diff --git a/docs/main/.doctrees/background.doctree b/docs/main/.doctrees/background.doctree index a52cf20..4cfb169 100644 Binary files a/docs/main/.doctrees/background.doctree and b/docs/main/.doctrees/background.doctree differ diff --git a/docs/main/.doctrees/environment.pickle b/docs/main/.doctrees/environment.pickle index 6fe1b30..7a25f85 100644 Binary files a/docs/main/.doctrees/environment.pickle and b/docs/main/.doctrees/environment.pickle differ diff --git a/docs/main/_sources/background.rst.txt b/docs/main/_sources/background.rst.txt index 4529260..eb86e2a 100644 --- a/docs/main/_sources/background.rst.txt +++ b/docs/main/_sources/background.rst.txt @@ -126,7 +126,7 @@ Fourier transform of :math:`\eqref{dlrexp}` yields .. math:: \begin{equation} - G(i nu_n) \approx \sum_{l=1}^r K(i \nu_n,\omega_l) \widehat{g}_l, \label{dlrexp_imfreq} \tag{2} + G(i \nu_n) \approx \sum_{l=1}^r K(i \nu_n,\omega_l) \widehat{g}_l, \label{dlrexp_imfreq} \tag{2} \end{equation} so we see that the DLR expansion can be evaluated directly in imaginary time or @@ -267,4 +267,4 @@ containing the point :math:`i \nu_n = 0` must have an odd number of points. Since it is undesirable to disallow this point, and to make sure all grids have the same number :math:`r` of points, we force :math:`r` to be odd. This requires including in each grid, by hand, a single point of high symmetry, and then allowing the -pivoted Gram-Schmidt procedure to select the rest of the points symmetrically. \ No newline at end of file +pivoted Gram-Schmidt procedure to select the rest of the points symmetrically. diff --git a/docs/main/background.html b/docs/main/background.html index 2dc5c10..5ba45d1 100644 --- a/docs/main/background.html +++ b/docs/main/background.html @@ -193,7 +193,7 @@
so we see that the DLR expansion can be evaluated directly in imaginary time or
imaginary frequency, i.e. the Fourier transform is performed analytically. As in
diff --git a/docs/main/searchindex.js b/docs/main/searchindex.js
index 7308b35..ab32fcf 100644
--- a/docs/main/searchindex.js
+++ b/docs/main/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"docnames": ["ChangeLog", "background", "documentation", "examples", "index", "install", "issues"], "filenames": ["ChangeLog.md", "background.rst", "documentation.rst", "examples.rst", "index.rst", "install.rst", "issues.rst"], "titles": ["Changelog", "Background", "Reference documentation", "Examples", "cppdlr
: Imaginary time calculations using the discrete Lehmann representation", "Installation", "Reporting issues"], "terms": {"thi": [0, 1, 3, 5], "i": [0, 1, 3, 4, 5], "initi": 0, "releas": [0, 5], "cppdlr": [0, 1, 5, 6], "c": [0, 1, 4], "librari": [0, 5], "implement": [0, 1, 4], "discret": [0, 3], "lehmann": [0, 3], "represent": [0, 3], "imaginari": 0, "time": 0, "green": [0, 3, 4], "": [0, 3, 4], "function": [0, 3, 4], "we": [0, 1, 3, 5], "thank": 0, "all": [0, 1, 3, 5, 6], "contributor": 0, "thoma": 0, "hahn": 0, "jason": [0, 4], "kay": [0, 4], "hugo": [0, 4], "u": [0, 1, 4, 5], "r": [0, 1, 3, 4], "strand": [0, 4], "nil": 0, "wentzel": 0, "page": [1, 3, 4, 6], "give": [1, 3], "brief": [1, 3, 4], "review": 1, "establish": 1, "definit": [1, 3], "convent": [1, 3], "us": [1, 3, 5], "which": [1, 3, 4, 5], "can": [1, 3, 4, 5], "vari": 1, "from": [1, 3, 4, 5], "one": [1, 3, 4], "refer": 1, "anoth": 1, "If": [1, 3, 4, 5], "you": [1, 3, 4, 5], "ar": [1, 3, 4, 5], "alreadi": 1, "familiar": [1, 4], "should": [1, 3, 4], "probabl": 1, "still": [1, 4], "read": [1, 3, 4], "section": [1, 3, 5], "rel": [1, 3], "below": [1, 3, 4, 5], "For": [1, 3], "more": [1, 3, 4], "detail": [1, 3, 4], "descript": [1, 3], "pleas": [1, 3, 4, 5, 6], "see": [1, 3, 5], "list": [1, 