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| SUBROUTINE SVDCMP(A,M,N,MP,NP,W,V)
PARAMETER (NMAX=800)
DIMENSION A(MP,NP),W(NP),V(NP,NP),RV1(NMAX)
G=0.0
SCALE=0.0
ANORM=0.0
DO 25 I=1,N
L=I+1
RV1(I)=SCALE*G
G=0.0
S=0.0
SCALE=0.0
IF (I.LE.M) THEN
DO 11 K=I,M
SCALE=SCALE+ABS(A(K,I))
11 CONTINUE
IF (SCALE.NE.0.0) THEN
DO 12 K=I,M
A(K,I)=A(K,I)/SCALE
S=S+A(K,I)*A(K,I)
12 CONTINUE
F=A(I,I)
G=-SIGN(SQRT(S),F)
H=F*G-S
A(I,I)=F-G
IF (I.NE.N) THEN
DO 15 J=L,N
S=0.0
DO 13 K=I,M
S=S+A(K,I)*A(K,J)
13 CONTINUE
F=S/H
DO 14 K=I,M
A(K,J)=A(K,J)+F*A(K,I)
14 CONTINUE
15 CONTINUE
ENDIF
DO 16 K= I,M
A(K,I)=SCALE*A(K,I)
16 CONTINUE
ENDIF
ENDIF
W(I)=SCALE *G
G=0.0
S=0.0
SCALE=0.0
IF ((I.LE.M).AND.(I.NE.N)) THEN
DO 17 K=L,N
SCALE=SCALE+ABS(A(I,K))
17 CONTINUE
IF (SCALE.NE.0.0) THEN
DO 18 K=L,N
A(I,K)=A(I,K)/SCALE
S=S+A(I,K)*A(I,K)
18 CONTINUE
F=A(I,L)
G=-SIGN(SQRT(S),F)
H=F*G-S
A(I,L)=F-G
DO 19 K=L,N
RV1(K)=A(I,K)/H
19 CONTINUE
IF (I.NE.M) THEN
DO 23 J=L,M
S=0.0
DO 21 K=L,N
S=S+A(J,K)*A(I,K)
21 CONTINUE
DO 22 K=L,N
A(J,K)=A(J,K)+S*RV1(K)
22 CONTINUE
23 CONTINUE
ENDIF
DO 24 K=L,N
A(I,K)=SCALE*A(I,K)
24 CONTINUE
ENDIF
ENDIF
ANORM=MAX(ANORM,(ABS(W(I))+ABS(RV1(I))))
25 CONTINUE
DO 32 I=N,1,-1
IF (I.LT.N) THEN
IF (G.NE.0.0) THEN
DO 26 J=L,N
V(J,I)=(A(I,J)/A(I,L))/G
26 CONTINUE
DO 29 J=L,N
S=0.0
DO 27 K=L,N
S=S+A(I,K)*V(K,J)
27 CONTINUE
DO 28 K=L,N
V(K,J)=V(K,J)+S*V(K,I)
28 CONTINUE
29 CONTINUE
ENDIF
DO 31 J=L,N
V(I,J)=0.0
V(J,I)=0.0
31 CONTINUE
ENDIF
V(I,I)=1.0
G=RV1(I)
L=I
32 CONTINUE
DO 39 I=N,1,-1
L=I+1
G=W(I)
IF (I.LT.N) THEN
DO 33 J=L,N
A(I,J)=0.0
33 CONTINUE
ENDIF
IF (G.NE.0.0) THEN
G=1.0/G
IF (I.NE.N) THEN
DO 36 J=L,N
S=0.0
DO 34 K=L,M
S=S+A(K,I)*A(K,J)
34 CONTINUE
F=(S/A(I,I))*G
DO 35 K=I,M
A(K,J)=A(K,J)+F*A(K,I)
35 CONTINUE
36 CONTINUE
ENDIF
DO 37 J=I,M
A(J,I)=A(J,I)*G
37 CONTINUE
ELSE
DO 38 J= I,M
A(J,I)=0.0
38 CONTINUE
ENDIF
A(I,I)=A(I,I)+1.0
39 CONTINUE
DO 49 K=N,1,-1
DO 48 ITS=1,30
DO 41 L=K,1,-1
NM=L-1
IF ((ABS(RV1(L))+ANORM).EQ.ANORM) GO TO 2
IF ((ABS(W(NM))+ANORM).EQ.ANORM) GO TO 1
41 CONTINUE
1 C=0.0
S=1.0
DO 43 I=L,K
F=S*RV1(I)
IF ((ABS(F)+ANORM).NE.ANORM) THEN
G=W(I)
H=SQRT(F*F+G*G)
W(I)=H
H=1.0/H
C= (G*H)
S=-(F*H)
DO 42 J=1,M
Y=A(J,NM)
Z=A(J,I)
A(J,NM)=(Y*C)+(Z*S)
A(J,I)=-(Y*S)+(Z*C)
42 CONTINUE
ENDIF
43 CONTINUE
2 Z=W(K)
IF (L.EQ.K) THEN
IF (Z.LT.0.0) THEN
W(K)=-Z
DO 44 J=1,N
V(J,K)=-V(J,K)
44 CONTINUE
ENDIF
GO TO 3
ENDIF
IF (ITS.EQ.30) stop
!PAUSE 'No convergence in 30 iterations'
!pause
X=W(L)
NM=K-1
Y=W(NM)
G=RV1(NM)
H=RV1(K)
F=((Y-Z)*(Y+Z)+(G-H)*(G+H))/(2.0*H*Y)
G=SQRT(F*F+1.0)
F=((X-Z)*(X+Z)+H*((Y/(F+SIGN(G,F)))-H))/X
C=1.0
S=1.0
DO 47 J=L,NM
I=J+1
G=RV1(I)
Y=W(I)
H=S*G
G=C*G
Z=SQRT(F*F+H*H)
RV1(J)=Z
C=F/Z
S=H/Z
F= (X*C)+(G*S)
G=-(X*S)+(G*C)
H=Y*S
Y=Y*C
DO 45 NM=1,N
X=V(NM,J)
Z=V(NM,I)
V(NM,J)= (X*C)+(Z*S)
V(NM,I)=-(X*S)+(Z*C)
45 CONTINUE
Z=SQRT(F*F+H*H)
W(J)=Z
IF (Z.NE.0.0) THEN
Z=1.0/Z
C=F*Z
S=H*Z
ENDIF
F= (C*G)+(S*Y)
X=-(S*G)+(C*Y)
DO 46 NM=1,M
Y=A(NM,J)
Z=A(NM,I)
A(NM,J)= (Y*C)+(Z*S)
A(NM,I)=-(Y*S)+(Z*C)
46 CONTINUE
47 CONTINUE
RV1(L)=0.0
RV1(K)=F
W(K)=X
48 CONTINUE
3 CONTINUE
49 continue
RETURN
END |
PROBLEME SUBROUTINE SVD NUMERICAL RECIPES
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