LDLt decomposition?
01-26-2015, 12:30 PM (This post was last modified: 02-06-2015 10:42 PM by salvomic.)
Post: #1
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
LDLt decomposition?
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
06-01-2015, 05:54 PM
Post: #2
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: LDLt decomposition?
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

thanks!
Salvo

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
06-01-2015, 10:51 PM
Post: #3
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: LDLt decomposition?

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?

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∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
06-02-2015, 11:26 AM
Post: #4
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: LDLt decomposition?
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;

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06-02-2015, 12:10 PM (This post was last modified: 06-02-2015 02:23 PM by salvomic.)
Post: #5
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: LDLt decomposition?
(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...

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∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
06-02-2015, 05:54 PM (This post was last modified: 06-02-2015 07:20 PM by salvomic.)
Post: #6
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: LDLt decomposition?
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;

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
06-02-2015, 10:05 PM
Post: #7
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: LDLt decomposition?
I tried both SWAPROW() and SWAPCOL() on a 3x3 matrix and neither worked from the command line or HOME program, for me.

-Dale-
06-02-2015, 10:15 PM
Post: #8
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: LDLt decomposition?
(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?

Strange, however...

Salvo

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
06-02-2015, 11:05 PM
Post: #9
 Helge Gabert Senior Member Posts: 467 Joined: Dec 2013
RE: LDLt decomposition?
06-03-2015, 11:59 AM
Post: #10
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: LDLt decomposition?
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-
06-03-2015, 12:19 PM (This post was last modified: 06-03-2015 02:51 PM by salvomic.)
Post: #11
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: LDLt decomposition?
(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.

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
06-03-2015, 01:22 PM (This post was last modified: 06-05-2015 06:40 PM by salvomic.)
Post: #12
 salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: LDLt decomposition?
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.