4], "main": [1, 3], "exampl": [1, 4], "concept": 1, "The": [1, 3, 4, 5], "singl": [1, 4], "particl": [1, 4], "defin": [1, 3], "term": [1, 3], "order": 1, "expect": 1, "valu": [1, 3], "g_": 1, "ab": 1, "tau": [1, 3], "langl": 1, "mathcal": 1, "t": 1, "c_a": 1, "c_b": 1, "dagger": 1, "0": [1, 3, 5], "rangl": 1, "where": [1, 5], "dagger_b": 1, "creation": 1, "state": 1, "b": [1, 4], "annihil": 1, "interv": 1, "beta": [1, 3], "invers": [1, 3], "temperatur": [1, 3], "extend": 1, "period": 1, "anti": 1, "properti": 1, "xi": 1, "boson": [1, 3], "1": [1, 3, 5], "fermion": [1, 3], "respect": [1, 3], "spectral": [1, 3], "given": [1, 3], "g": [1, 3], "int_": 1, "infti": 1, "k": [1, 3], "omega": [1, 3], "rho": [1, 3], "d": 1, "correspond": [1, 3], "analyt": [1, 3], "continu": 1, "kernel": 1, "frac": [1, 3], "e": [1, 3], "take": [1, 3, 4], "fourier": [1, 3], "transform": [1, 3], "nu_n": [1, 3], "tanh": 1, "2": [1, 3, 5], "here": [1, 3], "n": [1, 3], "pi": 1, "2n": 1, "make": [1, 5], "low": 1, "rank": 1, "approxim": 1, "interpol": [1, 4], "decomposit": 1, "let": [1, 5], "dimensionless": 1, "cutoff": [1, 3], "paramt": 1, "lambda": [1, 3], "equiv": [1, 3], "omega_": [1, 3], "max": [1, 3], "outsid": 1, "In": [1, 3, 5], "practic": [1, 3], "typic": 1, "known": [1, 3], "estim": 1, "user": [1, 3, 4], "specifi": [1, 3, 5], "paramet": [1, 3], "case": [1, 3], "exactli": 1, "result": [1, 3], "converg": [1, 3], "error": [1, 3], "toler": [1, 3], "epsilon": [1, 3], "an": [1, 3, 5], "begin": [1, 3, 4], "equat": [1, 3], "approx": [1, 3], "sum_": [1, 3], "l": [1, 3], "omega_l": [1, 3], "widehat": [1, 3], "_l": [1, 3], "label": 1, "dlrexp": 1, "tag": [1, 5], "end": 1, "equal": 1, "accuraci": [1, 3], "determin": [1, 3], "carefulli": 1, "chosen": 1, "pivot": 1, "gram": 1, "schmidt": 1, "procedur": 1, "depend": [1, 4], "onli": [1, 3], "itself": [1, 5], "As": 1, "close": 1, "relat": 1, "intermedi": 1, "spars": 1, "ir": 1, "orthogon": 1, "non": [1, 3], "explicit": 1, "have": [1, 3, 5], "o": 1, "log": 1, "thu": 1, "enabl": 1, "highli": 1, "effici": [1, 4], "high": 1, "accur": 1, "number": [1, 3], "degre": 1, "freedom": 1, "independ": 1, "specif": [1, 4], "structur": 1, "beyond": 1, "its": [1, 3], "coeffici": [1, 3], "must": 1, "some": [1, 3], "sampl": 1, "done": [1, 3], "fit": [1, 3], "data": [1, 3], "via": [1, 4, 5], "ordinari": 1, "least": 1, "squar": 1, "node": [1, 3], "tau_k": [1, 3], "These": [1, 3], "also": [1, 3, 4, 5], "particular": [1, 3, 5], "solv": [1, 3], "linear": [1, 3], "system": [1, 3, 4], "problem": [1, 3, 6], "obtain": [1, 3], "evalu": [1, 4], "eqref": 1, "yield": [1, 3], "dlrexp_imfreq": 1, "so": [1, 3], "directli": [1, 3], "perform": [1, 3], "nu_": 1, "n_k": 1, "whereupon": 1, "sinc": [1, 3], "common": 1, "straightforwardli": 1, "repres": 1, "them": 1, "includ": [1, 3, 5], "explain": 1, "abov": [1, 3, 5], "switch": 1, "between": 1, "addit": [1, 5], "product": 1, "simpli": [1, 3], "multipli": 1, "h": 1, "f": 1, "recov": 1, "convolut": [1, 3], "full": 1, "int_0": 1, "requir": [1, 5], "condit": 1, "inner": 1, "etc": 1, "form": [1, 4], "vector": [1, 3], "matric": 1, "tensor": 1, "act": 1, "either": 1, "friendli": [1, 3], "manner": 1, "new": [1, 5], "request": 1, "github": [1, 4, 5, 6], "issu": [1, 4, 5], "first": [1, 3], "scale": 1, "becaus": [1, 3], "work": [1, 3, 4, 5], "variabl": [1, 3], "whenev": 1, "possibl": 1, "mani": 1, "unnecessari": 1, "explicitli": 1, "second": 1, "store": 1, "peculiar": 1, "call": [1, 3, 5], "subtl": 1, "awar": 1, "want": [1, 5], "suppli": [1, 3], "tldr": 1, "skip": 1, "guidelin": 1, "even": 1, "discuss": [1, 3], "than": [1, 3, 5], "appendix": 1, "paper": [1, 4], "follow": [1, 3, 4, 5], "5": 1, "normal": 1, "howev": [1, 