s34085w@saha.hut.fi (Per Johan Evert Stenius) (08/29/90)
Here's a prog that I converted into 48sx format. I'm sure some of you
have seen it before. This copy should be free from typos. However, if
problems occur try to reach LOZAN (I don't have his complete address)
and please post the revised version!
-just remove all crap until here*
%%HP: T(3)A(R)F(.);
DIR
@ SYMBOLIC MATRICES by Eliel Louzoun <LOZAN@TAUNOS>
@ -----------------
@ This is a set of programs which handle symbolic matrices for the hp48sx.
@ The matrices are entered as a list, for example {{A B }{ C D }}. This package
@ contains programs for determinant,inverse of matrices,eigen values,
@ multiplication of matrices & multiplication by a scalar.
@ Bugs: The eigenvalue program works only if the values are all real.
det
\<< DUP SIZE \-> A B
\<<
IF B 1 == @ det of a 1x1 matrix
THEN A 1 GET 1 GET
ELSE
IF B 2 ==
THEN A DET2 @ call basic case of 2x2 determinant
ELSE 0
1 B FOR I
A 1 GET I GET
\-> E \<< IF E 0 SAME THEN ELSE
A 1 I MINOR det E @ recursive call
* -1 1 I + ^ * +
END \>>
NEXT
END
END
\>>
\>>
@ This is an accessory program to compute A*D-B*C
DET2 @ from {{A B}{C D}}
\<< \-> A
\<< A 1 GET 1 GET
A 2 GET 2 GET *
A 1 GET 2 GET
A 2 GET 1 GET * -
\>>
\>>
@ This is also an accessory program to compute M(i,j) of
MINOR @ an element in the matrix
\<< \-> A B C
\<< A SIZE \-> S
\<< 1 S FOR I
IF B I \=/ THEN A I GET
\-> D
\<< 1 S FOR J
IF J C \=/ THEN D J GET
END NEXT
S 1 - \->LIST
\>>
END NEXT S 1 - \->LIST
\>>
\>>
\>>
@ Compute the inverse of the matrix in level 1.
@ The output is 2: B (a matrix)
@ 1: C (an algebraic expression)
@ where inv(A) = B / C .
@ This program use the cramer rule to compute the inverse.
inv
\<< DUP SIZE \-> A B
\<< 1 B FOR I
1 B FOR J
A J I MINOR det
-1 I J + ^ *
NEXT B \->LIST
NEXT B \->LIST
A det
\>>
\>>
@ matrices multiplication
@ input 2: A
@ 1: B
@ output 1: A*B
MMUL
\<< \-> A B
\<< A SIZE B SIZE B 1 GET SIZE
\-> L C R
\<< 1 L FOR I A I GET
\-> LI
\<< 1 R FOR J 0
1 C FOR K LI K GET
B K GET J GET
* +
NEXT
NEXT R \->LIST
\>>
NEXT L \->LIST
\>>
\>>
\>>
@ scalar multiplication program
@ input 2: scalar
@ 1: matrix
@ output 1: matrix = scalar * matrix
SCMUL
\<< DUP SIZE \-> M A S
\<< 1 S FOR I A I GET \-> C
\<< 1 S FOR J C J GET M *
NEXT
\>> S \->LIST
NEXT S \->LIST
\>>
\>>
@ eliminate one real root from polynom
@ input 3: a polynom in S [P(S)]
@ 2: the degree of this polynom
@ 1: the root we want to eliminate [a]
@ output 1: P(S)/(S-a)
DIVP
\<< \-> P K R
\<< P 'S' R - / 'S' K 1 - TAYLR \>>
\>>
eigf @ This program returns the eigen function of a given matrix
\<< DUP SIZE \-> A B
\<< B '-S' SIDN A
add det
\>>
\>>
@ sum of two matrices
@ input 2: A (matrix)
@ 1: B (matrix)
@ output 1: A + B
add
\<< DUP SIZE \-> B A S
\<< 1 S FOR I A I GET B I GET
\-> C D
\<< 1 S FOR J C J GET
D J GET +
NEXT
\>> S \->LIST
NEXT S \->LIST
\>>
\>>
@ This program return an identity matrix multiplied by a scalar
@ input 1: size (scalar)
@ 2: const (algbraic object)
@ output 1: const * I
SIDN
\<< \-> K S
\<< 1 K FOR I
1 K FOR J
I J == S *
NEXT K \->LIST
NEXT K \->LIST
\>>
\>>
EIGV @ returns the eigenvalues of a matrix
\<< \-> A
\<< A eigf STEQ A SIZE
1 FOR I RCEQ 'S' 0 ROOT
RCEQ I 3 PICK DIVP
STEQ
-1 STEP { S EQ } PURGE
\>>
\>>
Per Stenius, Helsinki Univ. of Technology, Dept. of E.E.
perre@aplac.hut.fi