HP 48G PROGRAMS FOR SYSTEM THEORY

There are currently SWs able to perform symbolic calculations and get results in short time. However having the ability to have a programmable calculator is still important during the exams. One of the programmable calculators that had a great story was the HP 48G. Below all the codes I did when examining the Systems Theory.

MATRIX RANGE

This HP48 program determines the range of a matrix. It outputs the basis vectors and handles matrices up to 4 dimensions.
1: MATRIX

« 
  TRN NUCLEO DROP
  DUP
  IF { } == THEN
    "IL RANGE RAPPRESENTA TUTTO LO SPAZIO" MSGBOX DROP
  ELSE
    DUP SIZE 'DIM' STO
    IF DIM(2) == 2 THEN
      { x1 x2 } 'vet' STO
      [ 0 0 ] 'NUL' STO
    END
    IF DIM(2) == 3 THEN
      { x1 x2 x3 } 'vet' STO
      [ 0 0 0 ] 'NUL' STO
    END
    IF DIM(2) == 4 THEN
      { x1 x2 x3 x4 } 'vet' STO
      [ 0 0 0 0 ] 'NUL' STO
    END

    DIM(1) EVAL 'DIM' STO
    0 'cont' STO
    1 DIM EVAL
    FOR j DUP
      IF NUL == THEN
        DROP DIM 1 - 'DIM' STO
      ELSE
        HOME RANGE vet
        *
      END
      ROLLD cont 1 + 'cont' STO
    NEXT
  END

  { cont NUL vet DIM n } PURGE
»

MATRIX CORE

This code is able to perform the matrix core in both vector form and equations
1: MATRIX

« 
  'Fr' STO  \ Store the input matrix in 'Fr'
  Fr Fr
  SIZE 'DIM' STO  \ Get the size of 'Fr' and store it in 'DIM'
  { 'DIM(1)' } 0 CON 'DIM(2)+1' EVAL COL+  \ Adjust dimensions
  'Fr' STO  \ Store the adjusted matrix back in 'Fr'

  \ Handle different dimensions
  IF 'DIM(2)==2' THEN
    { x1 x2 } 'vet' STO
    [ 0 0 ] 'NUL' STO
  END
  IF 'DIM(2)==3' THEN
    { x1 x2 x3 } 'vet' STO
    [ 0 0 0 ] 'NUL' STO
  END
  IF 'DIM(2)==4' THEN
    { x1 x2 x3 x4 } 'vet' STO
    [ 0 0 0 0 ] 'NUL' STO
  END

  Fr RREF  \ Reduced row echelon form of 'Fr'
  COL SWAP DROP 1 - COL ROW DROP 'DIM(1)' EVAL 'DIM' STO  \ Adjust matrix dimensions
  1 DIM 0 'cont' STO

  \ Loop through dimensions
  FOR j DUP
    IF NUL == THEN
      DROP DIM 1 - 'DIM' STO
    ELSE
      DUP HOME
      HURWI UTILITY A~~L
      HOME RANGE vet *
      LIST 0 = Q DIM 1 +
      ROLLD DIM 1 +
      ROLLD cont 1 + 'cont' STO
    END
  NEXT

  cont LIST 'eqz' STO
  cont ROW 'matr' STO
  { NUL vet cont Fr } PURGE

  matr SIZE 'DIM' STO
  'DIM(2)-DIM(1)' EVAL 'DIM3' STO

  \ Handle the case where DIM3 > 0
  IF DIM3 0 > THEN
    0 'n' STO
    DO
      { DIM3 'DIM(2)' } 0 CON 'matr2' STO
      matr ROW DROP

      IF n 0 < THEN
        1 DIM3 FOR q DROP NEXT
      END

      matr2 ROW DROP 'DIM(2)' EVAL ROW 'matr' STO
      n 1 + 'n' STO
      n 'm' STO
      'DIM(1)' EVAL 1 + 'DIM(2)' EVAL

      FOR j
        IF n > DIM(2) THEN
          1 'n' STO
        END
        matr {j n} 1 PUT 'matr' STO
        n 1 + 'n' STO
      NEXT

      m 'n' STO
    UNTIL matr RANK 'DIM(2)' EVAL == END

    { matr2 m } PURGE
    'DIM(1)' EVAL 1 + 'DIM(2)' EVAL

    FOR j
      { 'DIM(2)' } 0 CON { j } 1 PUT
      matr LSQ 4 RND
    NEXT

    DIM3 ROW
  ELSE
    { }
  END

  eqz { DIM DIM3 matr eqz n } PURGE
»

EIGENVECTORS GENERALIZED

AUTGEN
This cose is able to perform generalized eigenvectors
3: autovalore
2: autovettore generalizzato di ordine appena minore
1: matrice

'Fr' STO
'avt' STO
'avl' STO
Fr SIZE 'DIM' STO
HEAD IDN avl * Fr -
'Fr' STO
Fr avt NEG STO
DIM HEAD 1 + COL+
'Frplus' STO
IF Fr RANK Frplus RANK ==
THEN
    Frplus 'Fr' STO
END
IF 'DIM(2)==2'
THEN
    [ 0 0 ] 'NUL' STO
END
IF 'DIM(2)==3'
THEN
    [ 0 0 0 ] 'NUL' STO
END
IF 'DIM(2)==4'
THEN
    [ 0 0 0 0 ] 'NUL' STO
END
Fr RREF
COL SWAP 'avt' STO
1 - COL DROP ROW DROP
'DIM(1)' EVAL 'DIM' STO
1 DIM FOR j
    DUP IF NUL ==
    THEN
        DROP DIM 1 - 'DIM' STO
        ROW DROP 'avt' STO
    ELSE
        DIM ROLLD 'avt' STO
        nue ROW 'avt' STO
    END
NEXT
DIM ROW 'matr' STO
SIZE 'DIM' STO
(2)-DIM(1) EVAL 'DIM3' STO
IF DIM3 0 > THEN
    0 'n' STO
    DO
        DIM3 'DIM(2)' 0 CON 'matr2' STO
        DIM3 0 CON 'avt2' STO
        matr ROW DROP
        IF n 0 <
        THEN
            1 DIM3 FOR q DROP NEXT
        END
        avt ROW DROP 'nue' STO
        IF n 0 <
        THEN
            1 DIM3 FOR q DROP nue 1 - 'nue' STO NEXT
        END
        nue ROW 'avt' STO
        matr2 ROW DROP 'DIM(2)' EVAL ROW 'matr' STO
        avt ROW DROP avt2 ROW DROP 'DIM(2)' EVAL ROW 'avt' STO
        n 1 + 'n' STO
        'm' STO 'DIM(1)' EVAL 1 + 'DIM(2)' EVAL FOR j
        matr { j n } 1 PUT 'matr' STO n 1 + 'n' STO NEXT
        m 'n' STO UNTIL matr RANK 'DIM(2)' EVAL ==
    END
    'DIM(1)' EVAL 1 + 'DIM(2)' EVAL FOR j
    avt { j } 1 PUT 'matr' STO NEXT
    DIM3 ROW
ELSE
    { } "Non ci sono altri autovettori generalizzati" MSGBOX
END
{ DIM Fr avt2 nue Frplus avl matr2 m NUL vet cont DIM3 eqz n matr avt } PURGE

La lista completa di tutti le funzioni create sono presenti nel seguente file: