+001: cimport cython

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 002: cimport numpy as cnp

+003: import numpy as np

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 004: from libc.math cimport pow, exp, sqrt

+005: from scipy.sparse import lil_matrix

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+006: from functools import wraps

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+007: cnp.import_array()

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 008: from cpython cimport bool

+009: from scipy.sparse.linalg import eigsh, spsolve

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 010: 

 011: ctypedef fused CMat:

 012:     cnp.ndarray[cnp.complex128_t,ndim=3]

 013:     cnp.ndarray[cnp.float64_t,ndim=3]

 014: 

 015: ctypedef fused scalar_var:

 016:     cnp.ndarray[cnp.complex128_t,ndim=1]

 017:     cnp.ndarray[cnp.float64_t,ndim=1]

 018: 

 019: 

 020: #@cython.boundscheck(False)

 021: #@cython.wraparound(False)

 022: #@cython.cdivision(True)

+023: cpdef assemble_stiffness_matrix(

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 028:     """ Assemble a stiffness matrix from the coefficients of the differential equation.

 029: 

 030:     Cythonized assembly method, call as `assemble_stiffness_matrix(C0, Cl, Cr, C2, dzn, dirichelet1, dirichelet2)`.

 031: 

 032:     For the mathematics/definitions of the :math:`C` terms, see :ref:`FEM`.

 033:     All non-scalar arguments should be defined on the mid mesh,

 034:     and all the :math:`C` matrices should be three-dimensional, even if they are just scalars.

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 039:     Args:

 040:         C0,Cl,Cr,C2: material-dependent differential equation coefficients

 041:         dzn: the spacings between mesh nodes

 042:         dirichelet1,dirichelet2 (bool): whether to treat boundary 1, 2 as Dirichelet (True, default) or Neumann.

 043: 

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 045:         A stiffness matrix in sparse CSC form

 046:     """

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 049:         list rinds, rdata

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 104: 

 105: #@cython.boundscheck(False)

 106: #@cython.wraparound(False)

 107: #@cython.cdivision(True)

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 113: 

 114:     Cythonized assembly method, call as `assemble_load_matrix(w, dzn, n)`.

 115: 

 116:     For the mathematics/definitions of the :math:`w` term, see :ref:`FEM`.

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 118: 

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 120:         w: load-side coefficient

 121:         dzn: the spacings between mesh nodes

 122:         n: the size of the :math:`C` matrices (eg 1 for scalar equation, 6 for 6x6 kp equation)

 123:         dirichelet1,dirichelet2 (bool): whether to treat boundary 1, 2 as Dirichelet (True, default) or Neumann.

 124: 

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 165:     """ Solve the eigenvalue problem.

 166: 

 167:     For the mathematics/definitions of terms, see :ref:`FEM`.

 168: 

 169:     Args:

 170:         stiffness_matrix: a stiffness matrix :math:`A` from :func:`pynitride.fem.assemble_stiffness_matrix`

 171:         load_matrix: a load matrix :math:`M` from :func:`pynitride.fem.assemble_load_matrix`

 172:         eigval_out: an array into which to fill the eigenvalues, should be shape (number of eigenvalues)

 173:         eigvec_out: an array into which to fill the eigenvectors, should be shape (number of eigenvalues x n x len(zn))

 174:         n: dimension of the differential equation

 175:         dirichelet1,dirichelet2 (bool): whether to treat boundary 1, 2 as Dirichelet (True, default) or Neumann.

 176:         pairwise_GS: in the case of near degeneracy, the eigensolver often returns eigenvectors which are not totally

 177:             orthogonal.  For instance in a 6x6 wurtzite k.p problem with small CR coupling term, the states form pairs

 178:             that are very close in energy.  This option breaks the eigenvectors into those pairs [note, it just assumes

 179:             the pairing 0-1, 2-3, 4-5, etc, it doesn't actually check the energies], and in each pair, performs a single

 180:             Gram-Schmidt to ensure the nearly-degenerate eigenvectors are orthogonal.

 181:         ascending (bool): by default, energies are sorted from min to max, but for valence band problems,

 182:             you want the highest absolute energies first, so set `ascending=False`

 183:         *args: passed onto

 184:             `scipy.sparse.eigsh <https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html>`_

 185:             along with the main arguments `A` (stiffness) and `M` (load)

 186:         **kwargs: passed onto

 187:             `scipy.sparse.eigsh <https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html>`_

 188:             along with the main arguments `A` (stiffness) and `M` (load)

 189: 

 190:     Returns:

 191:         None

 192:     """

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 200:     # Re-order the energies

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 240:     """ Solve the linear matrix equation

 241: 

 242:     For the mathematics/definitions of terms, see :ref:`FEM`.

 243: 

 244:     Args:

 245:         stiffness_matrix: a stiffness matrix :math:`A` from :func:`pynitride.fem.assemble_stiffness_matrix`

 246:         load_matrix: a load matrix :math:`M` from :func:`pynitride.fem.assemble_load_matrix`

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 248:         val_out: an array into which to fill the solution, should be shape (len(zn))

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 256:             along with the main arguments `A` (stiffness) and `M@b` (load)

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 258:     Returns:

 259:         the solution (same shape as `load_vec`)

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 276: 

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 279:     """ Finds the signed error vector of the test solution.

 280: 

 281:     The error is :math:`b-M^{-1}Ax`, where :math:`x` is the supplied test solution.

 282:     For the mathematics/definitions of terms, see :ref:`FEM`.

 283: 

 284:     Args:

 285:         stiffness_matrix: a stiffness matrix :math:`A` from :func:`pynitride.fem.assemble_stiffness_matrix`

 286:         load_matrix: a load matrix :math:`M` from :func:`pynitride.fem.assemble_load_matrix`

 287:         load_vec: the load vector :math:`b`, should be shape (len(zn))

 288:         test: the test solution vector :math:`x`, should be shape (len(zn))

 289:         err_out: an array into which to fill the error, should be shape (len(zn))

 290:         n: dimension of the differential equation

 291:         dirichelet1,dirichelet2 (bool): whether to treat boundary 1, 2 as Dirichelet (True, default) or Neumann.

 292:         *args: passed onto

 293:             `scipy.sparse.spsolve <https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.spsolve.html>`_

 294:             along with the main arguments `M` and `A@x`

 295:         **kwargs: passed onto

 296:             `scipy.sparse.spsolve <https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.spsolve.html>`_

 297:             along with the main arguments `M` and `A@x`

 298: 

 299:     Returns:

 300:         the error (same shape as `test`)

 301:     """

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