3], "instead": [1, 5], "other": [1, 4, 5], "word": [1, 3], "neg": 1, "distanc": 1, "rather": [1, 3], "standard": 1, "absolut": 1, "straightforward": 1, "rel2ab": 1, "reason": 1, "ha": [1, 3], "do": [1, 3], "maintain": [1, 4], "float": 1, "arithmet": 1, "To": [1, 3, 4, 5], "sometim": [1, 3], "need": [1, 3, 4], "comput": [1, 3, 4], "veri": 1, "loss": 1, "due": 1, "catastroph": 1, "cancel": 1, "appear": 1, "extrem": 1, "physic": [1, 3], "regim": 1, "exploit": 1, "symmetri": 1, "avoid": 1, "ever": 1, "annoy": 1, "price": 1, "arithm": 1, "But": 1, "larg": [1, 3], "ignor": 1, "notic": 1, "your": [1, 3, 4, 5], "applic": [1, 4, 5], "provid": [1, 4], "carri": 1, "out": 1, "usual": 1, "hide": 1, "technic": 1, "complic": [1, 3], "situat": 1, "two": [1, 3], "option": [1, 4], "power": 1, "accord": 1, "instruct": [1, 4], "relev": [1, 3], "therebi": 1, "calcul": 1, "don": 1, "care": 1, "about": [1, 3, 4], "minor": 1, "digit": 1, "come": 1, "subtleti": 1, "convert": [1, 3], "abs2rel": 1, "start": [1, 3], "life": 1, "cannot": 1, "compat": 1, "subroutin": 1, "happen": 1, "equispac": [1, 3], "eqpts_rel": 1, "gener": [1, 3], "integ": 1, "whether": 1, "statistic_t": 1, "By": 1, "default": 1, "nor": 1, "inde": 1, "would": [1, 3], "constraint": 1, "select": 1, "necessari": [1, 3], "most": [1, 3], "might": [1, 3], "desir": [1, 3], "flag": [1, 5], "capabl": [1, 4], "test": [1, 3, 5], "showcas": 1, "small": 1, "note": [1, 3, 4], "alwai": 1, "A": 1, "contain": [1, 3, 4], "odd": 1, "undesir": 1, "disallow": 1, "sure": 1, "same": 1, "forc": 1, "each": [1, 3], "hand": 1, "allow": 1, "rest": 1, "step": [3, 4], "basic": 3, "usag": 3, "within": 3, "overview": [3, 4], "background": [3, 4], "further": 3, "thorough": 3, "document": [3, 4, 5], "found": 3, "directori": [3, 5], "repositori": [3, 4, 5], "serv": 3, "good": [3, 4], "point": [3, 4], "write": 3, "own": 3, "code": [3, 5], "being": 3, "cover": 3, "compon": 3, "though": 3, "thei": 3, "therefor": 3, "current": [3, 5], "temporari": 3, "measur": 3, "until": 3, "comprehens": 3, "set": 3, "program": 3, "file": 3, "dlr_interpol": 3, "cpp": 3, "know": [3, 5], "look": [3, 4, 5], "up": 3, "find": 3, "inform": [3, 4], "header": 3, "hpp": 3, "namespac": 3, "gfun": 3, "simpl": 3, "sum": 3, "delta": 3, "a_i": 3, "taken": 3, "symmetr": [3, 4], "matrix": 3, "There": 3, "noth": 3, "special": 3, "except": 3, "conveni": 3, "matsubara": [3, 4], "space": 3, "direct": 3, "next": 3, "move": [3, 5], "orbit": 3, "indic": 3, "our": [3, 4], "took": 3, "less": 3, "width": 3, "safe": 3, "unknown": 3, "recommend": [3, 5], "after": 3, "both": [3, 4], "now": 3, "build_dlr_rf": 3, "input": 3, "31": 3, "shown": 3, "although": 3, "dimension": 3, "consid": 3, "back": 3, "origin": [3, 4], "figur": 3, "object": 3, "type": 3, "imtime_op": 3, "class": [3, 4], "respons": 3, "oper": [3, 4], "grid": [3, 4], "extract": 3, "get_itnod": 3, "method": 3, "could": 3, "involv": 3, "plot": 3, "vals2coef": 3, "basi": [3, 4], "constitut": 3, "character": 3, "ani": [3, 5], "coefs2ev": 3, "eqptsrel": 3, "format": [3, 4], "true": 3, "compar": 3, "pointwis": 3, "top": 3, "left": 3, "entri": 3, "g_00": 3, "correct": 3, "10": 3, "construct": [3, 4], "imfreq_op": 3, "analog": 3, "index": 3, "again": 3, "agreement": 3, "themselv": 3, "describ": 3, "unit": 3, "sever": 3, "fit_scalar": 3, "fit_matrix": 3, "fit_matrix_cmplx": 3, "convolve_scalar_r": 3, "convolve_scalar_cmplx": 3, "convolve_matrix_r": 3, "convolve_matrix_cmplx": 3, "reflect": 3, "mapsto": 3, "refl_matrix": 3, "interp_scalar": 3, "interp_matrix": 3, "interp_matrix_sym_f": 3, "interp_matrix_sym_bo": 3, "show": 3, "how": 3, "fix": 3, "self": 3, "energi": 3, "dyson": 3, "dyson_it": 3, "dyson_vs_ed_r": 3, "dyson_vs_ed_cmplx": 