finished circle_counting
This commit is contained in:
William Ball
parent
6ca162ec1d
commit
6148ee8e36
10 changed files with 9004 additions and 1553 deletions
1142
Presentation.nb
1142
Presentation.nb
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170
fractal_dimension/circle_counting_new/Cargo.lock
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170
fractal_dimension/circle_counting_new/Cargo.lock
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@ -2,6 +2,15 @@
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# It is not intended for manual editing.
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# It is not intended for manual editing.
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version = 3
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version = 3
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[[package]]
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||||||
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name = "ansi_term"
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version = "0.11.0"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "ee49baf6cb617b853aa8d93bf420db2383fab46d314482ca2803b40d5fde979b"
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dependencies = [
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"winapi",
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]
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[[package]]
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[[package]]
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name = "approx"
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name = "approx"
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version = "0.5.0"
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version = "0.5.0"
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@ -11,12 +20,29 @@ dependencies = [
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"num-traits",
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"num-traits",
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]
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]
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[[package]]
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name = "atty"
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version = "0.2.14"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "d9b39be18770d11421cdb1b9947a45dd3f37e93092cbf377614828a319d5fee8"
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dependencies = [
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"hermit-abi",
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"libc",
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"winapi",
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]
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[[package]]
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[[package]]
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name = "autocfg"
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name = "autocfg"
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version = "1.0.1"
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version = "1.0.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
checksum = "cdb031dd78e28731d87d56cc8ffef4a8f36ca26c38fe2de700543e627f8a464a"
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checksum = "cdb031dd78e28731d87d56cc8ffef4a8f36ca26c38fe2de700543e627f8a464a"
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[[package]]
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name = "bitflags"
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version = "1.2.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "cf1de2fe8c75bc145a2f577add951f8134889b4795d47466a54a5c846d691693"
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||||||
[[package]]
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[[package]]
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||||||
name = "cfg-if"
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name = "cfg-if"
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version = "1.0.0"
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version = "1.0.0"
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@ -27,8 +53,25 @@ checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"
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||||||
name = "circle_counting"
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name = "circle_counting"
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||||||
version = "0.1.0"
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version = "0.1.0"
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||||||
dependencies = [
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dependencies = [
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||||||
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"ansi_term",
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||||||
"linregress",
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"linregress",
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"nalgebra",
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"nalgebra",
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"structopt",
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]
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||||||
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||||||
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[[package]]
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name = "clap"
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version = "2.33.3"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "37e58ac78573c40708d45522f0d80fa2f01cc4f9b4e2bf749807255454312002"
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dependencies = [
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"ansi_term",
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"atty",
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"bitflags",
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"strsim",
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"textwrap",
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"unicode-width",
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"vec_map",
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]
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]
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[[package]]
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[[package]]
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@ -42,6 +85,24 @@ dependencies = [
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"wasi",
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"wasi",
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]
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]
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[[package]]
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name = "heck"
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version = "0.3.3"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "6d621efb26863f0e9924c6ac577e8275e5e6b77455db64ffa6c65c904e9e132c"
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dependencies = [
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"unicode-segmentation",
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]
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||||||
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[[package]]
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name = "hermit-abi"
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version = "0.1.19"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "62b467343b94ba476dcb2500d242dadbb39557df889310ac77c5d99100aaac33"
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dependencies = [
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"libc",
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||||||
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]
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||||||
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[[package]]
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[[package]]
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name = "lazy_static"
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name = "lazy_static"
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version = "1.4.0"
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version = "1.4.0"
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@ -160,6 +221,30 @@ version = "0.2.10"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
checksum = "ac74c624d6b2d21f425f752262f42188365d7b8ff1aff74c82e45136510a4857"
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checksum = "ac74c624d6b2d21f425f752262f42188365d7b8ff1aff74c82e45136510a4857"
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[[package]]
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name = "proc-macro-error"
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version = "1.0.4"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "da25490ff9892aab3fcf7c36f08cfb902dd3e71ca0f9f9517bea02a73a5ce38c"
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dependencies = [
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||||||
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"proc-macro-error-attr",
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||||||
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"proc-macro2",
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"quote",
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"syn",
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"version_check",
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]
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[[package]]
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name = "proc-macro-error-attr"
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version = "1.0.4"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "a1be40180e52ecc98ad80b184934baf3d0d29f979574e439af5a55274b35f869"
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dependencies = [
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"proc-macro2",
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"quote",
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"version_check",
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]
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[[package]]
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[[package]]
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name = "proc-macro2"
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name = "proc-macro2"
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version = "1.0.27"
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version = "1.0.27"
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@ -259,6 +344,36 @@ dependencies = [
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"rand",
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"rand",
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]
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]
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[[package]]
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name = "strsim"
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version = "0.8.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "8ea5119cdb4c55b55d432abb513a0429384878c15dde60cc77b1c99de1a95a6a"
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[[package]]
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name = "structopt"
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version = "0.3.22"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "69b041cdcb67226aca307e6e7be44c8806423d83e018bd662360a93dabce4d71"
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||||||
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dependencies = [
|
||||||
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"clap",
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||||||
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"lazy_static",
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||||||
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"structopt-derive",
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||||||
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]
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||||||
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||||||
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[[package]]
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||||||
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name = "structopt-derive"
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||||||
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version = "0.4.15"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "7813934aecf5f51a54775e00068c237de98489463968231a51746bbbc03f9c10"
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||||||
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dependencies = [
|
||||||
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"heck",
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||||||
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"proc-macro-error",
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||||||
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"proc-macro2",
|
||||||
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"quote",
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||||||
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"syn",
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||||||
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]
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||||||
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[[package]]
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[[package]]
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name = "syn"
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name = "syn"
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version = "1.0.73"
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version = "1.0.73"
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@ -270,20 +385,75 @@ dependencies = [
