From 8b105aabe0f0fc9e36065aee65a553c557ddd684 Mon Sep 17 00:00:00 2001 From: MajaByr Date: Fri, 20 Mar 2026 00:42:09 +0100 Subject: [PATCH 1/3] :sparkles: Add matrix multiplication report --- CHANGELOG.md | 10 + generate_report.py | 7 +- pyproject.toml | 2 +- reports/imgs/time_benchmark.jpeg | Bin 0 -> 106873 bytes .../code.txt | 363 ++++++++++++++++++ .../report.pdf | Bin 0 -> 124442 bytes reports/matrix_multiplication_report.md | 70 ++++ 7 files changed, 449 insertions(+), 3 deletions(-) create mode 100644 reports/imgs/time_benchmark.jpeg create mode 100644 reports/matrix-multiplication-report-resources/code.txt create mode 100644 reports/matrix-multiplication-report-resources/report.pdf create mode 100644 reports/matrix_multiplication_report.md diff --git a/CHANGELOG.md b/CHANGELOG.md index 532a0c4..09de071 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,3 +1,13 @@ +## [1.3.0] - 2026-03-20 + +### Added + +- Matrix multiplication report + +### Fixed + +- `md` report generation - images and code blocks + ## [1.2.0] - 2026-03-19 ### Added diff --git a/generate_report.py b/generate_report.py index 4f4f74d..c48e260 100755 --- a/generate_report.py +++ b/generate_report.py @@ -15,8 +15,11 @@ def md_to_pdf(md_path: Path, pdf_path: Path): with open(md_path, encoding="utf-8") as f: md_text = f.read() - html = markdown.markdown(md_text) - HTML(string=html).write_pdf(str(pdf_path)) + html = markdown.markdown( + md_text, + extensions=["fenced_code", "codehilite"], + ) + HTML(string=html, base_url=md_path.parent).write_pdf(str(pdf_path)) def resolve_module_path(module_name): diff --git a/pyproject.toml b/pyproject.toml index c2847a0..a302f88 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta" [project] name = "matrix_calculus" -version = "1.2.0" +version = "1.3.0" description = "Matrix calculus toolkit" requires-python = ">=3.10" dependencies = ["numpy", "seaborn", "matplotlib", "weasyprint", "markdown"] diff --git 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zb+7X#B3bLo5=Gh{TiHf$=jK1y!ZtR&>n_Q~2hFH~7tao*|7@;b+rjJeFrr;B`S%Rc zaIv%Ud$TVG;edzM^?h^%%GDE_VQ>y?bCLFbj{GiBUY1(;mmE`2a3Ip#a@UiT>D`h) zqGsIgPl5JyRoBT_ZF`})CK={DU#bQ*_nMaC;(yhxbkWX6okAmxFCQ)?V&Dljm{F?@ z!3}NU)Dg$y* list[list[float]]: + + if len(matrix_1[0]) != len(matrix_2): + raise ValueError( + "Invalid matrices sizes. Given matrices cannot be multiplied.", + ) + + n_rows = len(matrix_1) + n_cols = len(matrix_2[0]) + + res = [[0.0 for _ in range(n_cols)] for _ in range(n_rows)] + + for row in range(n_rows): + for col in range(n_cols): + for k in range(len(matrix_1[0])): + res[row][col] += matrix_1[row][k] * matrix_2[k][col] + + return res + + @staticmethod + def strassen_matrix_multiplication( + matrix_1: list[list[float]], + matrix_2: list[list[float]], + ) -> list[list[float]]: + + rows_1 = len(matrix_1) + cols_1 = len(matrix_1[0]) + rows_2 = len(matrix_2) + cols_2 = len(matrix_2[0]) + + if not (rows_1 == cols_1 and rows_2 == cols_2 and rows_1 == rows_2): + raise ValueError( + "Both matrices must be squared matrices of the same size", + ) + + n = len(matrix_1) + + if n == 1: + return [[matrix_1[0][0] * matrix_2[0][0]]] + + m = _next_power_of_2(n) + + if m == n: + return _strassen(matrix_1, matrix_2, n) + + A_pad = _pad_matrix(matrix_1, m) + B_pad = _pad_matrix(matrix_2, m) + + C_pad = _strassen(A_pad, B_pad, m) + + return _unpad_matrix(C_pad, n) + + +========== utils.py ========== +from __future__ import annotations + + +def _zeroes_matrix(n): + return [[0 for _ in range(n)] for _ in range(n)] + + +# sub_matrix is a tuple of the form (matrix, row_start, col_start) + + +def _add_sub_matrices( + sub_matrix_1, + sub_matrix_2, + n, + result, + result_matrix_offset=(0, 0), +): + m1, r1, c1 = sub_matrix_1 + m2, r2, c2 = sub_matrix_2 + result_offset_row, result_offset_col = result_matrix_offset + for i in range(n): + for j in range(n): + result[result_offset_row + i][result_offset_col + j] = ( + m1[r1 + i][c1 + j] + m2[r2 + i][c2 + j] + ) + return result + + +def _subtract_sub_matrices( + sub_matrix_1, + sub_matrix_2, + n, + result, + result_matrix_offset=(0, 0), +): + m1, r1, c1 = sub_matrix_1 + m2, r2, c2 = sub_matrix_2 + result_offset_row, result_offset_col = result_matrix_offset + for i in range(n): + for j in range(n): + result[result_offset_row + i][result_offset_col + j] = ( + m1[r1 + i][c1 + j] - m2[r2 + i][c2 + j] + ) + return result + + +def _set_sub_matrix(sub_matrix, other_matrix, n): + m, r, c = sub_matrix + for i in range(n): + for j in range(n): + m[i + r][j + c] = other_matrix[i][j] + return m + + +def _sub_matrix_to_matrix(sub_matrix, n, result): + m, r, c = sub_matrix + for i in range(n): + for j in range(n): + result[i][j] = m[r + i][c + j] + return result + + +def _add_matrices(*matrices, result=None): + assert result is not None + for i in range(len(result)): + for j in range(len(result[0])): + result[i][j] = matrices[0][i][j] + for k in range(1, len(matrices)): + result[i][j] += matrices[k][i][j] + return result + + +def _subtract_matrix_from(target_matrix, matrix_to_subtract): + for i in range(len(target_matrix)): + for j in range(len(target_matrix[0])): + target_matrix[i][j] -= matrix_to_subtract[i][j] + return target_matrix + + +def _strassen(matrix_1, matrix_2, n): + if n == 2: + c11 = matrix_1[0][0] * matrix_2[0][0] + matrix_1[0][1] * matrix_2[1][0] + c12 = matrix_1[0][0] * matrix_2[0][1] + matrix_1[0][1] * matrix_2[1][1] + c21 = matrix_1[1][0] * matrix_2[0][0] + matrix_1[1][1] * matrix_2[1][0] + c22 = matrix_1[1][0] * matrix_2[0][1] + matrix_1[1][1] * matrix_2[1][1] + return [[c11, c12], [c21, c22]] + + else: + sub_matrix_dim = n >> 1 + + buffer_1 = _zeroes_matrix(sub_matrix_dim) + buffer_2 = _zeroes_matrix(sub_matrix_dim) + + a11 = (matrix_1, 0, 0) + a12 = (matrix_1, 0, sub_matrix_dim) + a21 = (matrix_1, sub_matrix_dim, 0) + a22 = (matrix_1, sub_matrix_dim, sub_matrix_dim) + + b11 = (matrix_2, 0, 0) + b12 = (matrix_2, 0, sub_matrix_dim) + b21 = (matrix_2, sub_matrix_dim, 0) + b22 = (matrix_2, sub_matrix_dim, sub_matrix_dim) + + m1 = _strassen( + _add_sub_matrices(a11, a22, sub_matrix_dim, buffer_1), + _add_sub_matrices(b11, b22, sub_matrix_dim, buffer_2), + sub_matrix_dim, + ) + m2 = _strassen( + _add_sub_matrices(a21, a22, sub_matrix_dim, buffer_1), + _sub_matrix_to_matrix(b11, sub_matrix_dim, buffer_2), + sub_matrix_dim, + ) + m3 = _strassen( + _sub_matrix_to_matrix(a11, sub_matrix_dim, buffer_1), + _subtract_sub_matrices(b12, b22, sub_matrix_dim, buffer_2), + sub_matrix_dim, + ) + m4 = _strassen( + _sub_matrix_to_matrix(a22, sub_matrix_dim, buffer_1), + _subtract_sub_matrices(b21, b11, sub_matrix_dim, buffer_2), + sub_matrix_dim, + ) + m5 = _strassen( + _add_sub_matrices(a11, a12, sub_matrix_dim, buffer_1), + _sub_matrix_to_matrix(b22, sub_matrix_dim, buffer_2), + sub_matrix_dim, + ) + m6 = _strassen( + _subtract_sub_matrices(a21, a11, sub_matrix_dim, buffer_1), + _add_sub_matrices(b11, b12, sub_matrix_dim, buffer_2), + sub_matrix_dim, + ) + m7 = _strassen( + _subtract_sub_matrices(a12, a22, sub_matrix_dim, buffer_1), + _add_sub_matrices(b21, b22, sub_matrix_dim, buffer_2), + sub_matrix_dim, + ) + + c = _zeroes_matrix(n) + + c11 = _add_matrices(m1, m4, m7, result=buffer_1) + _subtract_matrix_from(c11, m5) + _set_sub_matrix((c, 0, 0), c11, sub_matrix_dim) + + c12 = _add_matrices(m3, m5, result=buffer_1) + _set_sub_matrix((c, 0, sub_matrix_dim), c12, sub_matrix_dim) + + c21 = _add_matrices(m2, m4, result=buffer_1) + _set_sub_matrix((c, sub_matrix_dim, 0), c21, sub_matrix_dim) + + c22 = _add_matrices(m1, m3, m6, result=buffer_1) + _subtract_matrix_from(c22, m2) + _set_sub_matrix( + (c, sub_matrix_dim, sub_matrix_dim), + c22, + sub_matrix_dim, + ) + + return c + + +def _next_power_of_2(n): + return 1 if n == 0 else 2 ** ((n - 1).bit_length()) + + +def _pad_matrix(matrix, new_size): + old_size = len(matrix) + padded = [[0] * new_size for _ in range(new_size)] + + for i in range(old_size): + for j in range(old_size): + padded[i][j] = matrix[i][j] + + return padded + + +def _unpad_matrix(matrix, size): + return [row[:size] for row in matrix[:size]] diff --git a/reports/matrix-multiplication-report-resources/report.pdf b/reports/matrix-multiplication-report-resources/report.pdf new file mode 100644 index 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zku(TmKk2c5859XYTK-G_KX@S!|IRM69y<-b%;Cg!@D!Q(Zal^75Jw-hEV=Se)n%X-rHF>Zk-N7cdFmD5GiV-1;2ME=UfC8rAN-r zYrWCxjfyC`_W&N1VX}DrUShUh6*bI1vVVE$OWEj`XGwdQld7EmE+Crr_v^H{>y#iR R3k1r-5}{;hh;?&P`X}H*ylnsg literal 0 HcmV?d00001 diff --git a/reports/matrix_multiplication_report.md b/reports/matrix_multiplication_report.md new file mode 100644 index 0000000..89eaa6b --- /dev/null +++ b/reports/matrix_multiplication_report.md @@ -0,0 +1,70 @@ +# Mnożenie Macierzy + +## Tradycyjne mnożenie macierzy + +### Pseudokod + +Mnożenie macierzy kwadratowych o rozmiarach `SIZE x SIZE` + +``` +for (i = 0; i < SIZE; i++) { + for (j = 0; j < SIZE; j++) { + for (k = 0; k < SIZE; k++) { + s = s + m_1[i][k]*m_2[k][j]; + } + res[i][j] = s; + s = 0; + } + } +return res; +``` + +### Złożoność + +Tradycyjne mnożenie macierzy posiada ogólną złożoność n^3 + +Ilość operacji podczas mnożenia macierzy k x k: + +* Mnożenia: k^3 +* Dodawania: k^2 * (k-1) +* Dzielenia: 0 +* Odejmowania: 0 + +Algorytm nie