3, "dyson_beth": 3, "consist": 3, "express": 3, "dyson_bethe_fpi": 3, "dlr": 4, "quantiti": 4, "It": 4, "download": [4, 5], "instal": 4, "unfamiliar": 4, "introduct": 4, "import": 4, "softwar": 4, "publish": 4, "research": 4, "cite": 4, "citat": 4, "help": 4, "encourag": 4, "develop": 4, "open": 4, "sourc": [4, 5], "scientif": 4, "kun": 4, "chen": 4, "olivi": 4, "parcollet": 4, "phy": 4, "rev": 4, "105": 4, "235115": 4, "2022": 4, "arxiv": 4, "2107": 4, "13094": 4, "companion": 4, "libdlr": 4, "briefer": 4, "commun": 4, "280": 4, "108458": 4, "2110": 4, "06765": 4, "avail": [4, 5], "languag": 4, "python": [4, 5], "pydlr": 4, "fortran": 4, "julia": 4, "jl": 4, "toolbox": 4, "interact": 4, "quantum": 4, "triq": 4, "version": 4, "custom": 4, "cmake": 4, "compil": 4, "clang": 4, "maco": 4, "expans": 4, "frequenc": 4, "domain": 4, "report": 4, "stabl": 5, "troubl": 5, "gcc": 5, "12": 5, "later": 5, "OR": 5, "15": 5, "bla": 5, "lapack": 5, "hdf5": 5, "openmp": 5, "mpi": 5, "nda": 5, "built": 5, "automat": 5, "wish": 5, "build": 5, "libclang": 5, "packag": 5, "sphinx": 5, "nbsphinx": 5, "myst_pars": 5, "sphinx_rtd_them": 5, "linkifi": 5, "py": 5, "latest": 5, "clone": 5, "git": 5, "http": [5, 6], "com": [5, 6], "flatironinstitut": [5, 6], "src": 5, "creat": 5, "mkdir": 5, "cd": 5, "dcmake_install_prefix": 5, "path_to_install_dir": 5, "run": 5, "go": 5, "checkout": 5, "4": 5, "configur": 5, "doption1": 5, "value1": 5, "doption2": 5, "value2": 5, "syntax": 5, "path": 5, "path_to_triq": 5, "path_to_cppdlr": 5, "debug": 5, "mode": 5, "dcmake_build_typ": 5, "disabl": 5, "dbuild_test": 5, "off": 5, "dbuild_document": 5, "ON": 5, "command": 5, "3": 5, "dcmake_c_compil": 5, "dcmake_cxx_compil": 5, "dcmake_cxx_flag": 5, "stdlib": 5, "libc": 5, "doe": 5, "support": 5, "appleclang": 5, "homebrew": 5, "brew": 5, "llvm": 5, "prefix": 5, "opt": 5, "bin": 5, "bug": 6}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"changelog": 0, "version": [0, 5], "1": 0, "0": 0, "background": 1, "imaginari": [1, 3, 4], "time": [1, 3, 4], "green": 1, "": 1, "function": 1, "lehmann": [1, 4], "represent": [1, 4], "discret": [1, 4], "construct": 1, "dlr": [1, 3], "expans": [1, 3], "matsubara": 1, "frequenc": [1, 3], "domain": 1, "oper": 1, "basi": 1, "point": 1, "format": 1, "symmetr": 1, "grid": 1, "refer": [2, 4], "document": 2, "exampl": 3, "form": 3, "via": 3, "interpol": 3, "evalu": 3, "list": 3, "other": 3, "cppdlr": [3, 4], "capabl": 3, "calcul": 4, "us": 4, "get": 4, "start": 4, "relat": 4, "librari": 4, "content": 4, "instal": 5, "depend": 5, "step": 5, "custom": 5, "cmake": 5, "option": 5, "compil": 5, "clang": 5, "note": 5, "maco": 5, "user": 5, "report": 6, "issu": 6}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx.ext.todo": 2, "sphinx.ext.viewcode": 1, "sphinx": 57}, "alltitles": {"cppdlr: Imaginary time calculations using the discrete Lehmann representation": [[4, "cppdlr-imaginary-time-calculations-using-the-discrete-lehmann-representation"]], "Getting started": [[4, "getting-started"]], "References": [[4, "references"]], "Related libraries": [[4, "related-libraries"]], "Contents:": [[4, null]], "Installation": [[5, "installation"]], "Dependencies": [[5, "dependencies"]], "Installation steps": [[5, "installation-steps"]], "Versions": [[5, "versions"]], "Custom CMake options": [[5, "custom-cmake-options"]], "Compiling with clang": [[5, "compiling-with-clang"]], "Note for MacOS users": [[5, "note-for-macos-users"]], "Examples": [[3, "examples"]], "Example: form a DLR expansion via interpolation, and evaluate it in imaginary time and frequency": [[3, "example-form-a-dlr-expansion-via-interpolation-and-evaluate-it-in-imaginary-time-and-frequency"]], "List