Response tensor

Response tensor#

Response tensors up to 4th rank.

A12(i1, i2)[source]#

Anti-symmetric part of rank 2 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

A123(i1, i2, i3)[source]#

Anti-symmetric part of rank 3 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

A1234(i1, i2, i3, i4)[source]#

AAS part of rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

Ab1234(i1, i2, i3, i4)[source]#

AAA part of rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

M1234(i1, i2, i3, i4)[source]#

SA part of rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

Mb1234(i1, i2, i3, i4)[source]#

AS part of rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

P0()[source]#

Rank 0 tensor component.

Returns:

  • (list) – expression list, (coeff, multipole).

P1(i1)[source]#

Rank 1 tensor component.

Parameters:

i1 (int) – index 1, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

P2(i1, i2, opt=None)[source]#

Rank 2 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • opt (str, optional) – part, s/a.

Returns:

  • (list) – expression list, (coeff, multipole).

P3(i1, i2, i3, opt=None)[source]#

Rank 3 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • opt (str, optional) – part, s/a.

Returns:

  • (list) – expression list, (coeff, multipole).

P4(i1, i2, i3, i4, opt=None)[source]#

Rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

  • opt (str, optional) – part, sss/ssa/aas/aaa/sa/as/s/a/t.

Returns:

  • (list) – expression list, (coeff, multipole).

S0()[source]#

Rank 0 tensor component.

Returns:

  • (list) – expression list, (coeff, multipole).

S1(i1)[source]#

Rank 1 tensor component.

Parameters:

i1 (int) – index 1, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

S12(i1, i2)[source]#

Symmetric part of rank 2 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

S123(i1, i2, i3)[source]#

Symmetric part of rank 3 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

S1234(i1, i2, i3, i4)[source]#

SSS part of rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

Sb1234(i1, i2, i3, i4)[source]#

SSA part of rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

T1234(i1, i2, i3, i4)[source]#

S part of rank 4 tensor component.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2, 1-3.

  • i3 (int) – index 3, 1-3.

  • i4 (int) – index 4, 1-3.

Returns:

  • (list) – expression list, (coeff, multipole).

create_active_dict(active, cartesian_mp)[source]#
d1234(i1, i2, i3, i4)[source]#
d12345(i1, i2, i3, i4, i5)[source]#
d123456(i1, i2, i3, i4, i5, i6)[source]#
d1234567(i1, i2, i3, i4, i5, i6, i7)[source]#
d123456p(i1, i2, i3, i4, i5, i6)[source]#
d123456pp(i1, i2, i3, i4, i5, i6)[source]#
delta(i1, i2)[source]#

Kronecker delta.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2. 1-3.

Returns:

  • (sympy) – delta(i1,i2).

e1234(i1, i2, i3, i4)[source]#
e51234(i1, i2, i3, i4, i5)[source]#
e561234(i1, i2, i3, i4, i5, i6)[source]#
epsilon(i1, i2, i3)[source]#

Levi-Civita epsilon.

Parameters:

  • i1 (int) – index 1, 1-3.

  • i2 (int) – index 2. 1-3.

  • i3 (int) – index 3, 1-3.

Returns:

  • (sympy) – epsilon(i1,i2,i3).

g12534(i1, i2, i3, i4, i5)[source]#
g125634(i1, i2, i3, i4, i5, i6)[source]#
get_response_tensor_mp(rt, active_dict, axial_tensor, magnetic_tensor)[source]#
mp_string(lst, head, sort=True)[source]#

Multipole string.

Parameters:

  • head (str) – head of multipole.

  • sort (bool, optional) – sort subscript ?

Returns:

  • (str) – multipole string.

simplify_tensor(M)[source]#

Simplify tensor.

Parameters:

M (ndarray) – tensor, [[(symbol, expression)]].

Returns:

simplified tensor. - (dict): expression dict.

Return type:

  • (ndarray)

split_symbol(s)[source]#
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