mirror of
https://github.com/wassname/simpeg.git
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Rowan Cockett
99 lines
2.2 KiB
Python
99 lines
2.2 KiB
Python
from scipy import sparse as sp
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from utils import mkvc
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def sdiag(h):
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"""Sparse diagonal matrix"""
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return sp.spdiags(mkvc(h), 0, h.size, h.size, format="csr")
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def speye(n):
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"""Sparse identity"""
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return sp.identity(n, format="csr")
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def kron3(A, B, C):
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"""Three kron prods"""
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return sp.kron(sp.kron(A, B), C, format="csr")
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def spzeros(n1, n2):
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"""spzeros"""
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return sp.coo_matrix((n1, n2)).tocsr()
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def inv3X3BlockDiagonal(a11, a12, a13, a21, a22, a23, a31, a32, a33):
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""" B = inv3X3BlockDiagonal(a11, a12, a13, a21, a22, a23, a31, a32, a33)
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inverts a stack of 3x3 matrices
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Input:
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A - a11, a12, a13, a21, a22, a23, a31, a32, a33
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Output:
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B - inverse
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"""
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a11 = mkvc(a11)
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a12 = mkvc(a12)
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a13 = mkvc(a13)
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a21 = mkvc(a21)
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a22 = mkvc(a22)
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a23 = mkvc(a23)
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a31 = mkvc(a31)
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a32 = mkvc(a32)
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a33 = mkvc(a33)
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detA = a31*a12*a23 - a31*a13*a22 - a21*a12*a33 + a21*a13*a32 + a11*a22*a33 - a11*a23*a32
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b11 = +(a22*a33 - a23*a32)/detA
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b12 = -(a12*a33 - a13*a32)/detA
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b13 = +(a12*a23 - a13*a22)/detA
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b21 = +(a31*a23 - a21*a33)/detA
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b22 = -(a31*a13 - a11*a33)/detA
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b23 = +(a21*a13 - a11*a23)/detA
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b31 = -(a31*a22 - a21*a32)/detA
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b32 = +(a31*a12 - a11*a32)/detA
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b33 = -(a21*a12 - a11*a22)/detA
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B = sp.vstack((sp.hstack((sdiag(b11), sdiag(b12), sdiag(b13))),
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sp.hstack((sdiag(b21), sdiag(b22), sdiag(b23))),
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sp.hstack((sdiag(b31), sdiag(b32), sdiag(b33)))))
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return B
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def inv2X2BlockDiagonal(a11, a12, a21, a22):
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""" B = inv2X2BlockDiagonal(a11, a12, a21, a22)
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Inverts a stack of 2x2 matrices by using the inversion formula
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inv(A) = (1/det(A)) * cof(A)^T
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Input:
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A - a11, a12, a13, a21, a22, a23, a31, a32, a33
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Output:
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B - inverse
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"""
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a11 = mkvc(a11)
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a12 = mkvc(a12)
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a21 = mkvc(a21)
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a22 = mkvc(a22)
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# compute inverse of the determinant.
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detAinv = 1./(a11*a22 - a21*a12)
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b11 = +detAinv*a22
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b12 = -detAinv*a12
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b21 = -detAinv*a21
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b22 = +detAinv*a11
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B = sp.vstack((sp.hstack((sdiag(b11), sdiag(b12))),
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sp.hstack((sdiag(b21), sdiag(b22)))))
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return B
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