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*DECK ALSVDF
SUBROUTINE ALSVDF(A,M,N,MP,NP,W,V)
*
*-----------------------------------------------------------------------
*
*Purpose:
* singular value decomposition.
*
*Copyright:
* Copyright (C) 1993 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* A matrix to decompose.
* M,N first/second mathematical dimension of matrix A
* MP,NP first/second physical dimension of matrix A
*
*Parameters: output
* A first decomposed matrix.
* W singular values.
* V second decomposed matrix.
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
INTEGER M,MP,N,NP
DOUBLE PRECISION A(MP,NP),V(NP,NP),W(NP)
INTEGER I,ITS,J,JJ,K,L,NM
DOUBLE PRECISION ANORM,C,F,G,H,S,SCALE,X,Y,Z,RV0
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: RV1,RV2
*
ALLOCATE(RV1(NP))
NM=0
G=0.0D0
SCALE=0.0D0
ANORM=0.0D0
DO 25 I=1,N
L=I+1
RV1(I)=SCALE*G
G=0.0D0
S=0.0D0
SCALE=0.0D0
IF(I.LE.M)THEN
DO 11 K=I,M
SCALE=SCALE+ABS(A(K,I))
11 CONTINUE
IF(SCALE.NE.0.0D0)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
DO 15 J=L,N
S=0.0D0
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
DO 16 K=I,M
A(K,I)=SCALE*A(K,I)
16 CONTINUE
ENDIF
ENDIF
W(I)=SCALE*G
G=0.0D0
S=0.0D0
SCALE=0.0D0
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.0.0D0)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
DO 23 J=L,M
S=0.0D0
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
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.0.0D0)THEN
DO 26 J=L,N
V(J,I)=(A(I,J)/A(I,L))/G
26 CONTINUE
DO 29 J=L,N
S=0.0D0
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)=0.0D0
V(J,I)=0.0D0
31 CONTINUE
ENDIF
V(I,I)=1.0D0
G=RV1(I)
L=I
32 CONTINUE
DO 39 I=MIN(M,N),1,-1
L=I+1
G=W(I)
DO 33 J=L,N
A(I,J)=0.0D0
33 CONTINUE
IF(G.NE.0.0D0)THEN
G=1.0D0/G
DO 36 J=L,N
S=0.0D0
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
DO 37 J=I,M
A(J,I)=A(J,I)*G
37 CONTINUE
ELSE
DO 38 J= I,M
A(J,I)=0.0D0
38 CONTINUE
ENDIF
A(I,I)=A(I,I)+1.0D0
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) GOTO 2
IF((ABS(W(NM))+ANORM).EQ.ANORM) GOTO 1
41 CONTINUE
1 C=0.0D0
S=1.0D0
DO 43 I=L,K
F=S*RV1(I)
RV1(I)=C*RV1(I)
IF((ABS(F)+ANORM).EQ.ANORM) GOTO 2
G=W(I)
IF(ABS(F).GT.ABS(G))THEN
W(I)=ABS(F)*SQRT(1.0D0+(ABS(G)/ABS(F))**2)
ELSE
IF(ABS(G).EQ.0.0D0)THEN
W(I)=0.0D0
ELSE
W(I)=ABS(G)*SQRT(1.0D0+(ABS(F)/ABS(G))**2)
ENDIF
ENDIF
H=1.0D0/W(I)
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
43 CONTINUE
2 Z=W(K)
IF(L.EQ.K)THEN
IF(Z.LT.0.0D0)THEN
W(K)=-Z
DO 44 J=1,N
V(J,K)=-V(J,K)
44 CONTINUE
ENDIF
GOTO 3
ENDIF
IF(ITS.EQ.30) CALL XABORT('ALSVDF: NO CONVERGENCE.')
X=W(L)
NM=K-1
Y=W(NM)
G=RV1(NM)
H=RV1(K)
F=((Y-Z)*(Y+Z)+(G-H)*(G+H))/(2.0D0*H*Y)
IF(ABS(F).GT.1.0D0)THEN
G=ABS(F)*SQRT(1.0D0+(1.0D0/ABS(F))**2)
ELSE
G=SQRT(1.0D0+(ABS(F))**2)
ENDIF
F=((X-Z)*(X+Z)+H*((Y/(F+SIGN(G,F)))-H))/X
C=1.0D0
S=1.0D0
DO 47 J=L,NM
I=J+1
G=RV1(I)
Y=W(I)
H=S*G
G=C*G
IF(ABS(F).GT.ABS(H))THEN
Z=ABS(F)*SQRT(1.0D0+(ABS(H)/ABS(F))**2)
ELSE
IF(ABS(H).EQ.0.D0)THEN
Z=0.0D0
ELSE
Z=ABS(H)*SQRT(1.0D0+(ABS(F)/ABS(H))**2)
ENDIF
ENDIF
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 JJ=1,N
X=V(JJ,J)
Z=V(JJ,I)
V(JJ,J)= (X*C)+(Z*S)
V(JJ,I)=-(X*S)+(Z*C)
45 CONTINUE
IF(ABS(F).GT.ABS(H))THEN
Z=ABS(F)*SQRT(1.0D0+(ABS(H)/ABS(F))**2)
ELSE
IF(ABS(H).EQ.0.D0)THEN
Z=0.0D0
ELSE
Z=ABS(H)*SQRT(1.0D0+(ABS(F)/ABS(H))**2)
ENDIF
ENDIF
W(J)=Z
IF(Z.NE.0.0D0)THEN
Z=1.0D0/Z
C=F*Z
S=H*Z
ENDIF
F= (C*G)+(S*Y)
X=-(S*G)+(C*Y)
DO 46 JJ=1,M
Y=A(JJ,J)
Z=A(JJ,I)
A(JJ,J)= (Y*C)+(Z*S)
A(JJ,I)=-(Y*S)+(Z*C)
46 CONTINUE
47 CONTINUE
RV1(L)=0.0D0
RV1(K)=F
W(K)=X
48 CONTINUE
3 CONTINUE
49 CONTINUE
DEALLOCATE(RV1)
*
* Sort the data from highest to lowest singular value
ALLOCATE(RV1(M),RV2(N))
DO I=1,NP
DO J=1,NP-I
IF(W(J).LE.W(J+1)) THEN
RV0=W(J)
RV1(:M)=A(:M,J)
RV2(:N)=V(:N,J)
W(J)=W(J+1)
A(:M,J)=A(:M,J+1)
V(:N,J)=V(:N,J+1)
W(J+1)=RV0
A(:M,J+1)=RV1(:M)
V(:N,J+1)=RV2(:N)
ENDIF
ENDDO
ENDDO
DEALLOCATE(RV2,RV1)
RETURN
END
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