| Name | smallexpimv JSON |
| Version |
0.0.1
JSON |
| download |
| home_page | |
| Summary | A package to apply the imaginary exponential of a small-dimensional matrix to a vector. |
| upload_time | 2023-01-09 10:32:12 |
| maintainer | |
| docs_url | None |
| author | |
| requires_python | >=3.7 |
| license | |
| keywords |
matrix-exponential
|
| VCS |
|
| bugtrack_url |
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| requirements |
No requirements were recorded.
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# smallexpimv
This repository provides some Fortran routines and python wrappers to apply the imaginary exponential of a matrix (real tridiagonal or complex) to a vector. More precisely,
$$
\beta\mathrm{e}^{\pm\mathrm{i} t X} u \in\mathbb{C}^n,
$$
for a matrix $X\in\mathbb{C}^{n\times n}$, a time-step $t\in\mathbb{R}$, a scaling factor $\beta\in\mathbb{R}$, a vector $u\in\mathbb{C}^n$ and the imaginary number $\mathrm{i}^2 = -1 $. Our first routine computes this vector by an adaptive and restarted Taylor approximation. We also provide a second routine for a tridiagonal case, namely
$$
\beta\mathrm{e}^{\pm\mathrm{i} t T} e_1 \in\mathbb{C}^n,
$$
where $T\in\mathbb{R}^{n\times n}$ refers to a tridiagonal symmetric matrix and $e_1$ denotes the first unit vector, i.e., $e_1 = (1,0,\ldots,0)^\ast \in\mathbb{R}^{n}$. For the tridiagonal case, the action of the matrix exponential is computed using an eigendecomposition of $T$ via the lapack $\texttt{dstevr}$ routine.
The matrix exponentials above have some relevance for the Lanczos or Arnoldi approximations to the action of large-dimensional matrix exponentials, e.g., for time-dependent Schrödinger-type problems. In this context, $X$ or $T$ correspond to small dimensional Krylov representations of a large problem.
The main code is written in Fortran, and can be used in Python using f2py.
To generate the main python module smallexpimv.so run
> python3 -m numpy.f2py -c src/F_smallexpimv.F90 -m smallexpimv -lblas
optional, generate f2py header files:
> python3 -m numpy.f2py -h smexp.pyf -m smallexpimv src/F_smallexpimv.F90
For more user-friendly Python code which also handles working memory (most relevant when applying the matrix exponential multiple times)
we also provide the module smallexpimv_pyclass.py. Keep in mind that this module requires still the smallexpimv.so module.
makefile: run
> make test
to run the python and fortran tests, and
> make libs
to generate smallexpimv.so and smallexpimv_pyclass.pyc. To use the Makefile, first check that (in the makefile) the compiler commands and the f2py filename extension are defined correctly for your system!
python3.7 -m build --sdist
python3.7 -m twine upload --repository testpypi dist/*
python3.7 -m pip install --index-url https://test.pypi.org/simple/ --no-deps mypackagetjx
python3.7 -m pip install mypackagetjx==0.0.14 --extra-index-url=https://test.pypi.org/simple/
from mypackagetjx import onef
Raw data
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"description": "# smallexpimv\nThis repository provides some Fortran routines and python wrappers to apply the imaginary exponential of a matrix (real tridiagonal or complex) to a vector. More precisely,\n\n$$\n\\beta\\mathrm{e}^{\\pm\\mathrm{i} t X} u \\in\\mathbb{C}^n,\n$$\n\nfor a matrix $X\\in\\mathbb{C}^{n\\times n}$, a time-step $t\\in\\mathbb{R}$, a scaling factor $\\beta\\in\\mathbb{R}$, a vector $u\\in\\mathbb{C}^n$ and the imaginary number $\\mathrm{i}^2 = -1 $. Our first routine computes this vector by an adaptive and restarted Taylor approximation. We also provide a second routine for a tridiagonal case, namely\n\n$$\n\\beta\\mathrm{e}^{\\pm\\mathrm{i} t T} e_1 \\in\\mathbb{C}^n,\n$$\n\nwhere $T\\in\\mathbb{R}^{n\\times n}$ refers to a tridiagonal symmetric matrix and $e_1$ denotes the first unit vector, i.e., $e_1 = (1,0,\\ldots,0)^\\ast \\in\\mathbb{R}^{n}$. For the tridiagonal case, the action of the matrix exponential is computed using an eigendecomposition of $T$ via the lapack $\\texttt{dstevr}$ routine.\n\nThe matrix exponentials above have some relevance for the Lanczos or Arnoldi approximations to the action of large-dimensional matrix exponentials, e.g., for time-dependent Schr\u00f6dinger-type problems. In this context, $X$ or $T$ correspond to small dimensional Krylov representations of a large problem.\n\nThe main code is written in Fortran, and can be used in Python using f2py.\n\nTo generate the main python module smallexpimv.so run\n> python3 -m numpy.f2py -c src/F_smallexpimv.F90 -m smallexpimv -lblas\n\noptional, generate f2py header files:\n> python3 -m numpy.f2py -h smexp.pyf -m smallexpimv src/F_smallexpimv.F90\n\nFor more user-friendly Python code which also handles working memory (most relevant when applying the matrix exponential multiple times)\nwe also provide the module smallexpimv_pyclass.py. Keep in mind that this module requires still the smallexpimv.so module.\n\nmakefile: run\n> make test\n\nto run the python and fortran tests, and\n> make libs\n\nto generate smallexpimv.so and smallexpimv_pyclass.pyc. To use the Makefile, first check that (in the makefile) the compiler commands and the f2py filename extension are defined correctly for your system!\n\n\npython3.7 -m build --sdist\npython3.7 -m twine upload --repository testpypi dist/*\npython3.7 -m pip install --index-url https://test.pypi.org/simple/ --no-deps mypackagetjx\n\npython3.7 -m pip install mypackagetjx==0.0.14 --extra-index-url=https://test.pypi.org/simple/\n\nfrom mypackagetjx import onef\n",
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