From dac6d1dc536f0a628e9754207399e60d64b095c2 Mon Sep 17 00:00:00 2001 From: LordBaryhobal Date: Tue, 25 Jun 2024 01:15:17 +0200 Subject: [PATCH] added matrix + vector functions --- gallery/example1.pdf | Bin 0 -> 162097 bytes gallery/example1.typ | 36 ++ gallery/example2.pdf | 858 +++++++++++++++++++++++++++++++++++++++++++ gallery/example2.typ | 30 ++ src/lib.typ | 2 + src/mat.typ | 107 ++++++ src/vec.typ | 65 ++++ typst.toml | 14 + 8 files changed, 1112 insertions(+) create mode 100644 gallery/example1.pdf create mode 100644 gallery/example1.typ create mode 100644 gallery/example2.pdf create mode 100644 gallery/example2.typ create mode 100644 src/lib.typ create mode 100644 src/mat.typ create mode 100644 src/vec.typ create mode 100644 typst.toml diff --git a/gallery/example1.pdf b/gallery/example1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ac230b10bc9db04e388cae1b3f463838bf9ab286 GIT binary patch literal 162097 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m2) +#let m4 = mat.mul(m2, m1) + +$A = #mat.display(m1) quad B = #mat.display(m2)\ + C = A B = #mat.display(m3) quad D = B A = #mat.display(m4)$ + +#let m5 = mat.mat( + (1, 2), + (3, 4) +) + +#let m6 = mat.mat( + (5, 7), + (6, 8) +) + +#let m7 = mat.add(m5, m6) +#let m8 = mat.sub(m5, m6) +#let m9 = mat.transpose(m5) + +$E = #mat.display(m5) quad F = #mat.display(m6)\ + E + F = #mat.display(m7) quad E - F = #mat.display(m8)\ + E^T = #mat.display(m9)$ \ No newline at end of file diff --git a/gallery/example2.pdf b/gallery/example2.pdf new file mode 100644 index 0000000..97082aa --- /dev/null +++ b/gallery/example2.pdf @@ -0,0 +1,858 @@ +%PDF-1.7 +% + +4 0 obj +<< + /Type /Font + /Subtype /Type0 + /BaseFont /GHITOR+NewCMMath-Book-Identity-H + /Encoding /Identity-H + /DescendantFonts [5 0 R] + /ToUnicode 7 0 R +>> +endobj + +5 0 obj +<< + /Type /Font + /Subtype /CIDFontType0 + /BaseFont /GHITOR+NewCMMath-Book + /CIDSystemInfo << + /Registry (Adobe) + /Ordering (Identity) + /Supplement 0 + >> + /FontDescriptor 6 0 R + /DW 0 + /W [0 0 500 12 12 778 18 20 500 24 24 500 26 26 500 30 30 778 152 152 778 853 853 778 1032 1032 278 2676 2676 970 2685 2685 583 2710 2710 485 4505 4505 569 4507 4507 569 4542 4542 569 4551 4551 569 4585 4586 569 4592 4592 569 4598 4598 569 5211 5211 659 5677 5678 597 5743 5744 875] +>> +endobj + +6 0 obj +<< + /Type /FontDescriptor + /FontName /GHITOR+NewCMMath-Book + /Flags 131076 + /FontBBox [-1044 -3060 4087.9998 3560] + /ItalicAngle 0 + /Ascent 806 + /Descent -194 + /CapHeight 683 + /StemV 95.4 + /FontFile3 8 0 R +>> +endobj + +7 0 obj +<< + /Length 969 + /Type /CMap +>> +stream +%!PS-Adobe-3.0 Resource-CMap +%%DocumentNeededResources: procset CIDInit +%%IncludeResource: procset CIDInit +%%BeginResource: CMap Custom +%%Title: (Custom Adobe Identity 0) +%%Version: 1 +%%EndComments +/CIDInit /ProcSet findresource begin +12 dict begin +begincmap +/CIDSystemInfo 3 