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||||||
"unicode-xid",
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"unicode-xid",
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]
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]
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||||||
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[[package]]
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name = "textwrap"
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version = "0.11.0"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "d326610f408c7a4eb6f51c37c330e496b08506c9457c9d34287ecc38809fb060"
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||||||
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dependencies = [
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||||||
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"unicode-width",
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||||||
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]
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||||||
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[[package]]
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[[package]]
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name = "typenum"
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name = "typenum"
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||||||
version = "1.13.0"
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version = "1.13.0"
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||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
checksum = "879f6906492a7cd215bfa4cf595b600146ccfac0c79bcbd1f3000162af5e8b06"
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checksum = "879f6906492a7cd215bfa4cf595b600146ccfac0c79bcbd1f3000162af5e8b06"
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||||||
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||||||
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[[package]]
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||||||
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name = "unicode-segmentation"
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||||||
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version = "1.8.0"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "8895849a949e7845e06bd6dc1aa51731a103c42707010a5b591c0038fb73385b"
|
||||||
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||||||
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[[package]]
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||||||
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name = "unicode-width"
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||||||
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version = "0.1.8"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "9337591893a19b88d8d87f2cec1e73fad5cdfd10e5a6f349f498ad6ea2ffb1e3"
|
||||||
|
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||||||
[[package]]
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[[package]]
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||||||
name = "unicode-xid"
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name = "unicode-xid"
|
||||||
version = "0.2.2"
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version = "0.2.2"
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
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source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
checksum = "8ccb82d61f80a663efe1f787a51b16b5a51e3314d6ac365b08639f52387b33f3"
|
checksum = "8ccb82d61f80a663efe1f787a51b16b5a51e3314d6ac365b08639f52387b33f3"
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||||||
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||||||
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[[package]]
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||||||
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name = "vec_map"
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||||||
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version = "0.8.2"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "f1bddf1187be692e79c5ffeab891132dfb0f236ed36a43c7ed39f1165ee20191"
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||||||
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||||||
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[[package]]
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name = "version_check"
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||||||
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version = "0.9.3"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "5fecdca9a5291cc2b8dcf7dc02453fee791a280f3743cb0905f8822ae463b3fe"
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[[package]]
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[[package]]
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||||||
name = "wasi"
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name = "wasi"
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||||||
version = "0.10.2+wasi-snapshot-preview1"
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version = "0.10.2+wasi-snapshot-preview1"
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||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
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source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
checksum = "fd6fbd9a79829dd1ad0cc20627bf1ed606756a7f77edff7b66b7064f9cb327c6"
|
checksum = "fd6fbd9a79829dd1ad0cc20627bf1ed606756a7f77edff7b66b7064f9cb327c6"
|
||||||
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|
||||||
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[[package]]
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||||||
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name = "winapi"
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||||||
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version = "0.3.9"
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||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "5c839a674fcd7a98952e593242ea400abe93992746761e38641405d28b00f419"
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||||||
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dependencies = [
|
||||||
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"winapi-i686-pc-windows-gnu",
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||||||
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"winapi-x86_64-pc-windows-gnu",
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||||||
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]
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[[package]]
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name = "winapi-i686-pc-windows-gnu"
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||||||
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version = "0.4.0"
|
||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||||
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checksum = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
