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************************************************************************* |
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* |
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* Subroutine inter_B_inner.f |
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* |
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* it computes the magnetic field in a chosen point x,y,z inside the |
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* magnetic cavity, using a trilinear interpolation of |
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* B field measurements (read before by means of ./read_B.f) |
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* the value is computed for two different inner maps and then averaged |
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* |
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* needs: |
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* - ../common/common_B_inner.f |
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* |
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* input: coordinates in m |
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* output: magnetic field in T |
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* |
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************************************************************************* |
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|
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subroutine inter_B_inner(x,y,z,res) !coordinates in m, magnetic field in T |
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implicit double precision (a-h,o-z) |
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include './common_B_inner.for' |
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c------------------------------------------------------------------------ |
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c |
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c local variables |
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c |
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c------------------------------------------------------------------------ |
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|
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real*8 x,y,z !point of interpolation |
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real*8 res(3) !interpolated B components: res = (Bx, By, Bz) |
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real*8 res1(3),res2(3) !interpolated B components for the two maps |
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|
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integer ic !index for B components: |
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! ic=1 ---> Bx |
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! ic=2 ---> By |
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! ic=3 ---> Bz |
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|
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integer cube(3) !vector of indexes identifying the cube |
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! containing the point of interpolation |
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! (see later...) |
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real*8 xl,xh,yl,yh,zl,zh !cube vertexes coordinates |
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real*8 xr,yr,zr !reduced variables (coordinates of the |
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! point of interpolation inside the cube) |
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|
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real*8 Bp(8) !vector of values of B component |
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! being computed, on the eight cube vertexes |
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c------------------------------------------------------------------------ |
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c |
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c *** FIRST MAP *** |
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c |
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c------------------------------------------------------------------------ |
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do ic=1,3 !loops on the three B components |
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c------------------------------------------------------------------------ |
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c |
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c chooses the coordinates interval containing the input point |
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c |
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c------------------------------------------------------------------------ |
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c e.g.: |
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c |
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c x1 x2 x3 x4 x5... |
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c |-----|-+---|-----|-----|---- |
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c ~~~~~~~~x |
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c |
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c in this case the right interval is identified by indexes 2-3, so the |
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c value assigned to cube variable is 2 |
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|
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cube(1)=INT((nx-1)*(x-px1min(ic))/(px1max(ic)-px1min(ic))) +1 |
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cube(2)=INT((ny-1)*(y-py1min(ic))/(py1max(ic)-py1min(ic))) +1 |
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cube(3)=INT((nz-1)*(z-pz1min(ic))/(pz1max(ic)-pz1min(ic))) +1 |
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|
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c------------------------------------------------------------------------ |
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c |
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c if the point falls beyond the extremes of the grid... |
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c |
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c------------------------------------------------------------------------ |
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c |
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c ~~~~~~~~~~x1 x2 x3... |
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c - - + - - |-----|-----|---- |
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c ~~~~x |
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c |
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c in the case cube = 1 |
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c |
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c |
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c ...nx-2 nx-1 nx |
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c ----|-----|-----| - - - + - - |
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c ~~~~~~~~~~~~~~~~~~~~~~~~x |
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c |
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c in this case cube = nx-1 |
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if (cube(1).le.0) cube(1) = 1 |
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if (cube(2).le.0) cube(2) = 1 |
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if (cube(3).le.0) cube(3) = 1 |
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if (cube(1).ge.nx) cube(1) = nx-1 |
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if (cube(2).ge.ny) cube(2) = ny-1 |
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if (cube(3).ge.nz) cube(3) = nz-1 |
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|
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c------------------------------------------------------------------------ |
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c |
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c temporary variables definition for field computation |
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c |
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c------------------------------------------------------------------------ |