of examples": [[3, "list-of-examples"]], "List of other cppdlr capabilities": [[3, "list-of-other-cppdlr-capabilities"]], "Background": [[1, "background"]], "Imaginary time Green\u2019s functions and the Lehmann representation": [[1, "imaginary-time-green-s-functions-and-the-lehmann-representation"]], "Discrete Lehmann representation": [[1, "discrete-lehmann-representation"]], "Constructing a DLR expansion": [[1, "constructing-a-dlr-expansion"]], "DLR in the Matsubara frequency domain": [[1, "dlr-in-the-matsubara-frequency-domain"]], "Operations in the DLR basis": [[1, "operations-in-the-dlr-basis"]], "Imaginary time point format": [[1, "imaginary-time-point-format"]], "Matsubara frequency point format": [[1, "matsubara-frequency-point-format"]], "Symmetrized DLR grids": [[1, "symmetrized-dlr-grids"]], "Changelog": [[0, "changelog"]], "Version 1.0.0": [[0, "version-1-0-0"]], "Reference documentation": [[2, "reference-documentation"]], "Reporting issues": [[6, "reporting-issues"]]}, "indexentries": {}})
\ No newline at end of file
+Search.setIndex({"docnames": ["ChangeLog", "background", "documentation", "examples", "index", "install", "issues"], "filenames": ["ChangeLog.md", "background.rst", "documentation.rst", "examples.rst", "index.rst", "install.rst", "issues.rst"], "titles": ["Changelog", "Background", "Reference documentation", "Examples", "cppdlr
: Imaginary time calculations using the discrete Lehmann representation", "Installation", "Reporting issues"], "terms": {"thi": [0, 1, 3, 5], "i": [0, 1, 3, 4, 5], "initi": 0, "releas": [0, 5], "cppdlr": [0, 1, 5, 6], "c": [0, 1, 4], "librari": [0, 5], "implement": [0, 1, 4], "discret": [0, 3], "lehmann": [0, 3], "represent": [0, 3], "imaginari": 0, "time": 0, "green": [0, 3, 4], "": [0, 3, 4], "function": [0, 3, 4], "we": [0, 1, 3, 5], "thank": 0, "all": [0, 1, 3, 5, 6], "contributor": 0, "thoma": 0, "hahn": 0, "jason": [0, 4], "kay": [0, 4], "hugo": [0, 4], "u": [0, 1, 4, 5], "r": [0, 1, 3, 4], "strand": [0, 4], "nil": 0, "wentzel": 0, "page": [1, 3, 4, 6], "give": [1, 3], "brief": [1, 3, 4], "review": 1, "establish": 1, "definit": [1, 3], "convent": [1, 3], "us": [1, 3, 5], "which": [1, 3, 4, 5], "can": [1, 3, 4, 5], "vari": 1, "from": [1, 3, 4, 5], "one": [1, 3, 4], "refer": 1, "anoth": 1, "If": [1, 3, 4, 5], "you": [1, 3, 4, 5], "ar": [1, 3, 4, 5], "alreadi": 1, "familiar": [1, 4], "should": [1, 3, 4], "probabl": 1, "still": [1, 4], "read": [1, 3, 4], "section": [1, 3, 5], "rel": [1, 3], "below": [1, 3, 4, 5], "For": [1, 3], "more": [1, 3, 4], "detail": [1, 3, 4], "descript": [1, 3], "pleas": [1, 3, 4, 5, 6], "see": [1, 3, 5], "list": [1, 4], "main": [1, 3], "exampl": [1, 4], "concept": 1, "The": [1, 3, 4, 5], "singl": [1, 4], "particl": [1, 4], "defin": [1, 3], "term": [1, 3], "order": 1, "expect": 1, "valu": [1, 3], "g_": 1, "ab": 1, "tau": [1, 3], "langl": 1, "mathcal": 1, "t": 1, "c_a": 1, "c_b": 1, "dagger": 1, "0": [1, 3, 5], "rangl": 1, "where": [1, 5], "dagger_b": 1, "creation": 1, "state": 1, "b": [1, 4], "annihil": 1, "interv": 1, "beta": [1, 3], "invers": [1, 3], "temperatur": [1, 3], "extend": 1, "period": 1, "anti": 1, "properti": 1, "xi": 1, "boson": [1, 3], "1": [1, 3, 5], "fermion": [1, 3], "respect": [1, 3], "spectral": [1, 3], "given": [1, 3], "g": [1, 3], "int_": 1, "infti": 1, "k": [1, 3], "omega": [1, 3], "rho": [1, 3], "d": 1, "correspond": [1, 3], "analyt": [1, 3], "continu": 1, "kernel": 1, "frac": [1, 3], "e": [1, 3], "take": [1, 3, 4], "fourier": [1, 3], "transform": [1, 3], "nu_n": [1, 3], "tanh": 1, "2": [1, 3, 5], "here": [1, 3], "n": [1, 3], "pi": 1, "2n": 1, "make": [1, 5], "low": 1, "rank": 1, "approxim": 1, "interpol": [1, 4], "decomposit": 