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||||||
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||||||
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[[package]]
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||||||
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name = "winapi-x86_64-pc-windows-gnu"
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||||||
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version = "0.4.0"
|
||||||
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source = "registry+https://github.com/rust-lang/crates.io-index"
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||||||
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checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"
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||||||
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@ -1,6 +1,7 @@
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[package]
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[package]
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name = "circle_counting"
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name = "circle_counting"
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version = "0.1.0"
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version = "0.1.0"
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authors = [ "William Ball <wball1@swarthmore.edu> "]
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edition = "2018"
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edition = "2018"
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# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
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# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
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@ -8,3 +9,5 @@ edition = "2018"
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[dependencies]
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[dependencies]
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nalgebra = "*"
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nalgebra = "*"
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linregress = "*"
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linregress = "*"
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structopt = "*"
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ansi_term = "*"
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5
fractal_dimension/circle_counting_new/octahedron.txt
Normal file
5
fractal_dimension/circle_counting_new/octahedron.txt
Normal file
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@ -0,0 +1,5 @@
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{{{1., 0., 0., 0., 0.}, {0., 1., 0., 0., 0.}, {4., 3., 0., -1., 3.}, {4., 2., 0., -1., 4.}, {0., 0., 0., 0., 1.}}, {{1., 0., 0., 0., 0.}, {0., 1., 0., 0., 0.}, {0., 0., 1., 0., 0.}, {4., 3., 3., 0., -1.}, {4., 4., 2., 0., -1.}}, {{1., 0., 0., 0., 0.}, {4., -1., 4., 2., 0.}, {0., 0., 1., 0., 0.}, {0., 0., 0., 1., 0.}, {4., -1., 3., 3., 0.}}, {{1., 0., 0., 0., 0.}, {4., 0., -1., 3., 3.}, {4., 0., -1., 4., 2.}, {0., 0., 0., 1., 0.}, {0., 0., 0., 0., 1.}}, {{-1., 1., 0., 1., 0.}, {0., 1., 0., 0., 0.}, {0., 1., 0., 1., -1.}, {0., 0., 0., 1., 0.}, {0., 0., 0., 0., 1.}}}
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{-0.513181, 1.23893, 1.23893, 1.23893, 1.23893}
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{{0, 1, 4}, {0, 2, 1}, {0, 3, 2}, {0, 4, 3}, {1, 2, 3, 4}}
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101
fractal_dimension/circle_counting_new/src/lib.rs
Normal file
101
fractal_dimension/circle_counting_new/src/lib.rs
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@ -0,0 +1,101 @@
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use linregress::{FormulaRegressionBuilder, RegressionDataBuilder};
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use nalgebra::{DMatrix, DVector};
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use ansi_term::Color::Yellow;
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pub fn fractal_dimension(
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generators: Vec<DMatrix<f64>>,
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root: DVector<f64>,
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faces: Vec<Vec<usize>>,
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upper_bound: f64,
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n: usize,
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debug: bool,
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) -> Result<f64, linregress::Error> {
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let mut totals = vec![root.len(); n];
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let mut current = vec![(root, std::usize::MAX)];
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let mut next = vec![];
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let xs: Vec<f64> = (1..=n)
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.map(|x| (x as f64 * upper_bound / (n as f64)))
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.collect();
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let mut i = 0;
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loop {
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next.clear();
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for (tuple, previous_generator) in ¤t {
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for (i, generator) in generators.iter().enumerate() {
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if i != *previous_generator {
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let new_tuple = generator * tuple;
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let mut add = false;
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for (j, curvature) in new_tuple.iter().enumerate() {
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let mut skip = false;
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for face in &faces[i] {
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if j == *face {
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skip = true;
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break;
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}
|
||||||
|
}
|
||||||
|
if skip {
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
for (k, max) in xs.iter().enumerate() {
|
||||||
|
if curvature <= max {
|
||||||
|
if k == n - 1 {
|
||||||
|
add = true;
|
||||||
|
}
|
||||||
|
totals[k] += 1;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if add {
|
||||||
|
next.push((new_tuple, i));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
std::mem::swap(&mut current, &mut next);
|
||||||
|
|
||||||
|
i += 1;
|
||||||
|
if debug {
|
||||||
|
println!("Generation {}:", i);
|
||||||
|
println!("\tnumber of leaves:\t{}", current.len());
|
||||||
|
if !current.is_empty() {
|
||||||
|
println!("\trandom tuple:\t\t{}", current[current.len() / 2].0);
|
||||||
|
}
|
||||||
|
println!();
|
||||||
|
}
|
||||||
|
|
||||||
|
if current.is_empty() {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if debug {
