1、幫助文檔

svd

Singular value decomposition

Syntax

s = svd(X)
[U,S,V] = svd(X)
[U,S,V] = svd(X,0)
[U,S,V] = svd(X,'econ')

Description

The?svd?command computes the matrix singularvalue decomposition.

s = svd(X)?returns a vectorof singular values.

[U,S,V] = svd(X)?producesa diagonal matrix?S?of the same dimension as?X,with nonnegative diagonal elements in decreasing order, and unitarymatrices?U?and?V?so that?X= U*S*V'.

[U,S,V] = svd(X,0)?producesthe "economy size" decomposition. If?X?ism-by-n with m > n, then?svd?computes onlythe first?ncolumns of?U?and?S?isn-by-n.

[U,S,V] = svd(X,'econ')?also produces the"economy size" decomposition. If?X?ism-by-n with m >= n, it is equivalent tosvd(X,0).For m < n, only the first m columns of?V?arecomputed and?S?is m-by-m.

Examples

For the matrix

X =1 23 45 67 8

the statement

[U,S,V] = svd(X)

produces

U =-0.1525 -0.8226 -0.3945 -0.3800-0.3499 -0.4214 0.2428 0.8007-0.5474 -0.0201 0.6979 -0.4614-0.7448 0.3812 -0.5462 0.0407S =14.2691 00 0.62680 00 0V =-0.6414 0.7672-0.7672 -0.6414

The economy size decomposition generated by

[U,S,V] = svd(X,0)

produces

U =-0.1525 -0.8226-0.3499 -0.4214-0.5474 -0.0201-0.7448 0.3812 S =14.2691 00 0.6268 V =-0.6414 0.7672-0.7672 -0.6414

Diagnostics

If the limit of 75 QR step iterations is exhausted while seekinga singular value, this message appears:

Solution will not converge.

2、使用誤區

>> S=svd(A)
??? Undefined function or method 'svd' for input arguments of type 'uint8'.
出錯原因，A的數據類型為uint8 解決辦法S=svd（double（A））

>> S=SVD(double(A))
??? Undefined function or method 'SVD' for input arguments of type 'double'.
出錯原因，SVD在R2011a中不能被調用，區分大小寫 解決辦法S=svd（double（A）） 與50位技術專家面對面20年技術見證，附贈技術全景圖

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