wymaga dodatkowej pamięci do przechowywania macierzy w trakcie operacji. + +### Dodatkowe uwagi + +Ze względu na zasady czystego kodu zawarte w dokumentacji języka Python3, zaimplementowane rozwiązanie wykorzystuje nową macierz (alokuje pamięć). + +## Połączenie metod + +### Pseudokod + +Mnożenie macierzy kwadratowych o rozmiarach `SIZE x SIZE` + +``` +if SIZE<=2 { + for (i = 0; i < SIZE; i++) { + for (j = 0; j < SIZE; j++) { + for (k = 0; k < SIZE; k++) { + s = s + m_1[i][k]*m_2[k][j]; + } + res[i][j] = s; + s = 0; + } + } + return res; +} else { + # Paste Strassen pseudocode here +} +``` + +### Złożoność + +Ogólna złożoność wynosi niecałe n^3 + +## Porównanie Metod + + + +Dla niewielkich macierzy koszty algorytmów są zbliżone. Wraz z rozmiarem macierzy algorytm Strassena staje się wydajniejszy od tradycyjnego algorytmu. Oba algorytmy posiadają zbliżoną złożoność obliczeniową. From 49f6f0efe03a0534d8ca66c9a09dbed9b2cd6d3a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Micha=C5=82=20Kowalczyk?= Date: Fri, 20 Mar 2026 00:54:21 +0100 Subject: [PATCH 2/3] added pseudocode for strassen multiplication algorithm --- reports/matrix_multiplication_report.md | 26 ++++++++++++++++++++++++- 1 file changed, 25 insertions(+), 1 deletion(-) diff --git a/reports/matrix_multiplication_report.md b/reports/matrix_multiplication_report.md index 89eaa6b..854b343 100644 --- a/reports/matrix_multiplication_report.md +++ b/reports/matrix_multiplication_report.md @@ -55,7 +55,31 @@ if SIZE<=2 { } return res; } else { - # Paste Strassen pseudocode here + k = SIZE / 2 + + # Podział macierzy na bloki + podziel m_1 na: A11, A12, A21, A22 (każda k x k) + podziel m_2 na: B11, B12, B21, B22 (każda k x k) + + # Rekurencyjne obliczenie 7 iloczynów + M1 = Strassen(A11 + A22, B11 + B22) + M2 = Strassen(A21 + A22, B11) + M3 = Strassen(A11, B12 - B22) + M4 = Strassen(A22, B21 - B11) + M5 = Strassen(A11 + A12, B22) + M6 = Strassen(A21 - A11, B11 + B12) + M7 = Strassen(A12 - A22, B21 + B22) + + # Obliczenie bloków wynikowych + C11 = M1 + M4 - M5 + M7 + C12 = M3 + M5 + C21 = M2 + M4 + C22 = M1 - M2 + M3 + M6 + + # Złożenie macierzy wynikowej + wstaw C11, C12, C21, C22 do odpowiednich ćwiartek macierzy res + + return res; } ``` From 1cb9f21b7a7125f751ffef89907734c335eafad1 Mon Sep 17 00:00:00 2001 From: MajaByr Date: Fri, 20 Mar 2026 10:23:24 +0100 Subject: [PATCH 3/3] :bar_chart: Update matrix multiplication report --- reports/imgs/execution_time.png | Bin 0 -> 43666 bytes reports/imgs/image_time_logx.png | Bin 0 -> 80694 bytes .../report.pdf | Bin 124442 -> 0 bytes reports/matrix_multiplication_report.md | 49 ++++++++++++++---- .../matrix-multiplication}/code.txt | 0 .../matrix-multiplication/report.pdf | Bin 0 -> 251491 bytes 6 files changed, 39 insertions(+), 10 deletions(-) create mode 100644 reports/imgs/execution_time.png create mode 100644 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zku(TmKk2c5859XYTK-G_KX@S!|IRM69y<-b%;Cg!@D!Q(Zal^75Jw-hEV=Se)n%X-rHF>Zk-N7cdFmD5GiV-1;2ME=UfC8rAN-r zYrWCxjfyC`_W&N1VX}DrUShUh6*bI1vVVE$OWEj`XGwdQld7EmE+Crr_v^H{>y#iR R3k1r-5}{;hh;?