|
||||||
|
println!("{}", Yellow.paint("Done counting circles!"));
|
||||||
|
println!("sample points:\n{:?}", xs);
|
||||||
|
println!("\nnumber of circles fewer than each of those sample points:\n{:?}", totals);
|
||||||
|
}
|
||||||
|
|
||||||
|
let xs: Vec<f64> = xs.iter().map(|x| x.ln()).collect();
|
||||||
|
let ys: Vec<f64> = totals.iter().map(|x| (*x as f64).ln()).collect();
|
||||||
|
let data = vec![("Y", ys), ("X", xs)];
|
||||||
|
let data = RegressionDataBuilder::new().build_from(data)?;
|
||||||
|
|
||||||
|
let formula = "Y ~ X";
|
||||||
|
let model = FormulaRegressionBuilder::new()
|
||||||
|
.data(&data)
|
||||||
|
.formula(formula)
|
||||||
|
.fit()?;
|
||||||
|
|
||||||
|
if debug {
|
||||||
|
println!("\n{}", Yellow.paint("Built regression model!"));
|
||||||
|
println!("Model info:");
|
||||||
|
println!("\tr^2:\t\t{}", model.rsquared);
|
||||||
|
println!("\tp-value:\t{}", model.pvalues.pairs()[0].1);
|
||||||
|
println!("\tintercept:\t{}", model.parameters.intercept_value);
|
||||||
|
println!("\tslope:\t{}", model.parameters.regressor_values[0]);
|
||||||
|
}
|
||||||
|
|
||||||
|
let parameters = model.parameters;
|
||||||
|
|
||||||
|
Ok(parameters.regressor_values[0])
|
||||||
|
}
|
||||||
|
|
@ -1,79 +1,107 @@
|
||||||
use nalgebra::{SMatrix, SVector};
|
#![allow(dead_code)]
|
||||||
use linregress::{FormulaRegressionBuilder, RegressionDataBuilder};
|
|
||||||
|
|
||||||
type Matrix4 = SMatrix<f64, 4, 4>;
|
use crate::{lib::fractal_dimension, parser::read_file};
|
||||||
type Vector4 = SVector<f64, 4>;
|
use std::process;
|
||||||
|
use structopt::StructOpt;
|
||||||
|
|
||||||
fn search(generators: &Vec<Matrix4>, root: Vector4, upper_bound: f64) -> usize {
|
use ansi_term::Color::Yellow;
|
||||||
let mut current = vec![(root, 5)];
|
|
||||||
let mut next = vec![];
|
|
||||||
let mut total = 0;
|
|
||||||
loop {
|
|
||||||
next.clear();
|
|
||||||
for (tuple, previous_generator) in ¤t {
|
|
||||||
for (i, generator) in generators.iter().enumerate() {
|
|
||||||
let new_tuple = generator * tuple;
|
|
||||||
if !(i == 0 && *previous_generator == 3) && !(i == 1 && *previous_generator == 2) && i != *previous_generator && new_tuple[i] < upper_bound && new_tuple.iter().sum::<f64>() > tuple.iter().sum() {
|
|
||||||
next.push((new_tuple, i));
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
if current.is_empty() {
|
mod lib;
|
||||||
break;
|
mod parser;
|
||||||
}
|
|
||||||
total += next.len();
|
|
||||||
std::mem::swap(&mut current, &mut next);
|
|
||||||
}
|
|
||||||
2 * (total + root.len())
|
|
||||||
}
|
|
||||||
|
|
||||||
fn fractal_dimension(generators: Vec<Matrix4>, root: Vector4, upper_bound: f64, n: isize) -> Result<f64, linregress::Error> {
|
/// Compute fractal dimension of crystallographic packings via the circle counting method
|
||||||
let xs: Vec<f64> = (1..=n).map(|x| (x as f64 * upper_bound / (n as f64)).ln()).collect();
|
#[derive(StructOpt)]
|
||||||
let ys: Vec<f64> = xs.iter().map(|upper_bound| (search(&generators, root, upper_bound.exp()) as f64).ln()).collect();
|
#[structopt(name = "Circle Counter")]
|
||||||
|
struct Opt {
|
||||||
|
/// File containing data in the order generators, root, faces
|
||||||
|
#[structopt(name = "data file")]
|
||||||
|
data_file: String,
|
||||||
|
|
||||||
let data = vec![("Y", ys), ("X", xs)];
|
/// Activate debug mode
|
||||||
let data = RegressionDataBuilder::new().build_from(data)?;
|
#[structopt(short, long)]
|
||||||
|
debug: bool,
|
||||||
|
|
||||||
let formula = "Y ~ X";
|
/// Number of sample points in linear regression
|
||||||
let model = FormulaRegressionBuilder::new()
|
#[structopt(short, long, default_value = "50")]
|
||||||
.data(&data)
|
n: usize,
|
||||||
.formula(formula)
|
|
||||||
.fit()?;
|
|
||||||
|
|
||||||
let parameters = model.parameters;
|
/// Maximum curvature of circles
|
||||||
Ok(parameters.regressor_values[0])
|
#[structopt(short, long, default_value = "1000000")]
|
||||||
|
max: f64,
|
||||||
|
|
||||||
|
/// Whether or not to time excecution (automatically enabled by --debug)
|
||||||
|
#[structopt(short, long)]
|
||||||
|
time: bool,
|
||||||
}
|
}
|
||||||
|
|
||||||
fn main() {
|
fn main() {
|
||||||
let generators = vec![
|
let opt = Opt::from_args();
|
||||||
Matrix4::new(
|
let debug = opt.debug;
|
||||||
-1.0, 2.0, 2.0, 0.0,
|
let time = debug || opt.time;
|
||||||
0.0, 1.0, 0.0, 0.0,
|
|
||||||
0.0, 0.0, 1.0, 0.0,
|
|
||||||
0.0, 0.0, 0.0, 1.0,
|
|
||||||
),
|
|
||||||
Matrix4::new(
|
|
||||||
1.0, 0.0, 0.0, 0.0,
|
|
||||||
2.0, -1.0, 0.0, 2.0,
|
|
||||||
0.0, 0.0, 1.0, 0.0,
|
|
||||||
0.0, 0.0, 0.0, 1.0,
|
|
||||||
),
|
|
||||||
Matrix4::new(
|
|
||||||
1.0, 0.0, 0.0, 0.0,
|
|
||||||
0.0, 1.0, 0.0, 0.0,
|
|
||||||
2.0, 0.0, -1.0, 2.0,
|
|
||||||
0.0, 0.0, 0.0, 1.0,
|
|
||||||
),
|
|
||||||
Matrix4::new(
|
|
||||||
1.0, 0.0, 0.0, 0.0,
|
|
||||||
0.0, 1.0, 0.0, 0.0,
|
|
||||||
0.0, 0.0, 1.0, 0.0,
|
|
||||||
0.0, 2.0, 2.0, -1.0,
|
|
||||||
),
|
|
||||||
];
|
|
||||||
|
|
||||||
let root = Vector4::new(-2., 4., 5., 9.);
|
let beginning = std::time::Instant::now();
|
||||||
|
|
||||||
println!("{}", fractal_dimension(generators, root, 10_000_000.0, 50).unwrap());
|
let (generators, root, faces) = read_file(&opt.data_file).unwrap_or_else(|err| {
|
||||||
|
eprintln!("{}", err);
|
||||||
|
process::exit(-1);
|
||||||
|
});
|
||||||
|
|
||||||
|
let after_parsing = std::time::Instant::now();
|
||||||
|
if time {
|
||||||
|
let duration = after_parsing.duration_since(beginning);
|
||||||
|
println!(
|
||||||
|
"Took {}s to parse {}",
|
||||||
|
duration.as_secs_f64(),
|
||||||
|
opt.data_file
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
if debug {
|
||||||
|
println!(
|
||||||
|
"{} (parsed from command args):\t{}",
|
||||||
|
Yellow.paint("max"),
|
||||||
|
opt.max
|
||||||
|
);
|
||||||
|
println!(
|
||||||
|
"{} (parsed from command args):\t{}",
|
||||||
|
Yellow.paint("n"),
|
||||||
|
opt.n
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
if debug {
|
||||||
|
println!(
|
||||||
|
"{} (parsed from file {})",
|
||||||
|
Yellow.paint("Generators"),
|
||||||
|
opt.data_file
|
||||||
|
);
|
||||||
|
for generator in &generators {
|
||||||
|
println!("{}", generator);
|
||||||
|
}
|
||||||
|
println!(
|
||||||
|
"{} (parsed from file {}):",
|
||||||
|
Yellow.paint("Root Tuple"),
|
||||||
|
opt.data_file
|
||||||
|
);
|
||||||
|
println!("{}", root);
|
||||||
|
println!(
|
||||||
|
"{} (parsed from file {}):",
|
||||||
|
Yellow.paint("Faces"),
|
||||||
|
opt.data_file
|
||||||
|
);
|
||||||
|
println!("{:?}\n", faces);
|
||||||
|
}
|
||||||
|
|
||||||
|
let delta = fractal_dimension(generators, root, faces, opt.max, opt.n, debug).unwrap();
|
||||||
|
let after_computing = std::time::Instant::now();
|
||||||
|
if time {
|
||||||
|
let duration1 = after_computing.duration_since(after_parsing);
|
||||||
|
let duration2 = after_computing.duration_since(beginning);
|
||||||
|
println!(
|
||||||
|
"\nTook {}s to compute fractal dimension; {}s total",
|
||||||
|
duration1.as_secs_f64(),
|
||||||
|
