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norm
6 B7 u; C" p, C( jVector and matrix norms
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" @, r, @+ o: s8 |. r$ a- h: pn = norm(v)( Q3 V$ x. Z6 g0 g" r
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n = norm(v,p)
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n = norm(X)
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n = norm(X,p)
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3 U, N( O N0 K0 cn = norm(X,'fro')
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Description! T; [1 W1 f' [; ]( j' ^
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n = norm(v)返回向量v的欧几里德范数。该范数也称为2范数,向量幅度或欧几里德长度。
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n = norm(X)返回矩阵X的2范数或最大奇异值,其近似为max(svd(X))。% L9 h, T8 U: H. }
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n = norm(X,p)返回矩阵X的p范数,其中p为1,2或Inf:
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- 如果p = 1,则n是矩阵的最大绝对列和。
- 如果p = 2,则n近似为max(svd(X))。 这相当于norm(X)。
- 如果p = Inf,那么n是矩阵的最大绝对行和。
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" `" j. `$ M5 B$ _: Gn = norm(X,'fro')返回矩阵X的Frobenius范数。3 x' w' w7 B6 B% Z2 Z
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有关范数的基础知识,见上篇文章:MATLAB必备的范数的基础知识
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下面举例说明:7 o# l6 x5 j5 P' m7 j9 y
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Vector Magnitude(向量幅度)
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- %Create a vector and calculate the magnitude.
- v = [1 -2 3];
- n = norm(v)
- % n = 3.7417/ f" Z" D: v6 `; d9 Z
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1-Norm of Vector
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- clc
- clear
- close all
- % Calculate the 1-norm of a vector, which is the sum of the element magnitudes.
- X = [-2 3 -1];
- n = norm(X,1)
- % n = 68 m3 h2 e8 i/ B+ }. E+ b
% p# H* u0 F* }Euclidean Distance Between Two Points
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- clear
- close all
- % Calculate the distance between two points as the norm of the difference between the vector elements.
- %
- % Create two vectors representing the (x,y) coordinates for two points on the Euclidean plane.
- a = [0 3];
- b = [-2 1];
- % Use norm to calculate the distance between the points.
- d = norm(b-a)8 V2 [! G0 Y* t
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W3 k* b( G2 o; u# l, s4 U5 {2-Norm of Matrix4 G2 R* g! [' U) r/ n
s+ G; k/ i0 m- clc
- clear
- close all
- % Calculate the 2-norm of a matrix, which is the largest singular value.
- X = [2 0 1;-1 1 0;-3 3 0];
- n = norm(X)
- % n = 4.7234) T% X/ ^& P! C3 ^' X
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Frobenius Norm of Sparse Matrix
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- clc
- clear
- close all
- % 使用'fro'计算稀疏矩阵的Frobenius范数,该范数计算列向量的2范数S(:)。
- S = sparse(1:25,1:25,1);
- n = norm(S,'fro')
- % n = 5
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