def gen_hkl(bound, mt_tensor): m = 1.0 * bound h = math.ceil(math.sqrt(m / mt_tensor[0][0])) k = math.ceil(math.sqrt(m / mt_tensor[1][1])) l = math.ceil(math.sqrt(m / mt_tensor[2][2])) print h, k, l, "\n" x_csl = np.arange(-h, h + 1, 1.0) y_csl = np.arange(-k, k + 1, 1.0) z_csl = np.arange(-l, l + 1, 1.0) num_mi = np.size(x_csl) * np.size(y_csl) * np.size(z_csl) xx_csl, yy_csl, zz_csl = np.meshgrid(x_csl, y_csl, z_csl, indexing="xy") xx_csl, yy_csl, zz_csl = xx_csl.reshape(1, num_mi)[0], yy_csl.reshape(1, num_mi)[0], zz_csl.reshape(1, num_mi)[0] mil_ind = np.column_stack([xx_csl, yy_csl, zz_csl]) ind = np.where((mil_ind[:, 0] == 0) & (mil_ind[:, 1] == 0) & (mil_ind[:, 2] == 0))[0][0] ### deleting (0 0 0) mil_ind = np.delete(mil_ind, ind, 0) ### finding the unique miller indices mil_ind = GBim.int_finder(mil_ind, tol=1e-06, order="rows") mil_ind_csl = GBt.unique_rows_tol(mil_ind, tol=1e-06) ### Antipodal symmetry (h k l) ~ (-h -k -l) return mil_ind_csl
def csl_area_sort(bpn, l_rcsl_go, mt_cslr_go, return_hkl=False): mil_sphr = np.dot(np.linalg.inv(l_rcsl_go), bpn.transpose()).transpose() mil_sphr = GBim.int_finder(mil_sphr, tol=1e-06, order="rows") # mil_sphr = GBt.unique_rows_tol(mil_sphr, tol=1e-06) d_inv_sqr = np.diag(np.dot(np.dot(mil_sphr, mt_cslr_go), mil_sphr.transpose())) d_inv = np.sqrt(d_inv_sqr) ind_d_inv_sort = np.argsort(d_inv) # bpn = GBt.unique_rows_tol(bpn[ind_d_inv_sort], tol=1e-04) bpn_sort = bpn[ind_d_inv_sort] mil_sort = mil_sphr[ind_d_inv_sort] if return_hkl == True: return bpn_sort, mil_sort else: return bpn_sort
def test_int_finder(): """ Test cases for the int_finder function in integer_manipulations """ Mat = np.zeros(3, dtype=[('Matrix', '(3,3)float64'), ('row', '(1,3)float64'), ('col', '(3,1)float64')]) Mat['Matrix'][0] = np.array(([1.5, 2, 3.0e-7], [-4, 5, 6], [7, 2.0e-5, 1.0e-5])) Mat['Matrix'][1] = np.array(([1.5, 2, 3e-6], [-4, 0, 6], [3.5, -2e-6, 1e-6])) Mat['Matrix'][2] = np.array(([1.5, 2, 3e-7], [-4, 5, 6], [3.5, -2e-6, 1e-6])) Mat['row'][0] = np.array(([1.5e-7, 0, 3e-6])) Mat['row'][1] = np.array(([1.5e-7, 1, 3e-6])) Mat['row'][2] = np.array(([1.5, 4, 3e-7])) Mat['col'][0] = np.array(([1.5e-7], [0], [3e-6])) Mat['col'][1] = np.array(([1.5e-7], [1], [3e-6])) Mat['col'][2] = np.array(([1.5], [4], [3e-7])) order = np.zeros(2, 'a4') order = ['rows', 'col'] cnt = 0 for j in Mat.dtype.names: for i in range(Mat.shape[0]): for k in range(len(order)): cnt += 1 print('case:', cnt, '\n') print(Mat[j][i], '\n\n', 'order:', order[k], '\nanswer:\n') # a = int_man.int_finder(Mat[j][i], tolerance, order[k]) a = int_man.int_finder(Mat[j][i]) print(a, '\n', '--') a = int_man.int_finder(Mat[j][i], 1.0e-5, 'rows', 1.0e-5) # supposed to fail for cnt == 7? print(a, '\n', '--') a = int_man.int_finder(Mat[j][i], 1e-5, 'rows') print(a, '\n', '--') a = int_man.int_finder(Mat[j][i], 1e-5, 'col') print(a, '\n', '--') a = int_man.int_finder(Mat[j][i], 1e-5, 'columns') print(a, '\n', '--') a = int_man.int_finder(Mat[j][i], 1e-5, order[k], 1e-5) print(a, '\n', '--') print('\n', '-----------------------------------------') print(cnt, ' test cases have been tried.') if __name__ == '__main__': test_int_finder