duration2.as_secs_f64()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
println!("\n{}", delta);
|
||||||
}
|
}
|
||||||
|
|
|
||||||
393
fractal_dimension/circle_counting_new/src/parser.rs
Normal file
393
fractal_dimension/circle_counting_new/src/parser.rs
Normal file
|
|
@ -0,0 +1,393 @@
|
||||||
|
use std::fs;
|
||||||
|
|
||||||
|
use nalgebra::{DMatrix, DVector};
|
||||||
|
|
||||||
|
#[derive(Debug, PartialEq)]
|
||||||
|
enum TokenType {
|
||||||
|
OpenBracket,
|
||||||
|
CloseBracket,
|
||||||
|
Number(f64),
|
||||||
|
Error(String),
|
||||||
|
Comma,
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Debug, PartialEq)]
|
||||||
|
struct Token {
|
||||||
|
ttype: TokenType,
|
||||||
|
line: usize,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl Token {
|
||||||
|
#[allow(dead_code)]
|
||||||
|
fn new(ttype: TokenType, line: usize) -> Token {
|
||||||
|
Token { ttype, line }
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
struct TokenIterator<'a> {
|
||||||
|
data: std::iter::Peekable<std::str::Chars<'a>>,
|
||||||
|
line: usize,
|
||||||
|
}
|
||||||
|
|
||||||
|
impl<'a> Iterator for TokenIterator<'a> {
|
||||||
|
type Item = Token;
|
||||||
|
|
||||||
|
fn next(&mut self) -> Option<Self::Item> {
|
||||||
|
let mut current: char = self.data.next()?;
|
||||||
|
while current.is_whitespace() {
|
||||||
|
if current == '\n' {
|
||||||
|
self.line += 1;
|
||||||
|
}
|
||||||
|
current = self.data.next()?;
|
||||||
|
}
|
||||||
|
use TokenType::*;
|
||||||
|
match current {
|
||||||
|
'{' => {
|
||||||
|
return Some(Token {
|
||||||
|
ttype: OpenBracket,
|
||||||
|
line: self.line,
|
||||||
|
})
|
||||||
|
}
|
||||||
|
'}' => {
|
||||||
|
return Some(Token {
|
||||||
|
ttype: CloseBracket,
|
||||||
|
line: self.line,
|
||||||
|
})
|
||||||
|
}
|
||||||
|
',' => {
|
||||||
|
return Some(Token {
|
||||||
|
ttype: Comma,
|
||||||
|
line: self.line,
|
||||||
|
})
|
||||||
|
}
|
||||||
|
_ => (),
|
||||||
|
}
|
||||||
|
if current.is_numeric() || current == '-' {
|
||||||
|
let mut s: String = "".into();
|
||||||
|
loop {
|
||||||
|
s.push(current);
|
||||||
|
if let Some(c) = self.data.peek() {
|
||||||
|
current = *c;
|
||||||
|
} else {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
if !current.is_numeric() && current != '.' {
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
let _ = self.data.next();
|
||||||
|
}
|
||||||
|
|
||||||
|
Some(Token {
|
||||||
|
ttype: Number(s.parse().ok()?),
|
||||||
|
line: self.line,
|
||||||
|
})
|
||||||
|
} else {
|
||||||
|
Some(Token {
|
||||||
|
ttype: Error(format!("Invalid token {} on line {}", current, self.line)),
|
||||||
|
line: self.line,
|
||||||
|
})
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fn lex(data: &str) -> TokenIterator {
|
||||||
|
TokenIterator {
|
||||||
|
data: data.chars().peekable(),
|
||||||
|
line: 1,
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[derive(Debug, PartialEq)]
|
||||||
|
enum Value {
|
||||||
|
List(Vec<Value>),
|
||||||
|
Number(f64),
|
||||||
|
}
|
||||||
|
|
||||||
|
fn eval_full(data: String) -> Result<Vec<Value>, String> {
|
||||||
|
let mut data = lex(data.as_str()).peekable();
|
||||||
|
let mut values = vec![];
|
||||||
|
while data.peek().is_some() {
|
||||||
|
values.push(eval(&mut data)?);
|
||||||
|
}
|
||||||
|
Ok(values)
|
||||||
|
}
|
||||||
|
|
||||||
|
fn eval(data: &mut std::iter::Peekable<TokenIterator>) -> Result<Value, String> {
|
||||||
|
let token = data
|
||||||
|
.next()
|
||||||
|
.unwrap_or_else(|| Token::new(TokenType::Error("Unable to parse!".to_string()), 0));
|
||||||
|
match token.ttype {
|
||||||
|
TokenType::OpenBracket => {
|
||||||
|
let mut list = vec![];
|
||||||
|
while let Some(token) = data.peek() {
|
||||||
|
match &token.ttype {
|
||||||
|
TokenType::CloseBracket => {
|
||||||
|
data.next();
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
TokenType::Comma => {
|
||||||
|
return Err(format!("Unexpected ',' on line {}", token.line));
|
||||||
|
}
|
||||||
|
TokenType::Error(e) => return Err(e.into()),
|
||||||
|
_ => list.push(eval(data)?),
|
||||||
|
};
|
||||||
|
match data.peek() {
|
||||||
|
Some(Token {
|
||||||
|
ttype: TokenType::Comma,
|
||||||
|
..
|
||||||
|
}) => {
|
||||||
|
data.next();
|
||||||
|
}
|
||||||
|
Some(Token {
|
||||||
|
ttype: TokenType::CloseBracket,
|
||||||
|
..
|
||||||
|
}) => (),
|
||||||
|
Some(Token { ttype, line }) => {
|
||||||
|
return Err(format!(
|
||||||
|
"Expected ',' or '}}' near line {}; got {:?}",
|
||||||
|
line, ttype
|
||||||
|
))
|
||||||
|
}
|
||||||
|
None => {
|
||||||
|
return Err("Unexpected end of file".into());
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
Ok(Value::List(list))
|
||||||
|
}
|
||||||
|
TokenType::CloseBracket => Err(format!("Unexpected '}}' on line {}", token.line)),
|
||||||
|
TokenType::Number(num) => Ok(Value::Number(num)),
|
||||||
|
TokenType::Error(err) => Err(err),
|
||||||
|
TokenType::Comma => Err(format!("Unexpected ',' on line {}", token.line)),
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fn vector_to_rust_value(value: &Value) -> Result<Vec<f64>, String> {
|
||||||
|
let mut result = vec![];
|
||||||
|
|
||||||
|
if let Value::List(data) = value {
|
||||||
|
for datapoint in data {
|
||||||
|
if let Value::Number(num) = datapoint {
|
||||||
|
result.push(*num);
|
||||||
|
} else {
|
||||||
|
return Err(format!("Expected a number, got {:?}", datapoint));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
return Err(format!("Expected a list, got {:?}", value));
|
||||||
|
}
|
||||||
|
|
||||||
|
Ok(result)
|
||||||
|
}
|
||||||
|
|
||||||
|
fn matrix_to_rust_value(value: &Value) -> Result<Vec<Vec<f64>>, String> {
|
||||||
|
let mut result = vec![];
|
||||||
|
|
||||||
|
if let Value::List(data) = value {
|
||||||
|
for row in data {
|
||||||
|
if let Value::List(_) = row {
|
||||||
|
result.push(vector_to_rust_value(row)?);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
return Err(format!("Expected a list, got {:?}", value));
|
||||||
|
}
|
||||||
|
|
||||||
|
Ok(result)
|
||||||
|
}
|
||||||
|
|
||||||
|
fn matrix_to_rust_value_flat(value: &Value) -> Result<Vec<f64>, String> {
|
||||||
|
let mut result = vec![];
|
||||||
|
|
||||||
|
if let Value::List(data) = value {
|
||||||
|
for row in data {
|
||||||
|
if let Value::List(_) = row {
|
||||||
|
result.append(&mut vector_to_rust_value(row)?);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
return Err(format!("Expected a list, got {:?}", value));
|
||||||
|
}
|
||||||
|
|
||||||
|
Ok(result)
|
||||||
|
}
|
||||||
|
|
||||||
|
pub type Generator = DMatrix<f64>;
|
||||||
|
pub type Root = DVector<f64>;
|
||||||
|
pub type FaceList = Vec<Vec<usize>>;
|
||||||
|
pub type Data = (Vec<Generator>, Root, FaceList);
|
||||||
|
pub fn read_file(filename: &str) -> Result<Data, String> {
|
||||||
|
let contents = match fs::read_to_string(filename) {
|
||||||
|
Ok(contents) => contents,
|
||||||
|
_ => return Err(format!("Something went wrong with reading {}", filename)),
|
||||||
|
};
|
||||||
|
|
||||||
|
let results = eval_full(contents)?;
|
||||||
|
|
||||||
|
let mut generators = vec![];