dict dup begin + /Registry (Adobe) def + /Ordering (Identity) def + /Supplement 0 def 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+0000157257 00000 n +trailer +<< + /Size 15 + /Root 14 0 R + /Info 12 0 R + /ID [(WHmj50Lk4HtEPB9JVQdHrg==) (WHmj50Lk4HtEPB9JVQdHrg==)] +>> +startxref +157447 +%%EOF \ No newline at end of file diff --git a/gallery/example2.typ b/gallery/example2.typ new file mode 100644 index 0000000..8ab8ba5 --- /dev/null +++ b/gallery/example2.typ @@ -0,0 +1,30 @@ +#import "/src/lib.typ": * + +#let v1 = vec.vec(1, 2, 3) +#let v2 = vec.vec(4, 5, 6) + +#let v3 = vec.add(v1, v2) +#let v4 = vec.sub(v1, v2) +#let d = vec.dot(v1, v2) +#let v5 = vec.cross(v1, v2) + +$arrow(v_1) = #vec.display(v1) quad arrow(v_2) = #vec.display(v2)\ + arrow(v_1) + arrow(v_2) = #vec.display(v3)\ + arrow(v_1) - arrow(v_2) = #vec.display(v4)\ + arrow(v_1) dot arrow(v_2) = #d\ + arrow(v_1) times arrow(v_2) = #vec.display(v5)\ +$ + +#let m = mat.mat( + (1, 2), + (3, 4) +) +#let v = vec.vec( + 5, + 6 +) + +#let mv = mat.mul-vec(m, v) + +$M = #mat.display(m) quad V = #vec.display(v)\ +M V = #vec.display(mv)$ \ No newline at end of file diff --git a/src/lib.typ b/src/lib.typ new file mode 100644 index 0000000..d7d7bca --- /dev/null +++ b/src/lib.typ @@ -0,0 +1,2 @@ +#import "mat.typ" +#import "vec.typ" \ No newline at end of file diff --git a/src/mat.typ b/src/mat.typ new file mode 100644 index 0000000..793ee51 --- /dev/null +++ b/src/mat.typ @@ -0,0 +1,107 @@ +#let size(mat) = { + return str(mat.h) + "x" + str(mat.w) +} + +#let mat(..args) = { + let rows = args.pos() + //rows = rows.map(r => if r == none {()} else {r}) + let h = rows.len() + let w = if h == 0 {0} else {rows.first().len()} + if rows.find(r => r.len() != w) != none { + panic("All rows should have the same length") + } + return ( + rows: rows, + w: w, + h: h + ) +} + +#let of-size(h, w) = { + let rows = ((0,) * w,) * h + return mat(..rows) +} + +#let display(mat) = math.mat(..mat.rows) + +#let add(mat1, mat2) = { + if mat1.w != mat2.w or mat1.h != mat2.h { + panic("Can't add matrices of size " + size(mat1) + " and " + size(mat2)) + } + + let mat3 = of-size(mat1.h, mat1.w) + + for y in range(mat1.h) { + for x in range(mat1.w) { + mat3.rows.at(y).at(x) = mat1.rows.at(y).at(x) + mat2.rows.at(y).at(x) + } + } + + return mat3 +} + +#let sub(mat1, mat2) = { + if mat1.w != mat2.w or mat1.h != mat2.h { + panic("Can't subtract matrices of size " + size(mat1) + " and " + size(mat2)) + } + + let mat3 = of-size(mat1.h, mat1.w) + + for y in range(mat1.h) { + for x in range(mat1.w) { + mat3.rows.at(y).at(x) = mat1.rows.at(y).at(x) - mat2.rows.at(y).at(x) + } + } + + return mat3 +} + +#let mul(mat1, mat2) = { + if mat1.w != mat2.h { + panic("Can't multiply matrices of size " + size(mat1) + " and " + size(mat2)) + } + + let mat3 = of-size(mat1.h, mat2.w) + + for y in range(mat1.h) { + for x in range(mat2.w) { + let