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LU decomposition: Difference between revisions
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=={{header|BBC BASIC}}==
<lang bbcbasic> DIM A1(2,2)
A1() = 1, 3, 5, 2, 4, 7, 1, 1, 0
PROCLUdecomposition(A1(), L1(), U1(), P1())
PRINT "L1:" ' FNshowmatrix(L1())
PRINT "U1:" ' FNshowmatrix(U1())
PRINT "P1:" ' FNshowmatrix(P1())
DIM A2(3,3)
A2() = 11, 9, 24, 2, 1, 5, 2, 6, 3, 17, 18, 1, 2, 5, 7, 1
PROCLUdecomposition(A2(), L2(), U2(), P2())
PRINT "L2:" ' FNshowmatrix(L2())
PRINT "U2:" ' FNshowmatrix(U2())
PRINT "P2:" ' FNshowmatrix(P2())
END
DEF PROCLUdecomposition(a(), RETURN l(), RETURN u(), RETURN p())
LOCAL i%, j%, k%, n%, s, b() : n% = DIM(a(),2)
DIM l(n%,n%), u(n%,n%), b(n%,n%)
PROCpivot(a(), p())
b() = p() . a()
FOR j% = 0 TO n%
l(j%,j%) = 1
FOR i% = 0 TO j%
s = 0
FOR k% = 0 TO i% : s += u(k%,j%) * l(i%,k%) : NEXT
u(i%,j%) = b(i%,j%) - s
NEXT
FOR i% = j% TO n%
s = 0
FOR k% = 0 TO j% : s += u(k%,j%) * l(i%,k%) : NEXT
IF i%<>j% l(i%,j%) = (b(i%,j%) - s) / u(j%,j%)
NEXT
NEXT j%
ENDPROC
DEF PROCpivot(a(), RETURN p())
LOCAL i%, j%, m%, n%, r% : n% = DIM(a(),2)
DIM p(n%,n%) : FOR i% = 0 TO n% : p(i%,i%) = 1 : NEXT
FOR i% = 0 TO n%
m% = a(i%,i%)
r% = i%
FOR j% = i% TO n%
IF a(j%,i%) > m% m% = a(j%,i%) : r% = j%
NEXT
IF i%<>r% THEN
FOR j% = 0 TO n% : SWAP p(i%,j%),p(r%,j%) : NEXT
ENDIF
NEXT i%
ENDPROC
DEF FNshowmatrix(a())
LOCAL @%, i%, j%, a$
@% = &102050A
FOR i% = 0 TO DIM(a(),1)
FOR j% = 0 TO DIM(a(),2)
a$ += STR$(a(i%,j%)) + ", "
NEXT
a$ = LEFT$(LEFT$(a$)) + CHR$(13) + CHR$(10)
NEXT i%
= a$</lang>
'''Output:'''
<pre>
L1:
1.00000, 0.00000, 0.00000
0.50000, 1.00000, 0.00000
0.50000, -1.00000, 1.00000
U1:
2.00000, 4.00000, 7.00000
0.00000, 1.00000, 1.50000
0.00000, 0.00000, -2.00000
P1:
0.00000, 1.00000, 0.00000
1.00000, 0.00000, 0.00000
0.00000, 0.00000, 1.00000
L2:
1.00000, 0.00000, 0.00000, 0.00000
0.27273, 1.00000, 0.00000, 0.00000
0.09091, 0.28750, 1.00000, 0.00000
0.18182, 0.23125, 0.00360, 1.00000
U2:
11.00000, 9.00000, 24.00000, 2.00000
0.00000, 14.54545, 11.45455, 0.45455
0.00000, 0.00000, -3.47500, 5.68750
0.00000, 0.00000, 0.00000, 0.51079
P2:
1.00000, 0.00000, 0.00000, 0.00000
0.00000, 0.00000, 1.00000, 0.00000
0.00000, 1.00000, 0.00000, 0.00000
0.00000, 0.00000, 0.00000, 1.00000
</pre>
=={{header|C}}==
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