|
||||||
|
if let Value::List(gens) = &results[0] {
|
||||||
|
for val in gens {
|
||||||
|
let mat = matrix_to_rust_value(val)?;
|
||||||
|
let mat2 = matrix_to_rust_value_flat(val)?;
|
||||||
|
generators.push(DMatrix::from_row_slice(mat.len(), mat[0].len(), &mat2));
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
return Err(format!(
|
||||||
|
"Expected first value in file to be the generators; got {:?}",
|
||||||
|
results[0]
|
||||||
|
));
|
||||||
|
}
|
||||||
|
|
||||||
|
let root = vector_to_rust_value(&results[1])?;
|
||||||
|
let faces = matrix_to_rust_value(&results[2])?;
|
||||||
|
let faces = faces
|
||||||
|
.iter()
|
||||||
|
.map(|v| v.iter().map(|x| x.round() as usize).collect())
|
||||||
|
.collect();
|
||||||
|
|
||||||
|
Ok((generators, DVector::from_column_slice(&root), faces))
|
||||||
|
}
|
||||||
|
|
||||||
|
#[cfg(test)]
|
||||||
|
mod test {
|
||||||
|
use super::*;
|
||||||
|
use TokenType::*;
|
||||||
|
|
||||||
|
fn tok(ttype: TokenType, line: usize) -> Option<Token> {
|
||||||
|
Some(Token::new(ttype, line))
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn parens() {
|
||||||
|
let mut lex = lex("{}");
|
||||||
|
assert_eq!(lex.next(), tok(OpenBracket, 1));
|
||||||
|
assert_eq!(lex.next(), tok(CloseBracket, 1));
|
||||||
|
assert_eq!(lex.next(), None);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn nums() {
|
||||||
|
let mut lex = lex("1.12341\n3.1415926535");
|
||||||
|
assert_eq!(lex.next(), tok(Number(1.12341), 1));
|
||||||
|
assert_eq!(lex.next(), tok(Number(3.1415926535), 2));
|
||||||
|
assert_eq!(lex.next(), None);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn list() {
|
||||||
|
let mut lex = lex("{1, 2, 3, 4}");
|
||||||
|
assert_eq!(lex.next(), tok(OpenBracket, 1));
|
||||||
|
assert_eq!(lex.next(), tok(Number(1.), 1));
|
||||||
|
assert_eq!(lex.next(), tok(Comma, 1));
|
||||||
|
assert_eq!(lex.next(), tok(Number(2.), 1));
|
||||||
|
assert_eq!(lex.next(), tok(Comma, 1));
|
||||||
|
assert_eq!(lex.next(), tok(Number(3.), 1));
|
||||||
|
assert_eq!(lex.next(), tok(Comma, 1));
|
||||||
|
assert_eq!(lex.next(), tok(Number(4.), 1));
|
||||||
|
assert_eq!(lex.next(), tok(CloseBracket, 1));
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn nums_eval() {
|
||||||
|
let res = eval_full("1.23".into()).unwrap();
|
||||||
|
assert_eq!(res, vec![Value::Number(1.23)]);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn empty_list_eval() {
|
||||||
|
let res = eval_full("{}".into()).unwrap();
|
||||||
|
assert_eq!(res, vec![Value::List(vec![])]);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn simple_list_eval() {
|
||||||
|
let res = eval_full("{1.1}".into()).unwrap();
|
||||||
|
assert_eq!(res, vec![Value::List(vec![Value::Number(1.1)])]);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn list_eval() {
|
||||||
|
let res = eval_full("{\n1.23\n,\n2.3\n,\n1.5\n}".into()).unwrap();
|
||||||
|
assert_eq!(
|
||||||
|
res,
|
||||||
|
vec![Value::List(vec![
|
||||||
|
Value::Number(1.23),
|
||||||
|
Value::Number(2.3),
|
||||||
|
Value::Number(1.5),
|
||||||
|
])]
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn multiple_lines_eval() {
|
||||||
|
let res = eval_full("1.0 \n {1.0, 2.0}\n".into()).unwrap();
|
||||||
|
assert_eq!(
|
||||||
|
res,
|
||||||
|
vec![
|
||||||
|
Value::Number(1.0),
|
||||||
|
Value::List(vec![Value::Number(1.0), Value::Number(2.0)])
|
||||||
|
]
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn nested_list_eval() {
|
||||||
|
let res = eval_full("{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}".into()).unwrap();
|
||||||
|
assert_eq!(
|
||||||
|
res,
|
||||||
|
vec![Value::List(vec![
|
||||||
|
Value::List(vec![
|
||||||
|
Value::Number(1.0),
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(0.0)
|
||||||
|
]),
|
||||||
|
Value::List(vec![
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(1.0),
|
||||||
|
Value::Number(0.0)
|
||||||
|
]),
|
||||||
|
Value::List(vec![
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(1.0)
|
||||||
|
])
|
||||||
|
])]
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn vector() {
|
||||||
|
let test = Value::List(vec![Value::Number(1.0), Value::Number(2.0)]);
|
||||||
|
assert_eq!(vector_to_rust_value(&test).unwrap(), vec![1.0, 2.0]);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn matrix() {
|
||||||
|
let val = Value::List(vec![
|
||||||
|
Value::List(vec![
|
||||||
|
Value::Number(1.0),
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(0.0),
|
||||||
|
]),
|
||||||
|
Value::List(vec![
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(1.0),
|
||||||
|
Value::Number(0.0),
|
||||||
|
]),
|
||||||
|
Value::List(vec![
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(0.0),
|
||||||
|
Value::Number(1.0),
|
||||||
|
]),
|
||||||
|
]);
|
||||||
|
let res = matrix_to_rust_value(&val).unwrap();
|
||||||
|
assert_eq!(
|
||||||
|
res,
|
||||||
|
vec![
|
||||||
|
vec![1.0, 0.0, 0.0],
|
||||||
|
vec![0.0, 1.0, 0.0],
|
||||||
|
vec![0.0, 0.0, 1.0]
|
||||||
|
]
|
||||||
|
);
|
||||||
|
}
|
||||||
|
}
|
||||||
30
fractal_dimension/circle_counting_new/tetrahedron.txt
Normal file
30
fractal_dimension/circle_counting_new/tetrahedron.txt
Normal file
|
|
@ -0,0 +1,30 @@
|
||||||
|
{
|
||||||
|
{
|
||||||
|
{-1, 2, 2, 2},
|
||||||
|
{0, 1, 0, 0},
|
||||||
|
{0, 0, 1, 0},
|
||||||
|
{0, 0, 0, 1}
|
||||||
|
},
|
||||||
|
{
|
||||||
|
{1, 0, 0, 0},
|
||||||
|
{2, -1, 2, 2},
|
||||||
|
{0, 0, 1, 0},
|
||||||
|
{0, 0, 0, 1}
|
||||||
|
},
|
||||||
|
{
|
||||||
|
{1, 0, 0, 0},
|
||||||
|
{0, 1, 0, 0},
|
||||||
|
{2, 2, -1, 2},
|
||||||
|
{0, 0, 0, 1}
|
||||||
|
},
|
||||||
|
{
|
||||||
|
{1, 0, 0, 0},
|
||||||
|
{0, 1, 0, 0},
|
||||||
|
{0, 0, 1, 0},
|
||||||
|
{2, 2, 2, -1}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
{-6, 11, 14, 23}
|
||||||
|
|
||||||
|
{{1, 2, 3}, {0, 2, 3}, {0, 1, 3}, {0, 1, 2}}
|
||||||
File diff suppressed because it is too large
Load diff
|
|
@ -2,7 +2,7 @@
|
||||||
"cells": [
|
"cells": [
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 1,
|
"execution_count": 2,
|
||||||
"metadata": {
|
"metadata": {
|
||||||
"executionInfo": {
|
"executionInfo": {
|
||||||
"elapsed": 118,
|
"elapsed": 118,
|
||||||
|
|
@ -28,7 +28,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 2,
|
"execution_count": 3,
|
||||||
"metadata": {
|
"metadata": {
|
||||||
"id": "G01gxmY2QI64"
|
"id": "G01gxmY2QI64"
|
||||||
},
|
},
|
||||||
|
|
@ -95,7 +95,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 5,
|
"execution_count": 6,
|
||||||
"metadata": {
|
"metadata": {
|
||||||
"id": "xY_oNcRDl797"
|
"id": "xY_oNcRDl797"
|
||||||
},
|
},
|
||||||
|
|
@ -106,53 +106,35 @@
|
||||||
"text": [
|
"text": [
|
||||||
"[1]\n",
|
"[1]\n",
|
||||||
"[1, 2]\n",
|
"[1, 2]\n",
|
||||||
|
"[1, 2, 1]\n",
|
||||||
|
"[1, 2, 3]\n",
|
||||||
|
"[1, 2, 4]\n",
|
||||||
"[1, 3]\n",
|
"[1, 3]\n",
|
||||||
"[1, 3, 1]\n",
|
"[1, 3, 1]\n",
|
||||||
|
"[1, 3, 1, 2]\n",
|
||||||
|
"[1, 3, 1, 3]\n",
|
||||||
|
"[1, 3, 1, 4]\n",
|
||||||
"[1, 3, 2]\n",
|
"[1, 3, 2]\n",
|
||||||
"[1, 3, 4]\n",
|
"[1, 3, 4]\n",
|
||||||
"[1, 4]\n",
|
"[1, 4]\n",
