Gauche-CVで簡単な行列計算をする方法です。当たり前ですがnumpyと同じ結果になります。
Python numpy で行列計算
Pythonではnumpyを使えば、簡単に行列の計算ができます。
# -*- coding: utf-8 -*- __author__ = 'Natsutani' import numpy as np a = np.array([[ 1.0, -2.0, 3.0], [4.0, 5.0, 6.0], [-7.0, 8.0, -9.0]]) b = np.array([[10.0, -9.0, 8.0], [7.0, 6.0, 4.0], [-3.0, 2.0, -1.0]]) print("A + B") print(a + b) print("A - B") print(a - b) print("A * B (要素同士の積)") print(a * b) print("Aの逆行列") print(np.linalg.inv(a)) print("A ・ B") print(np.dot(a, b)) print("det A") print(np.linalg.det(a)) print("転置 A") print(np.transpose(a)) print("A + 5") print(a + 5) print("Aの5倍") print(a * 5) # 3次元ベクトルの内積・外積 c = np.array([ 1.0, -2.0, 3.0],) d = np.array([ 4.0, -5.0, 6.0],) print("C・D") print(np.dot(c, d)) print("C×D") print(np.cross(c, d))
実行結果
A + B [[ 11. -11. 11.] [ 11. 11. 10.] [-10. 10. -10.]] A - B [[-9. 7. -5.] [-3. -1. 2.] [-4. 6. -8.]] A * B (要素同士の積) [[ 10. 18. 24.] [ 28. 30. 24.] [ 21. 16. 9.]] Aの逆行列 [[-0.775 0.05 -0.225 ] [-0.05 0.1 0.05 ] [ 0.55833333 0.05 0.10833333]] A ・ B [[-13. -15. -3.] [ 57. 6. 46.] [ 13. 93. -15.]] det A 120.0 転置 A [[ 1. 4. -7.] [-2. 5. 8.] [ 3. 6. -9.]] A + 5 [[ 6. 3. 8.] [ 9. 10. 11.] [ -2. 13. -4.]] Aの5倍 [[ 5. -10. 15.] [ 20. 25. 30.] [-35. 40. -45.]] C・D 32.0 C×D [ 3. 6. 3.]
Gauche-CVで行列計算
行列とスカラー値の和、積はOpenCVに見つからなかったので自作しました。パフォーマンスを気にしなければ簡単です。
(use cv) ;; 行列の表示 (define print-2d-matrix (lambda (m . args) (let-keywords args ((name "")) (unless (string=? name "") (format #t "~A = " name)) (let ((rows (slot-ref m 'rows)) (cols (slot-ref m 'cols))) (display "[") (dotimes (r rows) (display " [") (dotimes (c cols) (format #t " ~A" (cv-get-real2d m r c))) (display " ]")) (display "]\n"))))) ;; 行列とスカラー値の和 (define cv-mat-adds-2d (lambda (src value dst) (cv-mat-operate-2d src dst (lambda (x) (+ x value))))) ;; 行列とスカラー値の和 (define cv-mat-muls-2d (lambda (src value dst) (cv-mat-operate-2d src dst (lambda (x) (* x value))))) ;; 行列の各要素に演算を行う (define cv-mat-operate-2d (lambda (src dst op) (let ((rows (slot-ref src 'rows)) (cols (slot-ref src 'cols))) (dotimes (r rows) (dotimes (c cols) (cv-set-real2d dst r c (op (cv-get-real2d src r c)))))))) (define a (make-cv-mat-from-uvector 3 3 1 #f64(1.0 -2.0 3.0 4.0 5.0 6.0 -7.0 8.0 -9.0))) (define b (make-cv-mat-from-uvector 3 3 1 #f64(10.0 -9.0 8.0 7.0 6.0 4.0 -3.0 2.0 -1.0))) (define x (cv-clone-mat a)) (print-2d-matrix a :name "A") (print-2d-matrix b :name "B") (cv-add a b x) (print-2d-matrix x :name "A + B") (cv-sub a b x) (print-2d-matrix x :name "A - B") (cv-mul a b x) (print-2d-matrix x :name " A mul B") (cv-invert a x) (print-2d-matrix x :name "inv(A)") (cv-mat-mul a b x) (print-2d-matrix x :name "A・B") ;(cv-cross-product a b x) ;(print-2d-matrix x :name "a×b") (format #t "det A = ~A~%" (cv-det a)) (cv-transpose a x) (print-2d-matrix x :name "転置 A") (cv-mat-adds-2d a 5 x) (print-2d-matrix x :name "A+5") (cv-mat-muls-2d a 5 x) (print-2d-matrix x :name "A*5") ;; 3次元ベクトルの内積、外積 (define c (make-cv-mat-from-uvector 3 1 1 #f64(1.0 -2.0 3.0))) (define d (make-cv-mat-from-uvector 3 1 1 #f64(4.0 -5.0 6.0))) (define x2 (cv-clone-mat c)) (format #t "C・D = ~A~%" (cv-dot-product c d)) (cv-cross-product c d x2) (print-2d-matrix x2 :name "A×B")
実行結果
A = [ [ 1.0 -2.0 3.0 ] [ 4.0 5.0 6.0 ] [ -7.0 8.0 -9.0 ]] B = [ [ 10.0 -9.0 8.0 ] [ 7.0 6.0 4.0 ] [ -3.0 2.0 -1.0 ]] A + B = [ [ 11.0 -11.0 11.0 ] [ 11.0 11.0 10.0 ] [ -10.0 10.0 -10.0 ]] A - B = [ [ -9.0 7.0 -5.0 ] [ -3.0 -1.0 2.0 ] [ -4.0 6.0 -8.0 ]] A mul B = [ [ 10.0 18.0 24.0 ] [ 28.0 30.0 24.0 ] [ 21.0 16.0 9.0 ]] inv(A) = [ [ -0.775 0.05 -0.225 ] [ -0.05 0.1 0.05 ] [ 0.5583333333333333 0.05 0.10833333333333334 ]] A・B = [ [ -13.0 -15.0 -3.0 ] [ 57.0 6.0 46.0 ] [ 13.0 93.0 -15.0 ]] det A = 120.0 転置 A = [ [ 1.0 4.0 -7.0 ] [ -2.0 5.0 8.0 ] [ 3.0 6.0 -9.0 ]] A+5 = [ [ 6.0 3.0 8.0 ] [ 9.0 10.0 11.0 ] [ -2.0 13.0 -4.0 ]] A*5 = [ [ 5.0 -10.0 15.0 ] [ 20.0 25.0 30.0 ] [ -35.0 40.0 -45.0 ]] C・D = 32.0 A×B = [ [ 3.0 ] [ 6.0 ] [ 3.0 ]]