sum = 0 + for i in range(mat1.w) { + sum += mat1.rows.at(y).at(i) * mat2.rows.at(i).at(x) + } + mat3.rows.at(y).at(x) = sum + } + } + + return mat3 +} + +#let transpose(mat) = { + let mat-t = of-size(mat.w, mat.h) + + for y in range(mat.h) { + for x in range(mat.w) { + mat-t.rows.at(x).at(y) = mat.rows.at(y).at(x) + } + } + + return mat-t +} + +#let to-vec(mat) = { + import "vec.typ" as _vec + return _vec.vec(..mat.rows.map(r => r.first())) +} + +#let mul-vec(mat1, vec) = { + import "vec.typ" as _vec + + if mat1.w != vec.size { + panic("Can't multiply matrix of size " + size(mat1) + " and vector of size " + _vec.size(vec)) + } + + let mat2 = _vec.to-mat(vec) + let res = mul(mat1, mat2) + + return to-vec(res) +} \ No newline at end of file diff --git a/src/vec.typ b/src/vec.typ new file mode 100644 index 0000000..1e7023f --- /dev/null +++ b/src/vec.typ @@ -0,0 +1,65 @@ +#let vec(..args) = { + let comps = args.pos() + let size = comps.len() + return ( + comps: comps, + size: size + ) +} + +#let of-size(size) = { + let comps = (0,) * size + return vec(..comps) +} + +#let display(vec) = math.vec(..vec.comps.map(c => [#c])) + +#let add(vec1, vec2) = { + if vec1.size != vec2.size { + panic("Can't add vectors of size " + str(vec1.size) + " and " + str(vec2.size)) + } + + let comps = vec1.comps.zip(vec2.comps).map(p => p.sum()) + return vec(..comps) +} + +#let sub(vec1, vec2) = { + if vec1.size != vec2.size { + panic("Can't subtract vectors of size " + str(vec1.size) + " and " + str(vec2.size)) + } + + let comps = vec1.comps.zip(vec2.comps).map(p => p.first() - p.last()) + return vec(..comps) +} + +#let dot(vec1, vec2) = { + if vec1.size != vec2.size { + panic("Can't compute dot product of vectors of size " + str(vec1.size) + " and " + str(vec2.size)) + } + + let res = vec1.comps.zip(vec2.comps) + .map(p => p.product()) + .sum(default: 0) + + return res +} + +#let cross(vec1, vec2) = { + if vec1.size != 3 or vec2.size != 3 { + panic("Can only compute cross product of vectors of size 3") + } + + let vec3 = of-size(3) + for i in range(3) { + let i1 = calc.rem(i + 1, 3) + let i2 = calc.rem(i1 + 1, 3) + vec3.comps.at(i) = vec1.comps.at(i1) * vec2.comps.at(i2) + vec3.comps.at(i) -= vec1.comps.at(i2) * vec2.comps.at(i1) + } + return vec3 +} + +#let to-mat(vec) = { + import "mat.typ" as _mat + return _mat.mat(..vec.comps.map(c => (c,))) +} \ No newline at end of file diff --git a/typst.toml b/typst.toml new file mode 100644 index 0000000..b11a77b --- /dev/null +++ b/typst.toml @@ -0,0 +1,14 @@ +[package] +name = "math-tools" +version = "0.0.1" +compiler = "0.11.0" +repository = "https://git.kb28.ch/HEL/math-tools" +entrypoint = "src/lib.typ" +authors = [ + "Louis Heredero " +] +categories = [ "scripting" ] +license = "Apache-2.0" +description = "A collection of useful mathematical tools" +keywords = [ "maths" ] +exclude = [ "/gallery/*" ] \ No newline at end of file