1, "let": [1, 5], "dimensionless": 1, "cutoff": [1, 3], "paramt": 1, "lambda": [1, 3], "equiv": [1, 3], "omega_": [1, 3], "max": [1, 3], "outsid": 1, "In": [1, 3, 5], "practic": [1, 3], "typic": 1, "known": [1, 3], "estim": 1, "user": [1, 3, 4], "specifi": [1, 3, 5], "paramet": [1, 3], "case": [1, 3], "exactli": 1, "result": [1, 3], "converg": [1, 3], "error": [1, 3], "toler": [1, 3], "epsilon": [1, 3], "an": [1, 3, 5], "begin": [1, 3, 4], "equat": [1, 3], "approx": [1, 3], "sum_": [1, 3], "l": [1, 3], "omega_l": [1, 3], "widehat": [1, 3], "_l": [1, 3], "label": 1, "dlrexp": 1, "tag": [1, 5], "end": 1, "equal": 1, "accuraci": [1, 3], "determin": [1, 3], "carefulli": 1, "chosen": 1, "pivot": 1, "gram": 1, "schmidt": 1, "procedur": 1, "depend": [1, 4], "onli": [1, 3], "itself": [1, 5], "As": 1, "close": 1, "relat": 1, "intermedi": 1, "spars": 1, "ir": 1, "orthogon": 1, "non": [1, 3], "explicit": 1, "have": [1, 3, 5], "o": 1, "log": 1, "thu": 1, "enabl": 1, "highli": 1, "effici": [1, 4], "high": 1, "accur": 1, "number": [1, 3], "degre": 1, "freedom": 1, "independ": 1, "specif": [1, 4], "structur": 1, "beyond": 1, "its": [1, 3], "coeffici": [1, 3], "must": 1, "some": [1, 3], "sampl": 1, "done": [1, 3], "fit": [1, 3], "data": [1, 3], "via": [1, 4, 5], "ordinari": 1, "least": 1, "squar": 1, "node": [1, 3], "tau_k": [1, 3], "These": [1, 3], "also": [1, 3, 4, 5], "particular": [1, 3, 5], "solv": [1, 3], "linear": [1, 3], "system": [1, 3, 4], "problem": [1, 3, 6], "obtain": [1, 3], "evalu": [1, 4], "eqref": 1, "yield": [1, 3], "dlrexp_imfreq": 1, "so": [1, 3], "directli": [1, 3], "perform": [1, 3], "nu_": 1, "n_k": 1, "whereupon": 1, "sinc": [1, 3], "common": 1, "straightforwardli": 1, "repres": 1, "them": 1, "includ": [1, 3, 5], "explain": 1, "abov": [1, 3, 5], "switch": 1, "between": 1, "addit": [1, 5], "product": 1, "simpli": [1, 3], "multipli": 1, "h": 1, "f": 1, "recov": 1, "convolut": [1, 3], "full": 1, "int_0": 1, "requir": [1, 5], "condit": 1, "inner": 1, "etc": 1, "form": [1, 4], "vector": [1, 3], "matric": 1, "tensor": 1, "act": 1, "either": 1, "friendli": [1, 3], "manner": 1, "new": [1, 5], "request": 1, "github": [1, 4, 5, 6], "issu": [1, 4, 5], "first": [1, 3], "scale": 1, "becaus": [1, 3], "work": [1, 3, 4, 5], "variabl": [1, 3], "whenev": 1, "possibl": 1, "mani": 1, "unnecessari": 1, "explicitli": 1, "second": 1, "store": 1, "peculiar": 1, "call": [1, 3, 5], "subtl": 1, "awar": 1, "want": [1, 5], "suppli": [1, 3], "tldr": 1, "skip": 1, "guidelin": 1, "even": 1, "discuss": [1, 3], "than": [1, 3, 5], "appendix": 1, "paper": [1, 4], "follow": [1, 3, 4, 5], "5": 1, "normal": 1, "howev": [1, 3], "instead": [1, 5], "other": [1, 4, 5], "word": [1, 3], "neg": 1, "distanc": 1, "rather": [1, 3], "standard": 1, "absolut": 1, "straightforward": 1, "rel2ab": 1, "reason": 1, "ha": [1, 3], "do": [1, 3], "maintain": [1, 4], "float": 1, "arithmet": 1, "To": [1, 3, 4, 5], "sometim": [1, 3], "need": [1, 3, 4], "comput": [1, 3, 4], "veri": 1, "loss": 1, "due": 1, "catastroph": 1, "cancel": 1, "appear": 1, "extrem": 1, "physic": [1, 3], "regim": 1, "exploit": 1, "symmetri": 1, "avoid": 1, "ever": 1, "annoy": 1, "price": 1, "arithm": 1, "But": 1, "larg": [1, 3], "ignor": 1, "notic": 1, "your": [1, 3, 4, 5], "applic": [1, 4, 5], "provid": [1, 4], "carri": 1, "out": 1, "usual": 1, "hide": 1, "technic": 1, "complic": [1, 3], "situat": 1, "two": [1, 3], "option": [1, 4], "power": 1, "accord": 1, "instruct": [1, 4], "relev": [1, 3], "therebi": 1, "calcul": 1, "don": 1, "care": 1, "about": [1, 3, 4], "minor": 1, "digit": 1, "come": 1, "subtleti": 1, "convert": [1, 3], "abs2rel": 1, "start": [1, 3], "life": 1, "cannot": 1, "compat": 1, "subroutin": 