/*
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 stat.MatrixNormal(Mxy, Sigma, Omega)
}