def gen_miller_ind(mesh_size): """ Returns an array of unique miller indices Parameters ---------- mesh_size: size of the mesh grid to create the indices array * positive integer Returns ------- mil_ind: array of unique miller indices stored row wise * numpy array of size (m x 3) * m is the number of unique indices created for a given mesh_size See Also -------- * GBpy.integer_manipulations.int_finder * GBpy.tools.unique_rows_tol """ ### Creating an array of boundary plane miller indices r = mesh_size x_csl = np.arange(-r, r+1, 1.0) y_csl = np.arange(-r, r+1, 1.0) z_csl = np.arange(-r, r+1, 1.0) num_mi = np.size(x_csl)*np.size(y_csl)*np.size(z_csl) xx_csl, yy_csl, zz_csl = np.meshgrid(x_csl, y_csl, z_csl, indexing='xy') xx_csl, yy_csl, zz_csl = xx_csl.reshape(1, num_mi)[0], yy_csl.reshape(1, num_mi)[0], zz_csl.reshape(1, num_mi)[0] mil_ind = np.column_stack([xx_csl, yy_csl, zz_csl]) ind = np.where((mil_ind[:, 0] == 0) & (mil_ind[:, 1] == 0) & (mil_ind[:, 2] == 0))[0][0] ### deleting (0 0 0) mil_ind = np.delete(mil_ind, ind, 0) ### finding the unique miller indices mil_ind = GBim.int_finder(mil_ind, tol=1e-06, order='rows') mil_ind = GBt.unique_rows_tol(mil_ind) # Try to remove (-h -k -l) for all (h k l) !!! return mil_ind
def pick_ctr(bp, l_rcsl_go, mt_cslr_go, grid_ctr, tol=1e-06): bpn = np.copy(bp) if len(bpn) == 1: return bpn, np.array([]) bpn_sphr = mf.cube2sphr_2d(bpn) mil_sphr = np.dot(np.linalg.inv(l_rcsl_go), bpn_sphr.transpose()).transpose() mil_sphr = GBim.int_finder(mil_sphr, tol=1e-06, order="rows") d_inv_sqr = np.diag(np.dot(np.dot(mil_sphr, mt_cslr_go), mil_sphr.transpose())) d_inv_sqr_min = np.min(d_inv_sqr) cond = np.abs(d_inv_sqr - d_inv_sqr_min) <= tol # ind1 = np.where(cond) bpn_min = bpn[cond] num_bpn_min = len(bpn_min) d_ctr = np.zeros(num_bpn_min) for ct1 in range(num_bpn_min): pt = bpn_min[ct1] d_ctr[ct1] = np.sqrt((grid_ctr[0] - pt[0]) ** 2 + (grid_ctr[1] - pt[1]) ** 2) ind = np.argsort(d_ctr) bpn_pick = bpn_min[ind][0] ind_r = np.where((bpn[:, 0] == bpn_pick[0]) & (bpn[:, 1] == bpn_pick[1]) & (bpn[:, 2] == bpn_pick[2]))[0] return bpn_pick, ind_r
def dsc_finder(L_G2_G1, L_G1_GO1): """ The DSC lattice is computed for the bi-crystal, if the transformation matrix l_g2_g1 is given and the basis vectors of the underlying crystal l_g_go (in the orthogonal reference go frame) are known. The following relationship is used: **The reciprocal of the coincidence site lattice of the reciprocal lattices is the DSC lattice** Parameters ---------------- l_g2_g1: numpy array transformation matrix (r_g1tog2_g1) l_g1_go1: numpy array basis vectors (as columns) of the underlying lattice expressed in the orthogonal 'go' reference frame Returns ------------ l_dsc_g1: numpy array The dsc lattice basis