1, "happen": 1, "equispac": [1, 3], "eqpts_rel": 1, "gener": [1, 3], "integ": 1, "whether": 1, "statistic_t": 1, "By": 1, "default": 1, "nor": 1, "inde": 1, "would": [1, 3], "constraint": 1, "select": 1, "necessari": [1, 3], "most": [1, 3], "might": [1, 3], "desir": [1, 3], "flag": [1, 5], "capabl": [1, 4], "test": [1, 3, 5], "showcas": 1, "small": 1, "note": [1, 3, 4], "alwai": 1, "A": 1, "contain": [1, 3, 4], "odd": 1, "undesir": 1, "disallow": 1, "sure": 1, "same": 1, "forc": 1, "each": [1, 3], "hand": 1, "allow": 1, "rest": 1, "step": [3, 4], "basic": 3, "usag": 3, "within": 3, "overview": [3, 4], "background": [3, 4], "further": 3, "thorough": 3, "document": [3, 4, 5], "found": 3, "directori": [3, 5], "repositori": [3, 4, 5], "serv": 3, "good": [3, 4], "point": [3, 4], "write": 3, "own": 3, "code": [3, 5], "being": 3, "cover": 3, "compon": 3, "though": 3, "thei": 3, "therefor": 3, "current": [3, 5], "temporari": 3, "measur": 3, "until": 3, "comprehens": 3, "set": 3, "program": 3, "file": 3, "dlr_interpol": 3, "cpp": 3, "know": [3, 5], "look": [3, 4, 5], "up": 3, "find": 3, "inform": [3, 4], "header": 3, "hpp": 3, "namespac": 3, "gfun": 3, "simpl": 3, "sum": 3, "delta": 3, "a_i": 3, "taken": 3, "symmetr": [3, 4], "matrix": 3, "There": 3, "noth": 3, "special": 3, "except": 3, "conveni": 3, "matsubara": [3, 4], "space": 3, "direct": 3, "next": 3, "move": [3, 5], "orbit": 3, "indic": 3, "our": [3, 4], "took": 3, "less": 3, "width": 3, "safe": 3, "unknown": 3, "recommend": [3, 5], "after": 3, "both": [3, 4], "now": 3, "build_dlr_rf": 3, "input": 3, "31": 3, "shown": 3, "although": 3, "dimension": 3, "consid": 3, "back": 3, "origin": [3, 4], "figur": 3, "object": 3, "type": 3, "imtime_op": 3, "class": [3, 4], "respons": 3, "oper": [3, 4], "grid": [3, 4], "extract": 3, "get_itnod": 3, "method": 3, "could": 3, "involv": 3, "plot": 3, "vals2coef": 3, "basi": [3, 4], "constitut": 3, "character": 3, "ani": [3, 5], "coefs2ev": 3, "eqptsrel": 3, "format": [3, 4], "true": 3, "compar": 3, "pointwis": 3, "top": 3, "left": 3, "entri": 3, "g_00": 3, "correct": 3, "10": 3, "construct": [3, 4], "imfreq_op": 3, "analog": 3, "index": 3, "again": 3, "agreement": 3, "themselv": 3, "describ": 3, "unit": 3, "sever": 3, "fit_scalar": 3, "fit_matrix": 3, "fit_matrix_cmplx": 3, "convolve_scalar_r": 3, "convolve_scalar_cmplx": 3, "convolve_matrix_r": 3, "convolve_matrix_cmplx": 3, "reflect": 3, "mapsto": 3, "refl_matrix": 3, "interp_scalar": 3, "interp_matrix": 3, "interp_matrix_sym_f": 3, "interp_matrix_sym_bo": 3, "show": 3, "how": 3, "fix": 3, "self": 3, "energi": 3, "dyson": 3, "dyson_it": 3, "dyson_vs_ed_r": 3, "dyson_vs_ed_cmplx": 3, "dyson_beth": 3, "consist": 3, "express": 3, "dyson_bethe_fpi": 3, "dlr": 4, "quantiti": 4, "It": 4, "download": [4, 5], "instal": 4, "unfamiliar": 4, "introduct": 4, "import": 4, "softwar": 4, "publish": 4, "research": 4, "cite": 4, "citat": 4, "help": 4, "encourag": 4, "develop": 4, "open": 4, "sourc": [4, 5], "scientif": 4, "kun": 4, "chen": 4, "olivi": 4, "parcollet": 4, "phy": 4, "rev": 4, "105": 4, "235115": 4, "2022": 4, "arxiv": 4, "2107": 4, "13094": 4, "companion": 4, "libdlr": 4, "briefer": 4, "commun": 4, "280": 4, "108458": 4, "2110": 4, "06765": 4, "avail": [4, 5], "languag": 4, "python": [4, 5], "pydlr": 4, "fortran": 4, "julia": 4, "jl": 4, "toolbox": 4, "interact": 4, "quantum": 4, "triq": 4, "version": 4, "custom": 4, "cmake": 4, "compil": 4, "clang": 4, "maco": 4, "expans": 4, "frequenc": 4, "domain": 4, "report": 4, "stabl": 5, "troubl": 5, "gcc": 5, "12": 5, "later": 5, "OR": 5, "15": 5, "bla": 5, "lapack": 5, "hdf5": 5, "openmp": 5, "mpi": 5, "nda": 5, "built": 5, "automat": 5, "wish": 5, "build": 5, "libclang": 