copied fortran code
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Martin Diehl
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@ -9,6 +9,150 @@ import damask
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scriptName = os.path.splitext(os.path.basename(__file__))[0]
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scriptName = os.path.splitext(os.path.basename(__file__))[0]
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scriptID = ' '.join([scriptName,damask.version])
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scriptID = ' '.join([scriptName,damask.version])
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def volTetrahedron(vertices=None, sides=None):
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"""
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Return the volume of the tetrahedron with given vertices or sides. If
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vertices are given they must be in a NumPy array with shape (4,3): the
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position vectors of the 4 vertices in 3 dimensions; if the six sides are
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given, they must be an array of length 6. If both are given, the sides
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will be used in the calculation.
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This method implements
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Tartaglia's formula using the Cayley-Menger determinant:
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|0 1 1 1 1 |
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|1 0 s1^2 s2^2 s3^2|
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288 V^2 = |1 s1^2 0 s4^2 s5^2|
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|1 s2^2 s4^2 0 s6^2|
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|1 s3^2 s5^2 s6^2 0 |
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where s1, s2, ..., s6 are the tetrahedron side lengths.
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from http://codereview.stackexchange.com/questions/77593/calculating-the-volume-of-a-tetrahedron
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"""
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# The indexes of rows in the vertices array corresponding to all
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# possible pairs of vertices
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vertex_pair_indexes = np.array(((0, 1), (0, 2), (0, 3),
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(1, 2), (1, 3), (2, 3)))
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# Get all the squares of all side lengths from the differences between
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# the 6 different pairs of vertex positions
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vertex1, vertex2 = vertex_pair_indexes[:,0], vertex_pair_indexes[:,1]
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sides_squared = np.sum((vertices[vertex1] - vertices[vertex2])**2,axis=-1)
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# Set up the Cayley-Menger determinant
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M = np.zeros((5,5))
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# Fill in the upper triangle of the matrix
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M[0,1:] = 1
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# The squared-side length elements can be indexed using the vertex
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# pair indices (compare with the determinant illustrated above)
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M[tuple(zip(*(vertex_pair_indexes + 1)))] = sides_squared
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# The matrix is symmetric, so we can fill in the lower triangle by
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# adding the transpose
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M = M + M.T
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return np.sqrt(det / 288)
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def mesh_volumeMismatch(size,F,nodes):
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"""
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calculates the mismatch between volume of reconstructed (compatible) cube and
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determinant of defgrad at the FP
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"""
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real(pReal), intent(in), dimension(:,:,:,:,:) :: &
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F
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real(pReal), dimension(size(F,3),size(F,4),size(F,5)) :: &
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vMismatch
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real(pReal), intent(in), dimension(:,:,:,:) :: &
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nodes
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real(pReal), dimension(3,8) :: coords
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volInitial = size.prod()/grid.prod()
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#--------------------------------------------------------------------------------------------------
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# calculate actual volume and volume resulting from deformation gradient
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for k in xrange(grid[2]):
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for j in xrange(grid[1]):
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for i in xrange(grid[0]):
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coords(0:3,0) = nodes[0:3,i, j, k ]
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coords(0:3,1) = nodes[0:3,i+1,j, k ]
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coords(0:3,2) = nodes[0:3,i+1,j+1,k ]
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coords(0:3,3) = nodes[0:3,i, j+1,k ]
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coords(0:3,4) = nodes[0:3,i, j, k+1]
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coords(0:3,5) = nodes[0:3,i+1,j, k+1]
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coords(0:3,6) = nodes[0:3,i+1,j+1,k+1]
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coords(0:3,7) = nodes[0:3,i, j+1,k+1]
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vMismatch[i,j,k] = &
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abs(volTetrahedron(coords[0:3,6],coords[0:3,0],coords[0:3,7],coords[0:3,3])) &
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+ abs(volTetrahedron(coords[0:3,6],coords[0:3,0],coords[0:3,7],coords[0:3,4])) &
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+ abs(volTetrahedron(coords[0:3,6],coords[0:3,0],coords[0:3,2],coords[0:3,3])) &
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+ abs(volTetrahedron(coords[0:3,6],coords[0:3,0],coords[0:3,2],coords[0:3,1])) &