vectors (as columns) expressed in the g1 reference Notes --------- The "Reduced" refer to the use of LLL algorithm to compute a basis that is as close to orthogonal as possible. (Refer to http://en.wikipedia.org/wiki/Lattice_reduction) for further detials on the concept of Lattice Reduction """ L_G2_G1 = np.array(L_G2_G1) L_G1_GO1 = np.array(L_G1_GO1) L_GO1_G1 = np.linalg.inv(L_G1_GO1) # % % Reciprocal lattice of G1 # -------------------------------------------------------------- L_rG1_GO1 = reciprocal_mat(L_G1_GO1) L_GO1_rG1 = np.linalg.inv(L_rG1_GO1) # L_rG1_G1 = np.dot(L_GO1_G1, L_rG1_GO1) # % % L_G1_rG1 = L_rG1_G1^(-1); # % % Reciprocal lattice of G2 L_G2_GO1 = np.dot(L_G1_GO1, L_G2_G1) L_rG2_GO1 = reciprocal_mat(L_G2_GO1) # % % Transformation of the Reciprocal lattices # % % R_rG1TorG2_rG1 = L_rG2_G1*L_G1_rG1; L_rG2_rG1 = np.dot(L_GO1_rG1, L_rG2_GO1) Sigma_star = sigma_calc(L_rG2_rG1) # % % CSL of the reciprocal lattices L_rCSL_rG1 = csl_finder_smith(L_rG2_rG1) L_rCSL_GO1 = np.dot(L_rG1_GO1, L_rCSL_rG1) # % % Reciprocal of the CSL of the reciprocal lattices L_DSC_GO1 = reciprocal_mat(L_rCSL_GO1) L_DSC_G1 = np.dot(L_GO1_G1, L_DSC_GO1) # % % Reduction of the DSC lattice in G1 reference frame DSC_Int = int_man.int_finder(L_DSC_G1, 1e-06) t_ind = np.where(abs(DSC_Int) == abs(DSC_Int).max()) t_ind_1 = t_ind[0][0] t_ind_2 = t_ind[1][0] Mult1 = DSC_Int[t_ind_1, t_ind_2] / L_DSC_G1[t_ind_1, t_ind_2] DSC_Reduced = lll_reduction(DSC_Int) DSC_Reduced = DSC_Reduced / Mult1 L_DSC_G1 = DSC_Reduced # % % % Check this assertion: L_DSC_G1 = [Int_Matrix]/Sigma if int_man.int_check(Sigma_star*L_DSC_G1, 10).all(): L_DSC_G1 = np.around(Sigma_star*L_DSC_G1) / Sigma_star else: raise Exception('L_DSC_G1 is not equal to [Int_Matrix]/Sigma') return L_DSC_G1
def bicryst_planar_den(inds, t_mat, l_g_go, inds_type='miller_index', mat_ref='g1'): """ The function computes the planar densities of the planes 1 and 2 and the two-dimensional CSL Parameters --------------- inds: numpy array The boundary plane indices inds_type: string {'miller_index', 'normal_go', 'normal_g'} t_mat: numpy array Transformation matrix from g1 to g2 in go1 reference frame mat_ref: string {'go1', 'g1'} lattice: Lattice class Attributes of the underlying lattice Returns ----------- pl_den_pl1, pl_den_pl2: numpy array The planar density of planes 1 and 2 pl_den_csl: numpy array The planare density of the two-dimensional CSL """ import GBpy.lattice as lat if isinstance(l_g_go, lat.Lattice): l_g_go = np.array(l_g_go.l_g_go, dtype=np.float64) l_g1_go1 = l_g_go l_rg1_go1 = fcd.reciprocal_mat(l_g1_go1) l_go1_rg1 = np.linalg.inv(l_rg1_go1) if inds_type == 'normal_go': bp1_go1 = inds miller1_inds = int_man.int_finder(np.dot(l_go1_rg1, bp1_go1)) elif inds_type == 'miller_index': miller1_inds = inds elif inds_type == 'normal_g': bp1_g1 = inds l_g1_rg1 = np.dot(l_go1_rg1, l_g1_go1) miller1_inds = int_man.int_finder(np.dot(l_g1_rg1, bp1_g1)) else: raise Exception('Wrong