5, "packag": 5, "sphinx": 5, "nbsphinx": 5, "myst_pars": 5, "sphinx_rtd_them": 5, "linkifi": 5, "py": 5, "latest": 5, "clone": 5, "git": 5, "http": [5, 6], "com": [5, 6], "flatironinstitut": [5, 6], "src": 5, "creat": 5, "mkdir": 5, "cd": 5, "dcmake_install_prefix": 5, "path_to_install_dir": 5, "run": 5, "go": 5, "checkout": 5, "4": 5, "configur": 5, "doption1": 5, "value1": 5, "doption2": 5, "value2": 5, "syntax": 5, "path": 5, "path_to_triq": 5, "path_to_cppdlr": 5, "debug": 5, "mode": 5, "dcmake_build_typ": 5, "disabl": 5, "dbuild_test": 5, "off": 5, "dbuild_document": 5, "ON": 5, "command": 5, "3": 5, "dcmake_c_compil": 5, "dcmake_cxx_compil": 5, "dcmake_cxx_flag": 5, "stdlib": 5, "libc": 5, "doe": 5, "support": 5, "appleclang": 5, "homebrew": 5, "brew": 5, "llvm": 5, "prefix": 5, "opt": 5, "bin": 5, "bug": 6}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"changelog": 0, "version": [0, 5], "1": 0, "0": 0, "background": 1, "imaginari": [1, 3, 4], "time": [1, 3, 4], "green": 1, "": 1, "function": 1, "lehmann": [1, 4], "represent": [1, 4], "discret": [1, 4], "construct": 1, "dlr": [1, 3], "expans": [1, 3], "matsubara": 1, "frequenc": [1, 3], "domain": 1, "oper": 1, "basi": 1, "point": 1, "format": 1, "symmetr": 1, "grid": 1, "refer": [2, 4], "document": 2, "exampl": 3, "form": 3, "via": 3, "interpol": 3, "evalu": 3, "list": 3, "other": 3, "cppdlr": [3, 4], "capabl": 3, "calcul": 4, "us": 4, "get": 4, "start": 4, "relat": 4, "librari": 4, "content": 4, "instal": 5, "depend": 5, "step": 5, "custom": 5, "cmake": 5, "option": 5, "compil": 5, "clang": 5, "note": 5, "maco": 5, "user": 5, "report": 6, "issu": 6}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx.ext.todo": 2, "sphinx.ext.viewcode": 1, "sphinx": 57}, "alltitles": {"cppdlr: Imaginary time calculations using the discrete Lehmann representation": [[4, "cppdlr-imaginary-time-calculations-using-the-discrete-lehmann-representation"]], "Getting started": [[4, "getting-started"]], "References": [[4, "references"]], "Related libraries": [[4, "related-libraries"]], "Contents:": [[4, null]], "Examples": [[3, "examples"]], "Example: form a DLR expansion via interpolation, and evaluate it in imaginary time and frequency": [[3, "example-form-a-dlr-expansion-via-interpolation-and-evaluate-it-in-imaginary-time-and-frequency"]], "List of examples": [[3, "list-of-examples"]], "List of other cppdlr capabilities": [[3, "list-of-other-cppdlr-capabilities"]], "Installation": [[5, "installation"]], "Dependencies": [[5, "dependencies"]], "Installation steps": [[5, "installation-steps"]], "Versions": [[5, "versions"]], "Custom CMake options": [[5, "custom-cmake-options"]], "Compiling with clang": [[5, "compiling-with-clang"]], "Note for MacOS users": [[5, "note-for-macos-users"]], "Background": [[1, "background"]], "Imaginary time Green\u2019s functions and the Lehmann representation": [[1, "imaginary-time-green-s-functions-and-the-lehmann-representation"]], "Discrete Lehmann representation": [[1, "discrete-lehmann-representation"]], "Constructing a DLR expansion": [[1, "constructing-a-dlr-expansion"]], "DLR in the Matsubara frequency domain": [[1, "dlr-in-the-matsubara-frequency-domain"]], "Operations in the DLR basis": [[1, "operations-in-the-dlr-basis"]], "Imaginary time point format": [[1, "imaginary-time-point-format"]], "Matsubara frequency point format": [[1, "matsubara-frequency-point-format"]], "Symmetrized DLR grids": [[1, "symmetrized-dlr-grids"]], "Reference documentation": [[2, "reference-documentation"]], "Changelog": [[0, "changelog"]], "Version 1.0.0": [[0, "version-1-0-0"]], "Reporting issues": [[6, "reporting-issues"]]}, "indexentries": {}})
\ No newline at end of file