matricesThe n maximum eigenvalue of the covariance matrix is obtained, then the x* corresponding eigenvector is reduced to n.1.4 Eig FunctionE=eig (a): All eigenvalues of Matrix A are evaluated, and the vector e is formed.[V,d]=eig (a): To find all the eigenvalues of matrix A, to form a diagonal array D, and the eigenvector of a to form the column vector of V.[V
provides the EIG function to break down the matrix feature values. The Calling formats of this function are as follows:
① d = eig(A)② d = eig(A,B)③ [V,D] = eig(A)④ [V,D] = eig(A,‘nobalance‘)⑤ [V,D] = eig(A,B)⑥ [V,D] =
);
Matrixadd (addpq,q,3,1);
Double a[16];
For (int i=0;i
a[i]=0;
For (int i=0;i
A[i+1]=divpq[i];
A[i*4+4]=divpq[i];
A[i+13]=addpq[i];
}
Double at[16],amul[16];
Matrixtran (a,at,4,4);
Matrixmul (a,at,amul,4,4,4,4);
Matrixadd (b,amul,4,4);
}
The original optimization problem can be converted to the minimum eigenvalues and eigenvectors of B, the specific code:
Using singular value decomposition to calculate eigenvalues and eigenvectors of B
double Eigen
,%% $ A ^ Ky = Xs ^ KB/approx/Alpha X_1 $%% That is the iteration will converge to the direction of X_1, which is% Eigenvector corresponding to the eigenvalue with the maximum module.% This leads to the following power method to solve the eigenvalue problem.
A = randn (10, 5 );% Sysmetric matrix to ensure real eigenvaluesB = A' *;% Find the column which has the maximum norm[Dum, idx] = max (sum (A. * ));X = a (:, idx );% Storage to Judge ConvergenceX0 = x-X;% Convergence tolerantTol = 1e-6;% Ite
Watervoles data from the HSAUR2 package for example. This data is a similarity matrix, which indicates the similarity of paddy rats in different regions. Load the data first and then analyze it with cmdscales.Library (GGPLOT2) data (watervoles, package = "HSAUR2") data (Watervoles) Voles.mds=cmdscale (watervoles,k=13,eig=t)The following calculates the proportions of the first two eigenvalues in all eigenvalues, in order to detect whether the distance
The first article is here: NumPy Library Advanced Tutorial (i) solving a linear equation groupSolving eigenvalues and eigenvectorsFor an introduction to eigenvalues and eigenvectors, click hereFirst create a matrixIn [1]: A=mat("3 -2;1 0")In [2]: AOut[2]: matrix([[ 3, -2], [ 1, 0]])In the Numpy.linalg module, the Eigvals function calculates the eigenvalues of the Matrix, and the EIG function can return a tuple containing the eigenvalues and co
to measure the length of a matrix or vector in a certain sense. There are multiple methods to define a norm. The norm value varies depending on its definition.(1) The three common vectors and their calculation functions are in MATLAB. The functions for finding the vector norms are:A, norm (V) or norm (V, 2): Calculate the 2-norm of vector V;B. norm (V, 1): calculates the 1-norm of vector V;C. norm (V, inf): Calculate the ∞-norm of vector V.(2) matrix norm and its calculation function MATLAB pro
and their corresponding eigen vectors
"""
Eigval,eigvec=linalg.eig (Lbar)
Dim=len (Eigval)
#查找前k小的eigval
Dicteigval=dict (Zip (Eigval,range (0,dim)))
Keig=np.sort (eigval) [0:k]
Ix=[dicteigval[k] for K in Keig]
return Eigval[ix],eigvec[:,ix]
def checkresult(lbar,eigvec,eigval,k):
"""
the input
"Matrix Lbar and K Eig values and K Eig vectors
"Print norm (Lbar*eigvec[:,i]
EXERCISE:PCA and Whitening
No. 0 Step: Data Preparation
UFLDL The downloaded file contains the dataset Images_raw, which is a 512*512*10 matrix, which is 10 images of 512*512
(a) data-loading
Using the Sampleimagesraw function, extract the numpatches image blocks from the Images_raw, each image block size is patchsize, and the extracted image blocks are stored in columns, respectively, in each column of the matrix patches, That is, patches (:, i) holds all the pixel values of the first image blo
Eig function in MATLAB to find the maximum feature root who can provide a method of PHP with the EIG function
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Eig function in MATLAB to find the maximum feature root who can provide a method of PHP with the EIG function
Too high-end, have never heard of; "matlab" should be a commercial math softw
Common LINALG functions
function
Description
Diag
Returns the diagonal (or non-diagonal) elements of a matrix in the form of a one-dimensional array, or converts a one-dimensional array to a matrix (non-diagonal element 0)
Dot
Standard matrix multiplication
Trace
Calculates the and of the diagonal elements
Det
Determinant of a computed matrix
Eigvals
Calculate the eigenvalues of a matrix
eigenvectors of B
, double eigen, qr[4];
Matrixeigen (B, eigen, QR, 4);
To compute the eigenvalue decomposition of n-order positive definite matrix M: Eigen is a eigenvalue, q is a eigenvector
void Matrixeigen (double *m, double *eigen, double *q, int n)
{
double * VEC, *eig;
VEC = new Double[n*n];
Eig = new Double[n];
Cvmat _m = Cvmat (n, N, cv_64f, m);
Cvmat _vec = Cvmat (n, N, cv_64f, VEC);
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the linear equations, use the backslash/A = hilb (3)B = [1 2 3]'A/B
Matrix feature value and feature vectorUse the EIG (v, d) function, [V, d] = EIG (a); where D returns the feature value, and V returns the corresponding feature vector, by default, the second parameter returns only the feature value.Syms a B C realA = [a B c; B c a; c a B];[V, d] = EIG ();
To ma
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Char * STR = "epmzm bpmzm QA eqtt bpmzm qa I EIG ";
The code in the future will operate on this string (the characters in the string are modified ). But changed
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