Start with the single move board
switch piece {
case Pawn:
singleMove = singlePawnMove
case Rook:
singleMove = singleRookMove
case Knight:
singleMove = singleKnightMove
case Bishop:
singleMove = singleBishopMove
case Queen:
singleMove = singleQueenMove
case King:
singleMove = singleKingMove
case Puppy:
singleMove = singlePuppyMove
}
result = shiftMatrix(singleMove, x-8, y-8)
for i := 0; i < 15; i++ {
for j := 0; j < 15; j++ {
if HoleBoard.Get(j, i) > float64(0) {
result.Set(j, i, 500)
}
}
}
// fmt.Println(HoleBoard.String())
// Get the secondary moves
for n := 1; n < 20; n++ {
// fmt.Println("Current State: \n", result.String())
for i := 0; i < 15; i++ {
for j := 0; j < 15; j++ {
// Check if the current position needs to generate it's child moves
if result.Get(i, j) == float64(n) {
// Shift the single move matrix
// fmt.Println("Generating moves from position (", j, ", ", i, ") as ", n)
result = addMovesToBoard(result, shiftMatrix(singleMove, j-7, 15-(i+8)), n+1)
}
}
}
}
// Remove the -1
for i := 0; i < 15; i++ {
for j := 0; j < 15; j++ {
// Check if the current position needs to generate it's child moves
if result.Get(i, j) == float64(-1) {
result.Set(i, j, 0)
}
}
}
// fmt.Println(result.String())
result = result.GetMatrix(7, 0, 8, 8)
// for i := 0; i < 8; i++ {
// for j := 0; j < 8; j++ {
// if HoleBoard.Get(i, j) == 1 {
// result.Set(j, i, 500)
// }
// }
// }
return result
}
func MatrixT_PDF(M, Omega, Sigma *mx.DenseMatrix, n int) func(T *mx.DenseMatrix) (l float64) {
checkMatrixT(M, Omega, Sigma, n)
nf := float64(n)
p := M.Rows()
pf := float64(p)
m := M.Cols()
mf := float64(m)
var norm float64 = 1
norm *= GammaPRatio(p, 0.5*(nf+mf+pf-1), 0.5*(nf+pf-1))
norm *= math.Pow(math.Pi, -0.5*mf*pf)
norm *= math.Pow(Omega.Det(), -0.5*mf)
norm *= math.Pow(Sigma.Det(), -0.5*pf)
SigmaInv, err := Sigma.Inverse()
if err != nil {
panic(err)
}
OmegaInv, err := Omega.Inverse()
if err != nil {
panic(err)
}
return func(T *mx.DenseMatrix) (l float64) {
l = norm
diff, err := T.MinusDense(M)
if err != nil {
panic(err)
}
inner := OmegaInv.Copy()
inner, _ = inner.TimesDense(diff)
inner, _ = inner.TimesDense(SigmaInv)
inner, _ = inner.TimesDense(diff.Transpose())
l *= math.Pow(inner.Det(), -0.5*(nf+mf+pf-1))
return
}
}
func checkMatrixNormal(M, Omega, Sigma *mx.DenseMatrix) {
p := M.Rows()
m := M.Cols()
if Omega.Rows() != p {
panic(fmt.Sprintf("Omega.Rows != M.Rows, %d != %d", Omega.Rows(), p))
}
if Omega.Cols() != Omega.Rows() {
panic("Omega is not square")
}
if Sigma.Rows() != m {
panic(fmt.Sprintf("Sigma.Cols != M.Cols, %d != %d", Sigma.Cols(), m))
}
if Sigma.Cols() != Sigma.Rows() {
panic("Sigma is not square")
}
}
func MatrixNormal_LnPDF(M, Omega, Sigma *mx.DenseMatrix) func(A *mx.DenseMatrix) float64 {
checkMatrixNormal(M, Omega, Sigma)
pf := float64(M.Rows())
mf := float64(M.Cols())
sinv, err := Sigma.Inverse()
if err != nil {
panic(err)
}
oinv, err := Omega.Inverse()
if err != nil {
panic(err)
}
norm := (2 * math.Pi) * (-0.5 * mf * pf)
norm += Omega.Det() * (-0.5 * mf)
norm += Sigma.Det() * (-0.5 * pf)
return func(X *mx.DenseMatrix) (lp float64) {
lp = norm
diff, err := X.MinusDense(M)
if err != nil {
panic(err)
}
inner := oinv
inner, err = inner.TimesDense(diff.Transpose())
if err != nil {
panic(err)
}
inner, err = inner.TimesDense(sinv)
if err != nil {
panic(err)
}
inner, err = inner.TimesDense(diff)
if err != nil {
panic(err)
}
innerTrace := inner.Trace()
lp += -0.5 * innerTrace
return
}
}
/*
M is the mean, Omega is the row covariance, Sigma is the column covariance.
*/
func MatrixNormal_PDF(M, Omega, Sigma *mx.DenseMatrix) func(A *mx.DenseMatrix) float64 {
checkMatrixNormal(M, Omega, Sigma)
pf := float64(M.Rows())
mf := float64(M.Cols())
norm := math.Pow(2*math.Pi, -0.5*mf*pf)
norm *= math.Pow(Omega.Det(), -0.5*mf)
norm *= math.Pow(Sigma.Det(), -0.5*pf)
return func(X *mx.DenseMatrix) (p float64) {
p = norm
sinv, err := Sigma.Inverse()
if err != nil {
panic(err)
}
oinv, err := Omega.Inverse()
if err != nil {
panic(err)
}
diff, err := X.MinusDense(M)
if err != nil {
panic(err)
}
inner := oinv
inner, err = inner.TimesDense(diff.Transpose())
if err != nil {
panic(err)
}
inner, err = inner.TimesDense(sinv)
if err != nil {
panic(err)
}
inner, err = inner.TimesDense(diff)
if err != nil {
panic(err)
}
innerTrace := inner.Trace()
p *= math.Exp(-0.5 * innerTrace)
return
}
}