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+ abs(volTetrahedron(coords[0:3,6],coords[0:3,4],coords[0:3,1],coords[0:3,5])) &
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+ abs(volTetrahedron(coords[0:3,6],coords[0:3,4],coords[0:3,1],coords[0:3,0]))
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vMismatch[i,j,k] = vMismatch[i,j,k]/math_det33(F(1:3,1:3,i,j,k))
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enddo; enddo; enddo
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return vMismatch/volInitial
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def mesh_shapeMismatch(gDim,F,nodes,centres):
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"""
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Routine to calculate the mismatch between the vectors from the central point to
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the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
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the initial volume element with the current deformation gradient
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"""
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implicit none
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real(pReal), intent(in), dimension(:,:,:,:,:) :: &
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F
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real(pReal), dimension(size(F,3),size(F,4),size(F,5)) :: &
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sMismatch
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real(pReal), intent(in), dimension(:,:,:,:) :: &
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nodes, &
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centres
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real(pReal), dimension(3,8) :: coordsInitial
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integer(pInt) i,j,k
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!--------------------------------------------------------------------------------------------------
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! initial positions
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coordsInitial(1:3,1) = [-gDim(1)/fRes(1),-gDim(2)/fRes(2),-gDim(3)/fRes(3)]
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coordsInitial(1:3,2) = [+gDim(1)/fRes(1),-gDim(2)/fRes(2),-gDim(3)/fRes(3)]
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coordsInitial(1:3,3) = [+gDim(1)/fRes(1),+gDim(2)/fRes(2),-gDim(3)/fRes(3)]
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coordsInitial(1:3,4) = [-gDim(1)/fRes(1),+gDim(2)/fRes(2),-gDim(3)/fRes(3)]
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coordsInitial(1:3,5) = [-gDim(1)/fRes(1),-gDim(2)/fRes(2),+gDim(3)/fRes(3)]
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coordsInitial(1:3,6) = [+gDim(1)/fRes(1),-gDim(2)/fRes(2),+gDim(3)/fRes(3)]
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coordsInitial(1:3,7) = [+gDim(1)/fRes(1),+gDim(2)/fRes(2),+gDim(3)/fRes(3)]
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coordsInitial(1:3,8) = [-gDim(1)/fRes(1),+gDim(2)/fRes(2),+gDim(3)/fRes(3)]
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coordsInitial = coordsInitial/2.0_pReal
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!--------------------------------------------------------------------------------------------------
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! compare deformed original and deformed positions to actual positions
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do k = 1_pInt,iRes(3)
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do j = 1_pInt,iRes(2)
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do i = 1_pInt,iRes(1)
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sMismatch(i,j,k) = &
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sqrt(sum((nodes(1:3,i, j, k ) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,1)))**2.0_pReal))&
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+ sqrt(sum((nodes(1:3,i+1_pInt,j, k ) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,2)))**2.0_pReal))&
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+ sqrt(sum((nodes(1:3,i+1_pInt,j+1_pInt,k ) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,3)))**2.0_pReal))&
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+ sqrt(sum((nodes(1:3,i, j+1_pInt,k ) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,4)))**2.0_pReal))&
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+ sqrt(sum((nodes(1:3,i, j, k+1_pInt) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,5)))**2.0_pReal))&
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+ sqrt(sum((nodes(1:3,i+1_pInt,j, k+1_pInt) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,6)))**2.0_pReal))&
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+ sqrt(sum((nodes(1:3,i+1_pInt,j+1_pInt,k+1_pInt) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,7)))**2.0_pReal))&
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+ sqrt(sum((nodes(1:3,i, j+1_pInt,k+1_pInt) - centres(1:3,i,j,k)&
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- math_mul33x3(F(1:3,1:3,i,j,k), coordsInitial(1:3,8)))**2.0_pReal))
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enddo; enddo; enddo
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return sMismatch
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# --------------------------------------------------------------------
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# --------------------------------------------------------------------
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# MAIN
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# MAIN
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# --------------------------------------------------------------------
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# --------------------------------------------------------------------
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@ -117,7 +261,6 @@ for name in filenames:
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idx += 1
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idx += 1
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F[0:3,0:3,x,y,z] = np.array(map(float,table.data[column:column+9]),'d').reshape(3,3)
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F[0:3,0:3,x,y,z] = np.array(map(float,table.data[column:column+9]),'d').reshape(3,3)
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Favg = damask.core.math.tensorAvg(F)
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centres = damask.core.mesh.deformedCoordsFFT(size,F,Favg,[1.0,1.0,1.0])
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centres = damask.core.mesh.deformedCoordsFFT(size,F,Favg,[1.0,1.0,1.0])
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nodes = damask.core.mesh.nodesAroundCentres(size,Favg,centres)
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nodes = damask.core.mesh.nodesAroundCentres(size,Favg,centres)
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