LDLt decomposition? - Printable Version

LDLt decomposition? - Printable Version

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LDLt decomposition? - salvomic - 01-26-2015 12:30 PM

hi all,
in HP Prime we have for a matrix LU decomposition (it give P, L, U so PA=LU) and Cholesky decomposition (for that A=LLt, Lt is TRAN(L))...
I can't find a factorization LDLt where D is a diagonal of pivot.
Is there a way to get it? a program or something?

Thank you!

Salvo

RE: LDLt decomposition? - salvomic - 06-01-2015 05:54 PM

I wonder still for this question and another one, connected (in my case):
With pivot(Mat, n,m) we get pivot for n,m: what's a simple way to get every pivots (Gauss' reduction); I forgot it Smile

thanks!
Salvo

RE: LDLt decomposition? - salvomic - 06-01-2015 10:51 PM

...to get Pivots I start with this code:

Code:

EXPORT gaussJordan(m)

// Gauss-Jordan elimination and pivots

// Salvo Micciché 2015

BEGIN

local temp, temp2, gj, r, c, j, piv;

r:=rowDim(m);

c:=colDim(m);

temp:=MAKEMAT(0,r,c);

gj:=MAKEMAT(0,r,c);

piv:=MAKELIST(0,X,1,r);

gj(1):= m(1);

piv(1):=gj(1,1);

    temp:= pivot(m,1,1);

FOR j FROM 2 TO r DO

    temp:=delrows(temp,1);

    temp:=delcols(temp,1);

    temp:=temp/piv(j-1);

    temp:= pivot(temp,1,1);

    piv(j):=temp(1,1);

    gj(j):= temp(1);

END; // for

RETURN {gj, piv};

END;

but I get wrong results (see image): I should get 0 below pivots at left, not ...at right; I'm trying SWAPROW() but it doesn't run...
Any help?

RE: LDLt decomposition? - DrD - 06-02-2015 11:26 AM

Is diag() useful for you?

Code:

EXPORT gjp()

BEGIN 

  M5:=[[2,1,1,5],[-8,-2,-12,0],[1,2,0,0]];  // Your matrix

  M6:=diag(M5);  //  Diagonal Matrix

  return M6;  

END;

RE: LDLt decomposition? - salvomic - 06-02-2015 12:10 PM

(06-02-2015 11:26 AM)DrD Wrote: Is diag() useful for you?

Code:

EXPORT gjp() BEGIN M5:=[[2,1,1,5],[-8,-2,-12,0],[1,2,0,0]]; // Your matrix M6:=diag(M5); // Diagonal Matrix return M6; END;

hi Dale,
diag() is also ok to get pivots, but after to have "pivot-ized" the original matrix: [[2,1,1,5],[4,-6,0,-2],[-2,7,2,9]]

My goal is to return a transformed matrix and a list with pivots (and also diag() could be ok).

EDIT:
Something like that, Dale:

Code:

EXPORT gaussJordan(m)

// Gauss-Jordan elimination and pivots

// Salvo Micciché 2015

BEGIN

local temp, k, gj, r, c, j, piv;

r:=rowDim(m);

c:=colDim(m);

temp:=MAKEMAT(0,r,c);

gj:=MAKEMAT(0,r,c);

piv:=MAKELIST(0,X,1,r);

temp:= m;

FOR j FROM 1 TO r DO

      temp:=pivot(temp,1,1);

      // gj(j):= temp(1);

    FOR k FROM 1 TO colDim(temp) DO

        gj(j, c-k+1):= temp(1, colDim(temp)-k+1);

    END; // inner for

      piv(j):=temp(1,1);

    IF (j<r) THEN

    temp:= delrows(temp,1);

    temp:= delcols(temp,1);

    END;

      temp:= temp/piv(j);  

END; // for

piv:= list2mat(piv, r);

RETURN {gj, piv};

END;

this runs, but with "singular" matrices it gives still division by 0 and in some cases fails (we need also swapping of some rows...), however now we have a base to calculate LDLt decomposition also...

RE: LDLt decomposition? - salvomic - 06-02-2015 05:54 PM

SWAPROW runs well in command line but not in a program? or am I missing something?