index type') if mat_ref == 'go1': l_2d_csl_g1, l_pl1_g1, l_pl2_g1 = gb_2d_csl(miller1_inds, t_mat, l_g_go, 'miller_index', 'go1') elif mat_ref == 'g1': l_2d_csl_g1, l_pl1_g1, l_pl2_g1 = gb_2d_csl(miller1_inds, t_mat, l_g_go, 'miller_index', 'g1') else: raise Exception('Wrong reference axis type') check_2d_csl(l_pl1_g1, l_pl2_g1, l_2d_csl_g1) pl_den_pl1 = pl_density(l_pl1_g1, l_g1_go1) pl_den_pl2 = pl_density(l_pl2_g1, l_g1_go1) pl_den_csl = pl_density(l_2d_csl_g1, l_g1_go1) return pl_den_pl1, pl_den_pl2, pl_den_csl
def gb_2d_csl(inds, t_mat, l_g_go, inds_type='miller_index', mat_ref='g1'): """ For a given boundary plane normal 'bp1_g1' and the misorientation matrix 't_g1tog2_g1', the two-dimensional CSL lattice is computed Parameters ------------------ inds: numpy array The boundary plane indices inds_type: string {'miller_index', 'normal_go', 'normal_g'} t_mat: numpy array Transformation matrix from g1 to g2 in 'mat_ref' reference frame mat_ref: string {'go1', 'g1'} lattice: Lattice class Attributes of the underlying lattice Returns ----------- l_2d_csl_g1, l_pl1_g1, l_pl2_g1: numpy arrays l_2d_csl_g1 is the 2d CSL in g1 ref frame l_pl1_g1 is the plane 1 basis in g1 ref frame l_pl2_g1 is the plane 2 basis in g1 ref frame """ import GBpy.lattice as lat if isinstance(l_g_go, lat.Lattice): l_g_go = np.array(l_g_go.l_g_go, dtype=np.float64) l_g1_go1 = l_g_go l_go1_g1 = np.linalg.inv(l_g1_go1) l_rg1_go1 = fcd.reciprocal_mat(l_g1_go1) l_go1_rg1 = np.linalg.inv(l_rg1_go1) if inds_type == 'normal_go': bp1_go1 = inds miller1_ind = int_man.int_finder(np.dot(l_go1_rg1, bp1_go1)) elif inds_type == 'miller_index': miller1_ind = inds elif inds_type == 'normal_g': bp1_g1 = inds l_g1_rg1 = np.dot(l_go1_rg1, l_g1_go1) miller1_ind = int_man.int_finder(np.dot(l_g1_rg1, bp1_g1)) else: raise Exception('Wrong index type') if mat_ref == 'go1': t_g1tog2_g1 = np.dot(l_go1_g1, np.dot(t_mat, l_g1_go1)) elif mat_ref == 'g1': t_g1tog2_g1 = t_mat else: raise Exception('Wrong reference axis type') bp1_go1 = int_man.int_finder(np.dot(l_rg1_go1, miller1_ind)) l_g2_g1 = t_g1tog2_g1 l_g2_go1 = np.dot(l_g1_go1, l_g2_g1) l_rg2_go1 = fcd.reciprocal_mat(l_g2_go1) l_go1_rg2 = np.linalg.inv(l_rg2_go1) # bp2_g2 = int_man.int_finder(np.dot(-l_go1_g2, bp1_go1)) miller2_ind = int_man.int_finder(np.dot(-l_go1_rg2, bp1_go1)) l_pl1_g1 = bp_basis(miller1_ind) l_pl2_g2 = bp_basis(miller2_ind) l_pl2_g1 = np.dot(l_g2_g1, l_pl2_g2) l_2d_csl_g1 = csl_finder_2d(l_pl1_g1, l_pl2_g1) return l_2d_csl_g1, l_pl1_g1, l_pl2_g1
def bp_basis(miller_ind): """ The function computes the primitve basis of the plane if the boundary plane indices are specified Parameters --------------- miller_ind: numpy array Miller indices of the plane (h k l) Returns ----------- l_pl_g1: numpy array The primitive basis of the plane in 'g1' reference frame """ miller_ind = int_man.int_finder(miller_ind) miller_ind = int_man.convert_array(miller_ind, dtype=np.int64, check=True) h = miller_ind[0] k = miller_ind[1] l = miller_ind[2] if h == 0 and k == 0 and l == 0: raise Exception('hkl indices cannot all be zero') else: if h != 0 and k != 0 and l != 0: gc_f1_p = gcd(k, l) bv1_g1 = np.array([[0], [-l / gc_f1_p], [k / gc_f1_p]]) bv2_g1 = compute_basis_vec([h, k, l]) else: if h == 0: if k == 0: bv1_g1 = np.array([[1], [0], [0]]) bv2_g1 = np.array([[0], [1], [0]]) elif l == 0: bv1_g1 = np.array([[0], [0], [1]]) bv2_g1 = np.array([[1], [0], [0]]) else: gc_f1_p = gcd(k, l) bv1_g1 = np.array([[0], [-l / gc_f1_p], [k / gc_f1_p]]) bv2_g1 = np.array([[1], [-l / gc_f1_p], [k / gc_f1_p]]) else: if k == 0: if l == 0: bv1_g1 = np.array([[0], [1], [0]]) bv2_g1 = np.array([[0], [0], [1]]) else: gc_f1_p = gcd(h, l) bv1_g1 = np.array([[-l / gc_f1_p], [0], [h / gc_f1_p]]) bv2_g1 = np.array([[-l / gc_f1_p], [1], [h / gc_f1_p]]) else: if l == 0: gc_f1_p = gcd(h, k) bv1_g1 = np.array([[-k / gc_f1_p], [h / gc_f1_p], [0]]) bv2_g1 = np.array([[-k / gc_f1_p], [h / gc_f1_p], [1]]) # The reduced basis vectors for the plane if bv1_g1.dtype == object: bv1_g1 = bv1_g1.ravel().astype(np.float64) # should these be integers? if bv2_g1.dtype == object: bv2_g1 = bv2_g1.ravel().astype(np.float64) # should these be integers? l_pl_g1 = lll_reduction(np.column_stack([bv1_g1, bv2_g1])) return l_pl_g1
def plots(mesh_size, sigma_val, n, lat_type): ### Creating an instance of lattice class elem = GBl.Lattice(lat_type) ### Getting the primitive lattice in orthogonal frame l_g_go = elem.l_g_go ### Creating a meshgrid of boundary plane miller indices in CSL lattice r = mesh_size x_csl = np.arange(-r, r+1, 1.0) y_csl = np.arange(-r, r+1, 1.0) z_csl = np.arange(-r, r+1, 1.0) num_mi = np.size(x_csl)*np.size(y_csl)*np.size(z_csl) xx_csl, yy_csl, zz_csl = np.meshgrid(x_csl, y_csl, z_csl, indexing='xy') xx_csl, yy_csl, zz_csl = xx_csl.reshape(1, num_mi)[0], yy_csl.reshape(1, num_mi)[0], zz_csl.reshape(1, num_mi)[0] mil_ind_csl = np.column_stack([xx_csl, yy_csl, zz_csl]) ind = np.where((mil_ind_csl[:, 0] == 0) & (mil_ind_csl[:, 1] == 0) & (mil_ind_csl[:, 2] == 0))[0][0] mil_ind_csl = np.delete(mil_ind_csl, ind, 0) mil_ind_csl = GBim.int_finder(mil_ind_csl, tol=1e-06, order='rows') mil_ind_csl = GBt.unique_rows_tol(mil_ind_csl) ### Try to remove (-h -k -l) for all (h k l) !!! gb_dir = os.path.dirname(inspect.getfile(GBpy)) pkl_path = gb_dir + '/pkl_files/cF_Id_csl_common_rotations.pkl' pkl_content = pickle.load(open(pkl_path)) sig_mis_N = pkl_content[str(sigma_val)]['N'][0] sig_mis_D = pkl_content[str(sigma_val)]['D'][0] ### Extracting the sigma misorientation from the pickle file ### Misorientation is in the primitive frame of associated lattice sig_mis_g = sig_mis_N/sig_mis_D ### Converting the misorientation to orthogonal frame/superlattice of the crystal ### Done using similarity transformation sig_mis_go = np.dot(np.dot(l_g_go, sig_mis_g), np.linalg.inv(l_g_go)).reshape(1,3,3)[0] ### Getting the csl basis in primitive frame l_csl_g, l_dsc_g = GBfcd.find_csl_dsc(l_g_go, sig_mis_g) ### Converting the csl basis to orthogonal frame l_csl_go = np.dot(l_g_go, l_csl_g) ### reciprocal csl basis in po frame l_rcsl_go = GBfcd.reciprocal_mat(l_csl_go) ### Converting the miller indices to normals in po frame bpn_go = np.dot(l_rcsl_go, mil_ind_csl.transpose()).transpose() ### Finding the boundary plane normals in the fz using five_param_fz bp_fz_norms_go1, bp_symm_grp, symm_grp_ax = five_param_fz(sig_mis_go, bpn_go) ### Finding unique normals bp_fz_norms_go1_unq, bfz_unq_ind = GBt.unique_rows_tol(bp_fz_norms_go1, return_index=True) ### Finding the input hkl indices corresponding to unique FZ normals mil_ind_csl_unq = mil_ind_csl[bfz_unq_ind] ############ Calculating interplanar distance (d sigma hkl) for unique FZ bpn ######### l_rcsl_go = GBfcd.reciprocal_mat(l_csl_go) mt_cslr_go = np.dot(l_rcsl_go.transpose(), l_rcsl_go) d_inv_sqr = np.diag(np.dot(np.dot(mil_ind_csl_unq, mt_cslr_go),mil_ind_csl_unq.transpose())) d_inv = np.sqrt(d_inv_sqr) d_sig_hkl = np.true_divide(1, d_inv) ############ Calculating unit cell area for 2-D csl unit cells for unique FZ bpn ######## # mil_ind_p = np.dot(np.linalg.inv(GBfcd.reciprocal_mat(l_g_go)), bpn_go.transpose()).transpose() # mil_ind_p = int_man.int_finder(mil_ind_p, 1e-06, 'rows') pl_den = [] num_bpn_unq = np.shape(bp_fz_norms_go1_unq)[0] for ct1 in range(num_bpn_unq): _, _, pl_den_csl = GBb2.bicryst_planar_den(bp_fz_norms_go1_unq[ct1, :], sig_mis_g, l_g_go, 'normal_go', 'g1') pl_den.append(pl_den_csl) pl_den = np.array(pl_den) a_sig_hkl = np.true_divide(1, pl_den) ### Checking the csl primitive unit cell volume equality v_sig_hkl = np.multiply(d_sig_hkl, a_sig_hkl) # print v_sig_hkl v_basis = abs(np.linalg.det(l_csl_go)) if np.all(abs(v_sig_hkl-v_basis) < 1e-04): print "The two volumes match!" else: print " Mismatch!" ### Sorting in increasing order of 2d csl primitive unit cell area ind_area_sort = np.argsort(a_sig_hkl) a_sig_hkl_sort = np.sort(a_sig_hkl) d_sig_hkl_sort = d_sig_hkl[ind_area_sort] bp_fz_norms_go1_unq_sort = bp_fz_norms_go1_unq[ind_area_sort] ### Check to ensure required number of unique bpn are returned if np.shape(bp_fz_norms_go1_unq_sort)[0] < n: print "Please input a larger mesh grid or reduce the number of boundaries!" n = np.shape(bp_fz_norms_go1_unq_sort)[0] ### Selecting the lowest 'n' area boundaries and their attributes for plotting a_plot = a_sig_hkl_sort[:n] pd_plot = np.true_divide(1, a_plot) d_plot = d_sig_hkl_sort[:n] bp_fz_plot = bp_fz_norms_go1_unq_sort[:n] ### d vs pd plot fig1 = plt.figure(figsize=(12, 12), facecolor='w') plt.margins(0.05) plt.xlabel('Interplanar spacing') plt.ylabel('Planar density of 2D-CSL') plt.plot(d_plot, pd_plot, 'ro') # plt.show() plt.savefig('d_vs_pd_' + str(r) + '_' + str(n)+ '.png', dpi=100, bbox_inches='tight') ### FZ plot for the sorted and selected boundaries na = '_'+ str(r) + '_'+ str(n) plot_fig(symm_grp_ax, bp_fz_plot, np.pi/6, na) # plt.show() return