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+--- Thread: (49G) Function of a Matrix (/thread-3786.html)
(49G) Function of a Matrix - Gerald H - 05-05-2015 03:47 PM
MFUN applies a function to a square matrix, calculator should be in approx & complex modes. For example, to find the natural log of matrix
M1=[[ -9. 0. -1. -4. ]
[ 4. 9. 3. 3. ]
[ 0. 4. -9. 9. ]
[ 5. -1. -6. -4. ]]
place M1 on stack level Y & 'LN(X)' on stack level X. MFUN returns the complex matrix
M2=[[ (2.17927367373,1.99350072846) (-.185449038469,-.25062812471) (.12978172209,1.13653167793) (-1.21072226166,-.24561453301) ]
[ (-.349990278973,-.725022350755) (2.17006519946,9.11517059164E-2) (.316994726521,-.413348667032) (-8.29926914019E-3,8.93282974816E-2) ]
[ (.499972969813,1.87320392796) (.360844076572,-.235504096367) (1.81399293871,1.06794824449) (2.26427803714,-.230793047339) ]
[ (1.5738586231,8.93453089839E-2) (.311847366461,-1.12327258886E-2) (-1.58567642989,5.09374150115E-2) (2.97368489567,-.011008025242) ]]
to stack level X.
As a check, you could then put 'e^X' on the stack & actuate MFUN again, to return
[[ (-8.99999999989,-1.62595437076E-10) (-7.789692811E-12,2.87950512152E-11) (-.999999999977,-1.80997814311E-10) (-3.99999999999,-1.76112719874E-11) ]
[ (3.99999999998,4.21474277251E-11) (9.00000000017,7.44661562123E-11) (2.99999999996,3.96498859739E-11) (3.00000000004,1.34469661894E-12) ]
[ (2.98413096713E-11,-1.53814112532E-10) (3.99999999998,4.04329178333E-11) (-8.99999999998,-1.19988781132E-10) (8.99999999994,1.82967287016E-10) ]
[ (4.99999999998,6.94233268647E-11) (-1.00000000004,6.827569037E-12) (-5.99999999997,-5.4121217567E-11) (-4.00000000003,1.19154531002E-10) ]]
where the imaginary parts are v small, so RE 0 RND looks more like the original M1.
I am sure the programme has enormous inefficiencies & would welcome improvements.
TI fans - the TI-92 does this out of the box, just use LN(M1).
Code:
::
CK2&Dispatch
# 49
::
{
Z1_
}
Z0_
NULL{}
DUPDUP
BINT1
BINT1
BINT0
FPTR2 ^RCLVX
'
NULLLAM
BINT11
NDUPN
DOBIND
BINT105
BINT110
ClrUserFlag
ClrUserFlag
BINT110
BINT110
SysITE
SetUserFlag
SetSysFlag
BINT105
BINT105
SysITE
::
SetUserFlag
11GETLAM
FPTR2 ^CKNUMARRY
11PUTLAM
;
DROP
11GETLAM
DUP
MDIMSDROP
DROP
4PUTLAM
FPTR2 ^MATEGVL
FPTR2 ^MATRIX2LIST
DUPLENCOMP
4GETLAM
#<
IT
::
BINT105
SetSysFlag
DROP
11GETLAM
FPTR2 ^CKNUMARRY
DUP
11PUTLAM
FPTR2 ^MATEGVL
FPTR2 ^MATRIX2LIST
;
7PUTLAM
BEGIN
4GETLAM
#0<>
WHILE
::
6GETLAM
7GETLAM
CARCOMP
>TCOMP
DUP
6PUTLAM
5GETLAM
BINT1
>TCOMP
5PUTLAM
3GETLAM
NTHCOMPDROP
7GETLAM
CDRCOMP
DUP
7PUTLAM
SWAP
EQUALPOSCOMP
2PUTLAM
BEGIN
2GETLAM
#0<>
WHILE
::
7GETLAM
INNERDUP
#2+
2GETLAM
#-
ROLLDROP
#1-{}N
DUP
7PUTLAM
5GETLAM
DUP
3GETLAM
NTHCOMPDROP
#1+
3GETLAM
ROT
PUTLIST
5PUTLAM
6GETLAM
3GETLAM
NTHCOMPDROP
EQUALPOSCOMP
2PUTLAM
;
REPEAT
3GETLAM
#1+
3PUTLAM
7GETLAM
LENCOMP
4PUTLAM
;
REPEAT
3GETLAM
#1-
3PUTLAM
11GETLAM
MDIMSDROP
DROP
4PUTLAM
9GETLAM
4GETLAM
ONE_DO
1GETLAM
INDEX@
FPTR2 ^#>Z
PTR 2EF1F
>TCOMP
LOOP
10GETLAM
>TCOMP
DUP
9PUTLAM
1GETLAM
6GETLAM
CARCOMP
PTR 2EF27
FPTR2 ^FLAGSYMBEXEC
FPTR2 ^LIST2MATRIX
5GETLAM
CARCOMP
BINT1
#>
IT
::
5GETLAM
CARCOMP
ONE_DO
9GETLAM
INDEX@
ZERO_DO
1GETLAM
FPTR2 ^DERIVext
LOOP
1GETLAM
6GETLAM
CARCOMP
PTR 2EF27
xSUBST
xAXL
LOOP
;
3GETLAM
BINT1
#>
IT
::
3GETLAM
#1+
BINT2
DO
9GETLAM
1GETLAM
6GETLAM
INDEX@
NTHCOMPDROP
PTR 2EF27
FPTR2 ^FLAGSYMBEXEC
FPTR2 ^LIST2MATRIX
5GETLAM
INDEX@
NTHCOMPDROP
BINT1
#>
IT
::
5GETLAM
INDEX@
NTHCOMPDROP
ONE_DO
9GETLAM
INDEX@
ZERO_DO
1GETLAM
FPTR2 ^DERIVext
LOOP
1GETLAM
6GETLAM
JINDEX@
NTHCOMPDROP
PTR 2EF27
xSUBST
xAXL
LOOP
;
LOOP
;
4GETLAM
FPTR 3 68
FPTR2 ^MATRREF
4GETLAM
#1+
FPTR2 ^MATRIX-COL
SWAPDROP
FPTR2 ^MATRIX2LIST
DUP
8PUTLAM
CARCOMP
4GETLAM
UNCOERCE
PTR 2F28F
FPTR2 ^SCL*MAT
4GETLAM
#1+
BINT2
DO
8GETLAM
INDEX@
NTHCOMPDROP
11GETLAM
INDEX@
#1-
FPTR2 ^#>Z
FPTR2 ^MAT^
FPTR2 ^SCL*MAT
FPTR2 ^MAT+
LOOP
ABND
FPTR2 ^FLAGEXPAND
BINT110
BINT110
UserITE
ClrUserFlag
ClrSysFlag
BINT105
BINT105
UserITE
ClrUserFlag
ClrSysFlag
;
;RE: HP 49G: Function of a Matrix - Gerald H - 05-15-2015 03:09 PM
Here a second attempt, shorter & faster.