|
||||||
"[1, 4, 1]\n",
|
|
||||||
"[1, 4, 2]\n",
|
|
||||||
"[1, 4, 3]\n",
|
|
||||||
"[1, 4, 3, 1]\n",
|
|
||||||
"[1, 4, 3, 2]\n",
|
|
||||||
"[1, 4, 3, 4]\n",
|
|
||||||
"[2]\n",
|
"[2]\n",
|
||||||
"[2, 1]\n",
|
"[2, 1]\n",
|
||||||
"[2, 1, 2]\n",
|
|
||||||
"[2, 1, 2, 1]\n",
|
|
||||||
"[2, 1, 2, 3]\n",
|
|
||||||
"[2, 1, 2, 4]\n",
|
|
||||||
"[2, 1, 3]\n",
|
|
||||||
"[2, 1, 3, 1]\n",
|
|
||||||
"[2, 1, 3, 2]\n",
|
|
||||||
"[2, 1, 3, 4]\n",
|
|
||||||
"[2, 1, 4]\n",
|
|
||||||
"[2, 1, 4, 1]\n",
|
|
||||||
"[2, 1, 4, 2]\n",
|
|
||||||
"[2, 1, 4, 3]\n",
|
|
||||||
"[2, 3]\n",
|
"[2, 3]\n",
|
||||||
|
"[2, 3, 1]\n",
|
||||||
|
"[2, 3, 2]\n",
|
||||||
|
"[2, 3, 4]\n",
|
||||||
|
"[2, 3, 4, 1]\n",
|
||||||
|
"[2, 3, 4, 2]\n",
|
||||||
|
"[2, 3, 4, 3]\n",
|
||||||
"[2, 4]\n",
|
"[2, 4]\n",
|
||||||
"[3]\n",
|
"[3]\n",
|
||||||
"[3, 1]\n",
|
"[3, 1]\n",
|
||||||
"[3, 1, 2]\n",
|
"[3, 1, 2]\n",
|
||||||
"[3, 1, 2, 1]\n",
|
|
||||||
"[3, 1, 2, 3]\n",
|
|
||||||
"[3, 1, 2, 3, 1]\n",
|
|
||||||
"[3, 1, 2, 3, 1, 2]\n",
|
|
||||||
"[3, 1, 2, 3, 1, 3]\n",
|
|
||||||
"[3, 1, 2, 3, 1, 4]\n",
|
|
||||||
"[3, 1, 2, 3, 1, 4, 1]\n",
|
|
||||||
"[3, 1, 2, 3, 1, 4, 2]\n",
|
|
||||||
"[3, 1, 2, 3, 1, 4, 3]\n",
|
|
||||||
"[3, 1, 2, 3, 2]\n",
|
|
||||||
"[3, 1, 2, 3, 2, 1]\n",
|
|
||||||
"[3, 1, 2, 3, 2, 3]\n",
|
|
||||||
"[3, 1, 2, 3, 2, 4]\n",
|
|
||||||
"[3, 1, 2, 3, 4]\n",
|
|
||||||
"[3, 1, 2, 4]\n",
|
|
||||||
"[3, 1, 3]\n",
|
"[3, 1, 3]\n",
|
||||||
"[3, 1, 4]\n",
|
"[3, 1, 4]\n",
|
||||||
|
"[3, 1, 4, 1]\n",
|
||||||
|
"[3, 1, 4, 2]\n",
|
||||||
|
"[3, 1, 4, 3]\n",
|
||||||
"[3, 2]\n",
|
"[3, 2]\n",
|
||||||
"[3, 2, 1]\n",
|
"[3, 2, 1]\n",
|
||||||
"[3, 2, 1, 2]\n",
|
"[3, 2, 1, 2]\n",
|
||||||
|
|
@ -162,42 +144,27 @@
|
||||||
"[3, 2, 4]\n",
|
"[3, 2, 4]\n",
|
||||||
"[3, 4]\n",
|
"[3, 4]\n",
|
||||||
"[3, 4, 1]\n",
|
"[3, 4, 1]\n",
|
||||||
"[3, 4, 1, 2]\n",
|
|
||||||
"[3, 4, 1, 3]\n",
|
|
||||||
"[3, 4, 1, 3, 1]\n",
|
|
||||||
"[3, 4, 1, 3, 2]\n",
|
|
||||||
"[3, 4, 1, 3, 4]\n",
|
|
||||||
"[3, 4, 1, 3, 4, 1]\n",
|
|
||||||
"[3, 4, 1, 3, 4, 2]\n",
|
|
||||||
"[3, 4, 1, 3, 4, 3]\n",
|
|
||||||
"[3, 4, 1, 4]\n",
|
|
||||||
"[3, 4, 2]\n",
|
"[3, 4, 2]\n",
|
||||||
"[3, 4, 2, 1]\n",
|
|
||||||
"[3, 4, 2, 3]\n",
|
|
||||||
"[3, 4, 2, 4]\n",
|
|
||||||
"[3, 4, 3]\n",
|
"[3, 4, 3]\n",
|
||||||
"[4]\n",
|
"[4]\n",
|
||||||
"[4, 1]\n",
|
"[4, 1]\n",
|
||||||
"[4, 2]\n",
|
"[4, 2]\n",
|
||||||
"[4, 2, 1]\n",
|
"[4, 2, 1]\n",
|
||||||
|
"[4, 2, 1, 2]\n",
|
||||||
|
"[4, 2, 1, 3]\n",
|
||||||
|
"[4, 2, 1, 4]\n",
|
||||||
|
"[4, 2, 1, 4, 1]\n",
|
||||||
|
"[4, 2, 1, 4, 2]\n",
|
||||||
|
"[4, 2, 1, 4, 3]\n",
|
||||||
"[4, 2, 3]\n",
|
"[4, 2, 3]\n",
|
||||||
"[4, 2, 4]\n",
|
"[4, 2, 4]\n",
|
||||||
"[4, 3]\n",
|
"[4, 2, 4, 1]\n",
|
||||||
"[4, 3, 1]\n",
|
"[4, 2, 4, 2]\n",
|
||||||
"[4, 3, 2]\n",
|
"[4, 2, 4, 2, 1]\n",
|
||||||
"[4, 3, 2, 1]\n",
|
"[4, 2, 4, 2, 3]\n",
|
||||||
"[4, 3, 2, 3]\n",
|
"[4, 2, 4, 2, 4]\n",
|
||||||
"[4, 3, 2, 3, 1]\n",
|
"[4, 2, 4, 3]\n",
|
||||||
"[4, 3, 2, 3, 2]\n",
|
"[4, 3]\n"
|
||||||
"[4, 3, 2, 3, 2, 1]\n",
|
|
||||||
"[4, 3, 2, 3, 2, 1, 2]\n",
|
|
||||||
"[4, 3, 2, 3, 2, 1, 3]\n",
|
|
||||||
"[4, 3, 2, 3, 2, 1, 4]\n",
|
|
||||||
"[4, 3, 2, 3, 2, 3]\n",
|
|
||||||
"[4, 3, 2, 3, 2, 4]\n",
|
|
||||||
"[4, 3, 2, 3, 4]\n",
|
|
||||||
"[4, 3, 2, 4]\n",
|
|
||||||
"[4, 3, 4]\n"
|
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
|
|
@ -215,7 +182,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 4,
|
"execution_count": 5,
|
||||||
"metadata": {
|
"metadata": {
|
||||||
"executionInfo": {
|
"executionInfo": {
|
||||||
"elapsed": 490,
|
"elapsed": 490,
|
||||||
|
|
@ -271,7 +238,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 6,
|
"execution_count": 7,
|
||||||
"metadata": {
|
"metadata": {
|
||||||
"executionInfo": {
|
"executionInfo": {
|
||||||
"elapsed": 3,
|
"elapsed": 3,
|
||||||
|
|
@ -307,7 +274,7 @@
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 7,
|
"execution_count": 9,
|
||||||
"metadata": {
|
"metadata": {
|
||||||
"colab": {
|
"colab": {
|
||||||
"base_uri": "https://localhost:8080/"
|
"base_uri": "https://localhost:8080/"
|
||||||
|
|
@ -331,18 +298,19 @@
|
||||||
"name": "stdout",
|
"name": "stdout",
|
||||||
"output_type": "stream",
|
"output_type": "stream",
|
||||||
"text": [
|
"text": [
|
||||||
"158\n",
|
"17\n",
|
||||||
"fractal dimension: 1.2179534297610568\n"
|
"[-6, 11, 14, 23, 51, 95, 42, 71, 15, 86, 35, 74, 71, 26, 59, 47, 78]\n",
|
||||||
|
"fractal dimension: 0.9506030253442043\n"
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"root = [-10, 18, 23, 27] #some base tuple, it will change as we go through the words since we are kinda only paying attention to the end of the word\n",
|
"root = [-6, 11, 14, 23] #some base tuple, it will change as we go through the words since we are kinda only paying attention to the end of the word\n",
|
||||||
"circlelist = list(root) #list of the curvatures, it starts with the root stuff and we will add to it \n",
|
"circlelist = list(root) #list of the curvatures, it starts with the root stuff and we will add to it \n",
|
||||||
"word = [1] #word that we are currently considering, it will change as we go through these, the first word we start with is just the word that consists of the first generator\n",
|
"word = [1] #word that we are currently considering, it will change as we go through these, the first word we start with is just the word that consists of the first generator\n",
|
||||||
"recentroot = [] #this will be an array of arrays. the recentroot[i] is the most recent tuple that wasn't too big for word of length i so that when we go back down we know which tuple to operate on\n",
|
"recentroot = [] #this will be an array of arrays. the recentroot[i] is the most recent tuple that wasn't too big for word of length i so that when we go back down we know which tuple to operate on\n",
|
||||||
"recentroot.append(root) #the root thing will be our 0th element of this array\n",
|
"recentroot.append(root) #the root thing will be our 0th element of this array\n",
|
||||||
"bound = 1000 #bound for what we want our curvatures to be under\n",
|
"bound = 100 #bound for what we want our curvatures to be under\n",
|
||||||
"\n",
|
"\n",
|
||||||
"while word: #this runs until you get back to the empty word\n",
|
"while word: #this runs until you get back to the empty word\n",
|
||||||
" #print(\"root : \" + str(root))\n",
|
" #print(\"root : \" + str(root))\n",
|
||||||
|
|
@ -365,8 +333,16 @@
|
||||||
"\n",
|
"\n",
|
||||||
"#print(circlelist)\n",
|
"#print(circlelist)\n",
|
||||||
"print(len(circlelist))\n",
|
"print(len(circlelist))\n",
|
||||||
|
"print(circlelist)\n",
|
||||||
"curvefit(20,bound,circlelist) #this will print our fractal dimension once the circlelist has been made"
|
"curvefit(20,bound,circlelist) #this will print our fractal dimension once the circlelist has been made"
|
||||||
]
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": []
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"metadata": {
|
"metadata": {
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue