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FUNCTION CCuij(UU,VV)
C ===============================================================
C Correlation coefficient between two (3x3) anisotropic
C displacement matrices Uij and Vij.
C See Merritt (1999) Acta Crystallographica D55, 1997-2004.
C Return 0 if any of the tensors involved are NPD
C ===============================================================
REAL CCuij V3VINV
REAL UU(3,3), VV(3,3), WW(3,3), UI(3,3), VI(3,3), WI(3,3)
REAL DUI, DVI, DWI
DUI = 1. / V3INV(UI,UU)
DVI = 1. / V3INV(VI,VV)
C Sylvester's criterion for NPD tensor
IF (DUI.LE.0 .OR. UU(1,1).LE.0
& .OR. (UU(1,1)*UU(2,2)-UU(1,2)*UU(2,1)).LE.0) THEN
CCuij = 0
RETURN
ENDIF
IF (DVI.LE.0 .OR. VV(1,1).LE.0
& .OR. (VV(1,1)*VV(2,2)-VV(1,2)*VV(2,1)).LE.0) THEN
CCuij = 0
RETURN
ENDIF
CALL M3ADD(WI,UI,VI)
DWI = V3INV(WW,WI)
IF (DWI.LE.0 .OR. WW(1,1).LE.0
& .OR. (WW(1,1)*WW(2,2)-WW(1,2)*WW(2,1)).LE.0) THEN
CCuij = 0
RETURN
ENDIF
CCuij = sqrt(sqrt(DUI*DVI))
& / sqrt(0.125*DWI)
RETURN
END
FUNCTION CCuv(U,V)
C ===============================================================
C Wrapper for CCuij()
C ===============================================================
REAL CCuv, CCuij
REAL U(6), V(6)
REAL UU(3,3), VV(3,3)
UU(1,1) = U(1)
UU(2,2) = U(2)
UU(3,3) = U(3)
UU(1,2) = U(4)
UU(2,1) = U(4)
UU(1,3) = U(5)
UU(3,1) = U(5)
UU(2,3) = U(6)
UU(3,2) = U(6)
VV(1,1) = V(1)
VV(2,2) = V(2)
VV(3,3) = V(3)
VV(1,2) = V(4)
VV(2,1) = V(4)
VV(1,3) = V(5)
VV(3,1) = V(5)
VV(2,3) = V(6)
VV(3,2) = V(6)
CCuv = CCuij(UU,VV)
RETURN
END
FUNCTION Suv(U,V)
C ===============================================================
C Normalized correlation coefficient ("similarity") between two
C anisotropic displacement vectors Uij and Vij.
C See Merritt (1999) Acta Crystallographica D55, 1997-2004.
C ===============================================================
REAL Suv, CCuij
REAL U(6), V(6)
REAL UU(3,3), VV(3,3), Uiso(3,3), Viso(3,3), WW(3,3)
REAL Ueq, Veq
UU(1,1) = U(1)
UU(2,2) = U(2)
UU(3,3) = U(3)
UU(1,2) = U(4)
UU(2,1) = U(4)
UU(1,3) = U(5)
UU(3,1) = U(5)
UU(2,3) = U(6)
UU(3,2) = U(6)
VV(1,1) = V(1)
VV(2,2) = V(2)
VV(3,3) = V(3)
VV(1,2) = V(4)
VV(2,1) = V(4)
VV(1,3) = V(5)
VV(3,1) = V(5)
VV(2,3) = V(6)
VV(3,2) = V(6)
Ueq = (UU(1,1) + UU(2,2) + UU(3,3)) / 3.
Veq = (VV(1,1) + VV(2,2) + VV(3,3)) / 3.
DO I = 1,3
DO J = 1,3
WW(I,J) = VV(I,J) * Ueq / Veq
Uiso(I,J) = 0
Viso(I,J) = 0
ENDDO
ENDDO
DO I = 1,3
Uiso(I,I) = Ueq
Viso(I,I) = Veq
ENDDO
Suv_top = CCuij(UU,WW)
Suv_bot = (CCuij(UU,Uiso) * CCuij(VV,Viso))
if (Suv_top.eq.0 .or. Suv_bot.eq.0) then
Suv = 0
else
Suv = Suv_top / Suv_bot
endif
RETURN
END
C =======================================================
C The rest of the file is just generic 3x3 matrix algebra
C =======================================================
SUBROUTINE V3CROSS(B,C,A)
C CROSS PRODUCT OF TWO VECTORS
C =======================
REAL A(3),B(3),C(3)
A(1)=B(2)*C(3)-C(2)*B(3)
A(2)=B(3)*C(1)-C(3)*B(1)
A(3)=B(1)*C(2)-C(1)*B(2)
RETURN
END
C
FUNCTION V3DOT(A,B)
C DOT PRODUCT OF TWO VECTORS
C ================
REAL A(3),B(3)
V3DOT=A(1)*B(1)+A(2)*B(2)+A(3)*B(3)
RETURN
END
C
SUBROUTINE M3ADD(A,B,C)
C A=B+C
C ========================
REAL A(3,3),B(3,3),C(3,3)
DO I=1,3
DO J=1,3
A(I,J) = B(I,J) + C(I,J)
ENDDO
ENDDO
RETURN
END
C
SUBROUTINE M3MUL(A,B,C)
C A=B*C
C ========================
REAL A(3,3),B(3,3),C(3,3),S
DO I=1,3
DO J=1,3
S=0
DO K=1,3
S=S+B(I,K)*C(K,J)
ENDDO
A(I,J)=S
ENDDO
ENDDO
RETURN
END
C
FUNCTION V3INV(A,B)
C INVERT A GENERAL 3X3 MATRIX AND RETURN DETERMINANT
C A=(B)-1
C ======================
REAL A(3,3),B(3,3),C(3,3),D
CALL V3CROSS(B(1,2),B(1,3),C(1,1))
CALL V3CROSS(B(1,3),B(1,1),C(1,2))
CALL V3CROSS(B(1,1),B(1,2),C(1,3))
D=V3DOT(B(1,1),C(1,1))
IF (ABS(D).LE.1.E-30) THEN
V3INV=0.0
RETURN
ENDIF
DO I=1,3
DO J=1,3
A(I,J)=C(J,I)/D
ENDDO
ENDDO
V3INV=D
RETURN
END
C
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