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 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
}
}
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()
}
}
/*
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
}
}
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 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 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
}
}
/*
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)
}