This code doesn't swap row 2 with 3...

Code:

EXPORT gaussJordan(m)

// Gauss-Jordan elimination and pivots

// Salvo Micciché 2015

BEGIN

local k, gj, r, c, j, piv;

r:=rowDim(m);

c:=colDim(m);

gj:=MAKEMAT(0,r,c);

piv:=MAKELIST(0,X,1,r);

M1:= m;

FOR j FROM 1 TO r DO

      M1:=pivot(M1,1,1);

      piv(j):=M1(1,1);

    IF (piv(j)==0) THEN 

PRINT("M1 first " + M1);

    M1:=m;

PRINT("M1 then " + M1);

    SWAPROW(M1, j, (j+1)); 

PRINT("M1 and after " + M1);

    CONTINUE; 

    END; // if

    FOR k FROM 1 TO colDim(M1) DO

        gj(j, c-k+1):= M1(1, colDim(M1)-k+1);

    END; // inner for

    IF (j<r) THEN

    M1:= delrows(M1,1);

    M1:= delcols(M1,1);

    END;

    IF piv(j)==0 THEN RETURN "Pivot is 0, division by 0"; END;

      M1:= M1/piv(j);  

END; // for

piv:= list2mat(piv, r);

RETURN {gj, piv};

END;

See the prints in Terminal (debug, hi) with this matrix
[[1,2,3],[2,4,3],[3,2,1]]
Normally it would give division by zero, so we must swap the row with its next...
The result should be [[1,2,3],[0,-4,-10],[0,0,-3]] with pivots d={1,-4,-3}

I'm using an "old C style" tip, and it works:

Code:

 // M1:= SWAPROW(M1, numpivot, (numpivot+1)); 

temp:= M1(numpivot); M1(numpivot):=M1(numpivot+1); M1(numpivot+1):=temp;

RE: LDLt decomposition? - DrD - 06-02-2015 10:05 PM

I tried both SWAPROW() and SWAPCOL() on a 3x3 matrix and neither worked from the command line or HOME program, for me.

-Dale-

RE: LDLt decomposition? - salvomic - 06-02-2015 10:15 PM

(06-02-2015 10:05 PM)DrD Wrote: I tried both SWAPROW() and SWAPCOL() on a 3x3 matrix and neither worked from the command line or HOME program, for me.

-Dale-

Please, could I suspect a bug? Smile

Strange, however...

Salvo

RE: LDLt decomposition? - Helge Gabert - 06-02-2015 11:05 PM

How about CAS.SWAPCOL()? Works here.

RE: LDLt decomposition? - DrD - 06-03-2015 11:59 AM

ALL similar matrix commands have the same requirement: ADDROW(), DELROW(), SWAPROW(), etc., all have the same CAS requirement in order to work on the HC and virtual calc. They seem to work ok on the Android app. I sent a bug report in, but, maybe this is intended behavior? If the command names were in lower case, it would serve as a hint that they need CAS handling.

-Dale-

RE: LDLt decomposition? - salvomic - 06-03-2015 12:19 PM

(06-03-2015 11:59 AM)DrD Wrote: ALL similar matrix commands have the same requirement: ADDROW(), DELROW(), SWAPROW(), etc., all have the same CAS requirement in order to work on the HC and virtual calc. They seem to work ok on the Android app. I sent a bug report in, but, maybe this is intended behavior? If the command names were in lower case, it would serve as a hint that they need CAS handling.

-Dale-

I agree.
Here I've issues with them in CAS, however, so I think maybe there could be some bugs with the last FW upgrade...

Salvo

EDIT:
here SWAPROW([[1,2,3],[0,0,-3],[0,-4,-10]],2,3) doesn't work nor in CAS neither in Home.

RE: LDLt decomposition? - salvomic - 06-03-2015 01:22 PM

however, please, see also this thread (for pivots calculation), that could help us to make an actual program to find Gauss elimination procedure, then pivots to use to find eventually LDLt decomposition.
Please, help Smile

EDIT:
working in progress in this thread in the Forum!