[hts-users:00761] Re: HGenS and WUW matrix

[Junichi Yamagishi <jyamagis@xxxxxxxxxxxx>]

Hi,

According to the comments from Toda-san,
the C is not a matrix but a vector.

Thanks,
Junichi


On 2007/08/02, at 10:55, Alexander Gutkin wrote:

> Hi,
>
> On 8/1/07, Tomoki Toda <tomoki@xxxxxxxxxxx> wrote:
> > Hi,
> >
> > >   I have a question regarding HTS internals (either HGenS or mlpg
> > > code in hts_engine). From what I am seeing the W^{T}U^{-1}W  
> > > matrix is
> > > stored as TxWidth, while the parameter matrix C is TxD, where D  
> > > is the
> > > order. For my modifications, in some instances (e.g. GV) I need to
> > > somehow compute the W^{T}U^{-1}WC product, but that's not
> > > straightforward as the matrix dimensions mismatch.
> >
> > Note that the actual size of the W^{T}U^{-1}W matrix is TD-by-TD.
> > It is a (4LD+1)-diagonal band symmetric matrix. Therefore, we need
> > to store only TD-by-(2LD+1) elements for it. The size of the C  
> > "vector"
> > is TD-by-1.
>
>     Is there a typo in your calculation above? I get the following:
>
>     1. W is TD-by-((2L+1)TD), U is ((2L+1)TD)-by-((2L+1)TD). This
> indeed results in a "WUW" of TD-by-TD,
>     2. M is a ((2L+1)TD)-by-1 ``vector'', resulting in "WUM" of TD- 
> by-1.
>
> But in case of diagonal covariances the bandwidth of "WUW" would be
> (2L + 1)D, wouldn't it? In this case your data structures indeed make
> sense, but that still leaves my question unanswered as the pseudo-code
> snippet in my original message does not produce the expected results
> and I suspect that the W^{T}U^{-1}WC product is calculated in a wrong
> fashion:
>
>     B = W^{T}U^{-1]M - W^{T}U^{-1}WC
>
>     //
>     // for a given dimension d \in [1 ; D]
>     //
>     for (t = 1; t <= pst->T; t++) {
>         B[t] = 0.0;
>         for (k = 1; (k <= pst->width) && (t + k <= pst->T); k++) {
>             B[t] += (pst->sm.WUW[t][k] * C[t + k][d]);
>         }
>         B[t] = pst->sm.WUM[t] - B[t];
>     }
>
> The above can be easily tested for the initial value of the parameters
> (C_0) that should yield  (for any given dimension d) a zero vector B.
> The test fails, however and I suspect that I got something badly
> wrong.
>
>                                                                
> Sincerely,
>
>     Alexander.
>
> > When using diagonal covariance matrices, we can calculate each of the
> > D-dimensions independently. Therefore, at each dimension, we need
> > to store only T-by-(2L+1) elements for W^{T}U^{-1}W and only
> > T-by-1 elements for C, where 2L+1=Width.
> >
> > Sincerely,
> > Tomoki Toda
> >   Nara Institute of Science and Technology
> >   E-mail: tomoki@xxxxxxxxxxx
> >   TEL: +81-743-72-5282
> >   FAX: +81-743-72-5289
> >
> > ----- Original Message -----
> > From: "Alexander Gutkin" <alexander.gutkin@xxxxxxxxx>
> > To: <hts-users@xxxxxxxxxxxxxxx>
> > Sent: Wednesday, August 01, 2007 11:54 PM
> > Subject: [hts-users:00758] HGenS and WUW matrix
> >
> >
> > > Hi,
> > >
> > >   I have a question regarding HTS internals (either HGenS or mlpg
> > > code in hts_engine). From what I am seeing the W^{T}U^{-1}W  
> > > matrix is
> > > stored as TxWidth, while the parameter matrix C is TxD, where D  
> > > is the
> > > order. For my modifications, in some instances (e.g. GV) I need to
> > > somehow compute the W^{T}U^{-1}WC product, but that's not
> > > straightforward as the matrix dimensions mismatch. I've tried  
> > > several
> > > approaches to computing the product but so far without any success.
> > >   The following code snippet from my code is a current broken
> > > implementation of computing the following term:
> > >
> > >    B = W^{T}U^{-1]M - W^{T}U^{-1}WC
> > >
> > >    // for a given m
> > >    for (t = 1; t <= pst->T; t++) {
> > >        B[t] = 0.0;
> > >        for (k = 1; (k <= pst->width) && (t + k <= pst->T); k++) {
> > >            B[t] += (pst->sm.WUW[t][k] * C[t + k][m]);
> > >        }
> > >        B[t] = pst->sm.WUM[t] - B[t];
> > >    }
> > >
> > >                   Thanks in advance,
> > >                                      Alexander.