Input is a square matrix & a programme,
eg
[Matrix]
<< LN >>
Code:
::
CK2&Dispatch
# 48
::
2DUP
BINT0
FPTR2 ^2LAMBIND
FPTR2 ^PUSHFLAGS_
FPTR2 ^CLREXACT
BINT103
SetSysFlag
FPTR2 ^MATEGV
FPTR2 ^XEQARRY>
INCOMPDROP
COERCEDUP
1PUTLAM
ZERO_DO
2GETLAM
EVAL
1GETLAM
ROLL
LOOP
1GETLAM
TYPEMATRIX_
COMPN_
1GETABND
DUP
TWO{}N
FPTR 3 6B
OVER
FPTR2 ^MATINV
FPTR2 ^MMMULT
FPTR2 ^MMMULT
FPTR2 ^POPFLAGS_
3UNROLL
xDROP2
;
;RE: (49G) Function of a Matrix - Gilles59 - 10-31-2017 05:16 PM
Hi Gerald
I think you can do this with the integrated DIAGMAP function. With your example :
Code:
[[ -9 0 -1 -4 ]
[ 4 9 3 3 ]
[ 0 4 -9 9 ]
[ 5 -1 -6 -4 ]]
'LN(X)' DIAGMAP XNUMtakes ~11,6s in approx mode on a 50g (i dont test with the 49g)
Then :
Code:
'EXP(X)' DIAGMAP XNUMRE: (49G) Function of a Matrix - Gerald H - 10-31-2017 10:04 PM
Well done, Gilles.
I've never used nor heard of DIAGMAP, how ignorant I am & how good a device the 50g is.
My programme above requires 6.7s to transform the example matrix, so remains of some use.
RE: (49G) Function of a Matrix - Gerald H - 10-31-2017 10:15 PM
If you try DIAGMAP with a your matrix * 1. &
<< LN >>
the time comes down to 6.7s.
RE: (49G) Function of a Matrix - Gilles59 - 10-31-2017 11:03 PM
(10-31-2017 10:15 PM)Gerald H Wrote: If you try DIAGMAP with << LN >>
the time comes down to 6.7s.
Interesting... And no need of XNUM in this case!
But the precision is less. Curious. It seems that for example 'LN(X)' syntax use partially a symbolic calculation (so need an XNUM). << LN >> is full numerical
RE: (49G) Function of a Matrix - Gerald H - 11-01-2017 01:19 PM
I shall use the programme below in future as I only require numerical answers. The programme also has the advantage of returning LASTARG if required.
FPTR 7 134 is internal DIAGMAP
FPTR 7 1DC is internal PUSH
FPTR 7 1DD is internal POP
All three addresses are the same in OS 1.19-6 & 2.10-8.
Size: 54.
CkSum: # D173h
Code:
::
CK2&Dispatch
# 48
::
2DUP
FPTR 7 1DC
FPTR2 ^CLREXACT
BINT103
SetSysFlag
FPTR 7 134
FPTR 7 1DD
3UNROLL
xDROP2
;
;RE: (49G) Function of a Matrix - pier4r - 11-01-2017 06:06 PM
(10-31-2017 10:04 PM)Gerald H Wrote: I've never used nor heard of DIAGMAP, how ignorant I am & how good a device the 50g is.
I agree with this a lot (and thanks Gilles for sharing!).
I estimate that I know the 50g way less than Gerald H, so I wonder how many years of problems I should solve before having a grasp of it.
PS: and thanks Gerald H to share your solutions, they provide nice inputs. I wish people would share their work often (I say this because in my experience many people don't share their work unless they know it is really good for many and that is a pity. See Gauss and his works, or Riemann. The same applies to small but potentially interesting works like little programs.)
RE: (49G) Function of a Matrix - Gerald H - 11-01-2017 06:27 PM
I agree with you wholeheartedly, pier4r.
Who knows what gems of programmes are never published.