def _fastInnerProductDeriv(self, projType, prop, invProp=False, invMat=False): """ :param str projType: 'E' or 'F' :param TensorType tensorType: type of the tensor :param bool invProp: inverts the material property :param bool invMat: inverts the matrix :rtype: function :return: dMdmu, the derivative of the inner product matrix """ assert projType in [ 'F', 'E' ], "projType must be 'F' for faces or 'E' for edges" tensorType = Utils.TensorType(self, prop) dMdprop = None if invMat: MI = self._fastInnerProduct(projType, prop, invProp=invProp, invMat=invMat) if tensorType == 0: Av = getattr(self, 'ave' + projType + '2CC') V = Utils.sdiag(self.vol) ones = sp.csr_matrix( (np.ones(self.nC), (range(self.nC), np.zeros(self.nC))), shape=(self.nC, 1)) if not invMat and not invProp: dMdprop = self.dim * Av.T * V * ones elif invMat and invProp: dMdprop = self.dim * Utils.sdiag( MI.diagonal()**2) * Av.T * V * ones * Utils.sdiag( 1. / prop**2) if tensorType == 1: Av = getattr(self, 'ave' + projType + '2CC') V = Utils.sdiag(self.vol) if not invMat and not invProp: dMdprop = self.dim * Av.T * V elif invMat and invProp: dMdprop = self.dim * Utils.sdiag( MI.diagonal()**2) * Av.T * V * Utils.sdiag(1. / prop**2) if tensorType == 2: # anisotropic Av = getattr(self, 'ave' + projType + '2CCV') V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol)) if not invMat and not invProp: dMdprop = Av.T * V elif invMat and invProp: dMdprop = Utils.sdiag(MI.diagonal()** 2) * Av.T * V * Utils.sdiag(1. / prop**2) if dMdprop is not None: def innerProductDeriv(v=None): if v is None: print 'Depreciation Warning: TensorMesh.innerProductDeriv. You should be supplying a vector. Use: sdiag(u)*dMdprop' return dMdprop return Utils.sdiag(v) * dMdprop return innerProductDeriv else: return None
def _fastInnerProductDeriv(self, projType, prop, invProp=False, invMat=False): """ :param str projType: 'E' or 'F' :param TensorType tensorType: type of the tensor :param bool invProp: inverts the material property :param bool invMat: inverts the matrix :rtype: function :return: dMdmu, the derivative of the inner product matrix """ assert projType in ['F', 'E'], ("projType must be 'F' for faces or 'E'" " for edges") tensorType = Utils.TensorType(self, prop) dMdprop = None if invMat or invProp: MI = self._fastInnerProduct(projType, prop, invProp=invProp, invMat=invMat) # number of elements we are averaging (equals dim for regular # meshes, but for cyl, where we use symmetry, it is 1 for edge # variables and 2 for face variables) if self._meshType == 'CYL': n_elements = np.sum(getattr(self, 'vn'+projType).nonzero()) else: n_elements = self.dim if tensorType == 0: # isotropic, constant Av = getattr(self, 'ave'+projType+'2CC') V = Utils.sdiag(self.vol) ones = sp.csr_matrix((np.ones(self.nC), (range(self.nC), np.zeros(self.nC))), shape=(self.nC, 1)) if not invMat and not invProp: dMdprop = n_elements * Av.T * V * ones elif invMat and invProp: dMdprop = n_elements * (Utils.sdiag(MI.diagonal()**2) * Av.T * V * ones * Utils.sdiag(1./prop**2)) elif invProp: dMdprop = n_elements * Av.T * V * Utils.sdiag(- 1./prop**2) elif invMat: dMdprop = n_elements * (Utils.sdiag(- MI.diagonal()**2) * Av.T * V) elif tensorType == 1: # isotropic, variable in space Av = getattr(self, 'ave'+projType+'2CC') V = Utils.sdiag(self.vol) if not invMat and not invProp: dMdprop = n_elements * Av.T * V elif invMat and invProp: dMdprop = n_elements * (Utils.sdiag(MI.diagonal()**2) * Av.T * V * Utils.sdiag(1./prop**2)) elif invProp: dMdprop = n_elements * Av.T * V * Utils.sdiag(-1./prop**2) elif invMat: dMdprop = n_elements * (Utils.sdiag(- MI.diagonal()**2) * Av.T * V) elif tensorType == 2: # anisotropic Av = getattr(self, 'ave'+projType+'2CCV') V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol)) if self._meshType == 'CYL': Zero = sp.csr_matrix((self.nC, self.nC)) Eye = sp.eye(self.nC) if projType == 'E': P = sp.hstack([Zero, Eye, Zero]) # print P.todense() elif projType == 'F': P = sp.vstack([sp.hstack([Eye, Zero, Zero]), sp.hstack([Zero, Zero, Eye])]) # print P.todense() else: P = sp.eye(self.nC*self.dim) if not invMat and not invProp: dMdprop = Av.T * P * V elif invMat and invProp: dMdprop = (Utils.sdiag(MI.diagonal()**2) * Av.T * P * V * Utils.sdiag(1./prop**2)) elif invProp: dMdprop = Av.T * P * V * Utils.sdiag(-1./prop**2) elif invMat: dMdprop = Utils.sdiag(- MI.diagonal()**2) * Av.T * P * V if dMdprop is not None: def innerProductDeriv(v=None): if v is None: warnings.warn("Depreciation Warning: " "TensorMesh.innerProductDeriv." " You should be supplying a vector. " "Use: sdiag(u)*dMdprop", FutureWarning) return dMdprop return Utils.sdiag(v) * dMdprop return innerProductDeriv else: return None