&P`X}H*ylnsg diff --git a/reports/matrix_multiplication_report.md b/reports/matrix_multiplication_report.md index 854b343..7747e5f 100644 --- a/reports/matrix_multiplication_report.md +++ b/reports/matrix_multiplication_report.md @@ -1,5 +1,7 @@ # Mnożenie Macierzy +*Autorzy: Maja Byrecka, Michał Kowalczyk* + ## Tradycyjne mnożenie macierzy ### Pseudokod @@ -30,18 +32,35 @@ Ilość operacji podczas mnożenia macierzy k x k: * Dzielenia: 0 * Odejmowania: 0 -Algorytm nie wymaga dodatkowej pamięci do przechowywania macierzy w trakcie operacji. +Algorytm nie wymaga alokacji dodatkowej pamięci (poza pamięcią na macierz wynikową), w trakcie wykonywania operacji. + +## Algorytm Strassena -### Dodatkowe uwagi +### Pseudokod -Ze względu na zasady czystego kodu zawarte w dokumentacji języka Python3, zaimplementowane rozwiązanie wykorzystuje nową macierz (alokuje pamięć). +``` +Strassen – funkcja główna z dopełnieniem do potęgi 2 +Input: A ∈ Rn×n, B ∈ Rn×n +Output: C = A · B ∈ Rn×n + +1 if (A i B nie są kwadratowe lub dim(A)̸ = dim(B)) then +2 return błąd +3 n ← dim(A) +4 if n = 1 then +5 return [[A11 · B11]] +6 m ← NextPowerOf2(n) +7 if m = n then +8 return StrassenRec(A, B, n) +9 A′ ← Pad(A, m) +10 B′ ← Pad(B, m) +11 C′ ← StrassenRec(A′, B′, m) +12 return Unpad(C′, n) +``` ## Połączenie metod ### Pseudokod -Mnożenie macierzy kwadratowych o rozmiarach `SIZE x SIZE` - ``` if SIZE<=2 { for (i = 0; i < SIZE; i++) { @@ -83,12 +102,22 @@ if SIZE<=2 { } ``` -### Złożoność - -Ogólna złożoność wynosi niecałe n^3 - ## Porównanie Metod -Dla niewielkich macierzy koszty algorytmów są zbliżone. Wraz z rozmiarem macierzy algorytm Strassena staje się wydajniejszy od tradycyjnego algorytmu. Oba algorytmy posiadają zbliżoną złożoność obliczeniową. + + + + + +Na podstawie przedstawionych wykresów można zauważyć, że dla badanych rozmiarów macierzy szybsze jest mnożenie tradycyjne. Jednocześnie widoczna jest tendencja wskazująca, że wraz ze wzrostem n algorytm Strassena powinien stać się korzystniejszy, a dla bardzo dużych n może wykonywać się szybciej od podejścia klasycznego. Oba algorytmy posiadają zbliżoną złożoność obliczeniową. + +--- + +Wykonanie: + +* Język: Python3 +* Podział zadań: + * Tradycyjne mnożenie macierzy, testy, analizy - Maja Byrecka + * Metoda Strassena, wykresy, analizy - Michał Kowalczyk diff --git a/reports/matrix-multiplication-report-resources/code.txt b/reports/resources/matrix-multiplication/code.txt similarity index 100% rename from reports/matrix-multiplication-report-resources/code.txt rename to reports/resources/matrix-multiplication/code.txt diff --git a/reports/resources/matrix-multiplication/report.pdf b/reports/resources/matrix-multiplication/report.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ebc305c4392140384bd9eed0d186ea64e85a0e8d GIT binary patch literal 251491 zcma&NV{k9fvn?3o7u&XNoY=N)+sTP-+qP}nc5-6dnE%ww)ZAP5)vNcdzwFvo-MiLW zy?Qs9f`}L$6Fmoj>@F|07{ErzNN8_l1>ogn5VN##F?Awj5VJ9KF%>a2wl^_lkTJD0 zcd;O3;$q|A=La~uIGGyS0z5WXv}WvZIbeHlm9Jn_63YMPGtNT*XCBQLYqW_*;a}yr 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