Source code for ktch.io._SPHARM_PDM
"""SPHARM-PDM file (_para.vtk, _surf.vtk, and .coef) I/O functions"""
# Copyright 2023 Koji Noshita
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from pathlib import Path
from typing import List, Tuple, Union
import numpy as np
import numpy.typing as npt
[docs]
def read_spharmpdm_coef(path: Union[str, Path]) -> List[npt.NDArray[np.complex128]]:
"""Read .coef file of SPHARM-PDM.
The .coef file is an output of the `ParaToSPHARMMesh` step
of `SPHARM-PDM <https://www.nitrc.org/projects/spharm-pdm>`_,
and contains SPHARM coefficients.
The file format consists of:
- First value: total number of coefficients (3*(lmax+1)^2)
- Remaining values: real and imaginary parts of coefficients
arranged in SPHARM-PDM's specific order
Parameters
----------
path : str or pathlib.Path
Path to the .coef file.
Returns
-------
coef : List[npt.NDArray[np.complex128]]
List of numpy arrays containing SPHARM coefficients for each coordinate.
Raises
------
FileNotFoundError
If the file does not exist.
ValueError
If the file format is invalid or coefficients are malformed.
"""
path = Path(path)
# Validate file existence and readability
if not path.exists():
raise FileNotFoundError(f"SPHARM-PDM coefficient file not found: {path}")
if not path.is_file():
raise ValueError(f"Path is not a file: {path}")
try:
with open(path, "r") as f:
coef_txt = f.read()
except IOError as e:
raise IOError(f"Error reading SPHARM-PDM file: {e}")
if not coef_txt.strip():
raise ValueError("SPHARM-PDM file is empty")
try:
cleaned_txt = coef_txt.translate(str.maketrans("", "", "{}\n"))
coef = [float(val) for val in cleaned_txt.split(",") if val.strip()]
except ValueError as e:
raise ValueError(f"Invalid coefficient format in SPHARM-PDM file: {e}")
if len(coef) < 1:
raise ValueError("SPHARM-PDM file must contain at least one value")
# Validate coefficient count
# First value is (lmax+1)^2, total coefficients should be 3 * (lmax+1)^2
n_coef_per_coord = int(coef[0])
expected_total = 3 * n_coef_per_coord
actual_count = len(coef) - 1
if actual_count != expected_total:
raise ValueError(
f"Coefficient count mismatch: expected {expected_total} (3 * {n_coef_per_coord}), found {actual_count}"
)
# Convert to numpy array and validate dimensions
try:
coef_array = np.array(coef[1:]).reshape((n_coef_per_coord, 3))
except Exception as e:
raise ValueError(f"Failed to convert coefficients to numpy array: {e}")
if coef_array.size == 0:
raise ValueError("No coefficients found after the count value")
lmax_plus_one = np.sqrt(n_coef_per_coord)
if not lmax_plus_one.is_integer():
raise ValueError(f"Invalid coefficient count: {n_coef_per_coord} != (lmax+1)^2")
coef = cvt_spharm_coef_spharmpdm_to_list(coef_array)
return coef
def cvt_spharm_coef_spharmpdm_to_list(
coef_spharmpdm: npt.NDArray[np.float64],
) -> List[npt.NDArray[np.complex128]]:
"""Convert SPHARM-PDM format coefficients to list format.
SPHARM-PDM stores coefficients in a specific order:
- For m=0: only real part is stored
- For m>0: real and imaginary parts are stored separately
- Complex conjugate symmetry is used for m<0
Parameters
----------
coef_spharmpdm : np.ndarray of shape ((lmax+1)^2,3)
Flattened array of SPHARM coefficients in SPHARM-PDM format.
Contains coefficients for x, y, z coordinates.
Returns
-------
coef_list : list of np.ndarray
List where coef_list[l] contains coefficients for degree l.
Each element is an array of shape (2*l+1, 3) with complex values.
The order is m = -l, -l+1, ..., l-1, l.
Raises
------
ValueError
If the input array has invalid shape or dimensions.
"""
lmax = int(np.sqrt(coef_spharmpdm.shape[0]) - 1)
if coef_spharmpdm.shape != ((lmax + 1) ** 2, 3):
raise ValueError(
f"Invalid coefficient array shape: expected {((lmax + 1) ** 2, 3)}, got {coef_spharmpdm.shape}"
)
# Convert to list format
coef_list = []
for l in range(lmax + 1):
coef_l = np.zeros((2 * l + 1, 3), dtype=np.complex128)
for idx, m in enumerate(range(-l, l + 1)):
if m == 0:
# m=0: only real part
coef_l[idx] = coef_spharmpdm[l**2]
elif m > 0:
# m>0: combine real and imaginary parts
real_idx = l**2 + 2 * m - 1
imag_idx = l**2 + 2 * m
coef_l[idx] = (
coef_spharmpdm[real_idx] - coef_spharmpdm[imag_idx] * 1j
) / 2
else:
# m<0: use complex conjugate symmetry
abs_m = abs(m)
real_idx = l**2 + 2 * abs_m - 1
imag_idx = l**2 + 2 * abs_m
coef_l[idx] = (
((-1) ** m)
* (coef_spharmpdm[real_idx] + coef_spharmpdm[imag_idx] * 1j)
/ 2
)
coef_list.append(coef_l)
return coef_list
def cvt_spharm_coef_list_to_spharmpdm(
coef_list: List[npt.NDArray[np.complex128]],
) -> npt.NDArray[np.float64]:
"""Convert list format coefficients to SPHARM-PDM format.
Converts complex spherical harmonic coefficients from standard
list format to SPHARM-PDM's specific storage format.
Parameters
----------
coef_list : list of np.ndarray
List where coef_list[l] contains coefficients for degree l.
Each element should have shape (2*l+1,) with complex values.
The order is m = -l, -l+1, ..., l-1, l.
Returns
-------
coef_spharmpdm : np.ndarray of shape ((lmax+1)^2, 3)
Flattened array of coefficients in SPHARM-PDM format.
Real and imaginary parts are stored separately.
Raises
------
ValueError
If the input list has invalid structure or dimensions.
Notes
-----
The conversion uses the complex conjugate symmetry property:
Y_l^{-m} = (-1)^m * conj(Y_l^m)
"""
if not isinstance(coef_list, list):
raise ValueError("coef_list must be a list")
if len(coef_list) == 0:
raise ValueError("coef_list cannot be empty")
lmax = len(coef_list) - 1
# Validate structure of coefficient list
for l, coef_l in enumerate(coef_list):
expected_len = 2 * l + 1
if len(coef_l) != expected_len:
raise ValueError(
f"coef_list[{l}] has length {len(coef_l)}, expected {expected_len}"
)
# Convert to SPHARM-PDM format
coef_spharmpdm = np.zeros(((lmax + 1) ** 2, 3))
for l in range(lmax + 1):
l_squared = l**2
# m = 0
coef_spharmpdm[l_squared] = coef_list[l][l].real
# m > 0
for m in range(1, l + 1):
# Get positive and negative m coefficients
coef_pos_m = coef_list[l][m + l]
coef_neg_m = coef_list[l][-m + l]
sign = (-1) ** m
# Real part: sum of positive and negative m
coef_spharmpdm[l_squared + 2 * m - 1] = (
coef_pos_m + sign * coef_neg_m
).real
# Imaginary part: difference of positive and negative m
coef_spharmpdm[l_squared + 2 * m] = (
(coef_pos_m - sign * coef_neg_m) * 1j
).real
return coef_spharmpdm