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xl = px1(cube(1),ic) !X coordinates of cube vertexes |
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xh = px1(cube(1)+1,ic) |
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yl = py1(cube(2),ic) !Y coordinates of cube vertexes |
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yh = py1(cube(2)+1,ic) |
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zl = pz1(cube(3),ic) !Z coordinates of cube vertexes |
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zh = pz1(cube(3)+1,ic) |
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xr = (x-xl) / (xh-xl) !reduced variables |
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yr = (y-yl) / (yh-yl) |
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zr = (z-zl) / (zh-zl) |
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Bp(1) = b1(cube(1) ,cube(2) ,cube(3) ,ic) !ic-th component of B |
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Bp(2) = b1(cube(1)+1,cube(2) ,cube(3) ,ic) ! on the eight cube |
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Bp(3) = b1(cube(1) ,cube(2)+1,cube(3) ,ic) ! vertexes |
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Bp(4) = b1(cube(1)+1,cube(2)+1,cube(3) ,ic) |
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Bp(5) = b1(cube(1) ,cube(2) ,cube(3)+1,ic) |
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Bp(6) = b1(cube(1)+1,cube(2) ,cube(3)+1,ic) |
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Bp(7) = b1(cube(1) ,cube(2)+1,cube(3)+1,ic) |
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Bp(8) = b1(cube(1)+1,cube(2)+1,cube(3)+1,ic) |
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|
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c------------------------------------------------------------------------ |
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c |
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c computes interpolated ic-th component of B in (x,y,z) |
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c |
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c------------------------------------------------------------------------ |
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res1(ic) = |
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+ Bp(1)*(1-xr)*(1-yr)*(1-zr) + |
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+ Bp(2)*xr*(1-yr)*(1-zr) + |
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+ Bp(3)*(1-xr)*yr*(1-zr) + |
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+ Bp(4)*xr*yr*(1-zr) + |
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+ Bp(5)*(1-xr)*(1-yr)*zr + |
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+ Bp(6)*xr*(1-yr)*zr + |
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+ Bp(7)*(1-xr)*yr*zr + |
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+ Bp(8)*xr*yr*zr |
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enddo |
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c------------------------------------------------------------------------ |
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c |
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c *** SECOND MAP *** |
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c |
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c------------------------------------------------------------------------ |
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c second map is rotated by 180 degree along the Z axis. so change sign |
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c of x and y coordinates and then change sign to Bx and By components |
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c to obtain the correct result |
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x=-x |
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y=-y |
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do ic=1,3 |
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cube(1)=INT((nx-1)*(x-px2min(ic))/(px2max(ic)-px2min(ic))) +1 |
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cube(2)=INT((ny-1)*(y-py2min(ic))/(py2max(ic)-py2min(ic))) +1 |
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cube(3)=INT((nz-1)*(z-pz2min(ic))/(pz2max(ic)-pz2min(ic))) +1 |
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if (cube(1).le.0) cube(1) = 1 |
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if (cube(2).le.0) cube(2) = 1 |
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if (cube(3).le.0) cube(3) = 1 |
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if (cube(1).ge.nx) cube(1) = nx-1 |
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if (cube(2).ge.ny) cube(2) = ny-1 |
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if (cube(3).ge.nz) cube(3) = nz-1 |
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xl = px2(cube(1),ic) |
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xh = px2(cube(1)+1,ic) |
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yl = py2(cube(2),ic) |
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yh = py2(cube(2)+1,ic) |
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zl = pz2(cube(3),ic) |
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zh = pz2(cube(3)+1,ic) |
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xr = (x-xl) / (xh-xl) |
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yr = (y-yl) / (yh-yl) |
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zr = (z-zl) / (zh-zl) |
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Bp(1) = b2(cube(1) ,cube(2) ,cube(3) ,ic) |
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Bp(2) = b2(cube(1)+1,cube(2) ,cube(3) ,ic) |
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Bp(3) = b2(cube(1) ,cube(2)+1,cube(3) ,ic) |
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Bp(4) = b2(cube(1)+1,cube(2)+1,cube(3) ,ic) |
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Bp(5) = b2(cube(1) ,cube(2) ,cube(3)+1,ic) |
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Bp(6) = b2(cube(1)+1,cube(2) ,cube(3)+1,ic) |
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Bp(7) = b2(cube(1) ,cube(2)+1,cube(3)+1,ic) |
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Bp(8) = b2(cube(1)+1,cube(2)+1,cube(3)+1,ic) |
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res2(ic) = |
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+ Bp(1)*(1-xr)*(1-yr)*(1-zr) + |
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+ Bp(2)*xr*(1-yr)*(1-zr) + |
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+ Bp(3)*(1-xr)*yr*(1-zr) + |
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+ Bp(4)*xr*yr*(1-zr) + |
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+ Bp(5)*(1-xr)*(1-yr)*zr + |
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+ Bp(6)*xr*(1-yr)*zr + |
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+ Bp(7)*(1-xr)*yr*zr + |
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+ Bp(8)*xr*yr*zr |
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enddo |
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c change Bx and By components sign |
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res2(1)=-res2(1) |
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res2(2)=-res2(2) |
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c change back the x and y coordinate signs |
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x=-x |
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y=-y |
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c------------------------------------------------------------------------ |
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c |
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c average the two maps results |
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c |
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c------------------------------------------------------------------------ |
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do ic=1,3 |
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res(ic)=(res1(ic)+res2(ic))/2 |
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enddo |
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|
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return |
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end |
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