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HuangCongQingHuangCongQing
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‎图像处理与分析19-20秋季/第十八讲-图像表示与描述（上）.pdf‎

2.62 MB
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‎模式识别19-20秋季/UCAS-AI模式识别2019-17-特征提取与选择02.pdf‎

2.8 MB
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‎计算机算法设计与分析19-20秋季/Lec8-IPM-draw-points.sh‎

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while read line; do x=`echo $line | cut -f 2 -d" "`; y=`echo $line | cut -f 3 -d " "`; echo "\\draw[red, fill=red] ($x, $y) circle (3pt);"; done < aaa

‎计算机算法设计与分析19-20秋季/Lec8-IPM-gnuplot.script‎

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f(x, y ) = 2*x + 1.5*y
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f1(x, y) = -( 12*x + 24*y -120)
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f2(x, y) = -( 16*x + 16*y - 120 )
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f3(x, y) = -( 30*x + 12*y - 120 )
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f4(x, y) = x - 15
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f5(x, y) = y-15
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f6(x,y) = - x
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f7( x, y) = -y
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t=100
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set contour
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set cntrparam levels 20
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set isosample 50
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splot [0:15] [y=0:15] f(x,y) - t*( log( -f1(x,y) ) + log( -f2(x,y) ) + log( -f3(x,y) ) + log( -f4(x,y) ) + log( -f5(x,y) ) + log( -f6(x,y) ) + log( -f7(x,y) ) )
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse
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pause mouse

‎计算机算法设计与分析19-20秋季/Lec8-IPM_CenteringPath-new.py‎

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import numpy as np;
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m=5;
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n=7;
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c = np.array( [2, 1.5, 0, 0, 0, 0, 0] );
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A = np.array( [ [12, 24, -1, 0, 0, 0, 0],
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[16, 16, 0, -1, 0, 0, 0],
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[30, 12, 0, 0, -1, 0, 0],
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[1, 0, 0, 0, 0, 1, 0],
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[0, 1, 0, 0, 0, 0, 1] ] );
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b = np.array( [ 120, 120, 120, 15, 15] );
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x = np.array( [12, 1, 72, 120, 312, 1, 14] );
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y = np.array( [0.01, 0.01, 0.01, -1, -1 ] );
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s = np.zeros( n );
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e = np.array( [ 1 ] * n );
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alpha = 0.95;
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epsilon = 0.001;
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beta = 0.8;
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num = 0;
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theta = 0;
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print(" iter x1 x2 theta max(xi*si) min(xi*si) mu #");
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while ( True ):
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found = True;
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print("============== iter: %d ============" % (num) );
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s = c - np.dot( np.transpose(A), y );
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maxxs = max( x * s );
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minxs = min( x * s );
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mu = beta * np.dot( x, s) / n;
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print(" %d %lf %lf %lf %lf %lf %lf #" % (num, x[0], x[1], theta, maxxs, minxs, mu) );
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num = num + 1;
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for i in range(n) :
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print("x[%d]: %lf s[%d]: %lf x*s[%d]: %lf " % (i, x[i], i, s[i], i, x[i]*s[i] ) );
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if ( x[i] * s[i] > epsilon ):
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found = False;
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if (found == True ):
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break;
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X = np.zeros( shape=(n,n) );
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for i in range(n) :
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X[i, i] = x[i];
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Xinv = np.zeros( shape=(n,n) );
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for i in range(n) :
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Xinv[i, i] = 1.0/x[i];
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X2 = np.zeros( shape=(n,n) );
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for i in range(n) :
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X2[i, i] = x[i]*x[i];
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AX2c = np.dot( A, np.dot( X2, c) );
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AX2Atr = np.dot( A, np.dot( X2, np.transpose(A)) );
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AX2Atry = np.dot( AX2Atr, y );
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muAXe = mu * np.dot( A, np.dot(X, e) );
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dy = np.linalg.solve( AX2Atr, -AX2c + AX2Atry + muAXe );
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X2c = np.dot( X2, c);
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X2Atry = np.dot( X2, np.dot( np.transpose(A), y) );
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muXe = mu * np.dot( X, e);
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X2Atr = np.dot( X2, np.transpose(A) );
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dx = 1/mu * ( X2c - X2Atry - muXe + np.dot(X2Atr, dy) );
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for i in range(n):
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print("dx[%d]: %lf" % (i, dx[i] ) );
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for i in range(m):
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print("dy[%d]: %lf" % (i, dy[i] ) );
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thetax = -1;
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for i in range(n) :
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if (dx[i] < 0 ):
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t = x[i] / (-dx[i]);
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print("t[%d]: %lf for dx" % (i, t) );
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if ( t < thetax or thetax < 0 ):
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thetax = t;
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Atrdy = np.dot( np.transpose(A), dy);
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s = s - mu * np.dot( Xinv, e );
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thetay = 9999999;
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for i in range(n):
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if(Atrdy[i] > 0 ):
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t = s[i] / (Atrdy[i]);
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print("t[%d]: %lf for dy" % (i, t) );
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if(t < thetay ):
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thetay = t;
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thetax = min( 1, thetax*alpha );
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thetay = min( 1, thetay*alpha );
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print("thetax: %lf thetay: %lf theta: %lf" % (thetax, thetay, theta) );
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x = x + thetax * dx;
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y = y + thetay * dy;
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‎计算机算法设计与分析19-20秋季/Lec8-IPM_CenteringPath1.py‎

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import numpy as np;
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m=5;
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n=7;
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c = np.array( [2, 1.5, 0, 0, 0, 0, 0] );
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A = np.array( [ [12, 24, -1, 0, 0, 0, 0],
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[16, 16, 0, -1, 0, 0, 0],
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[30, 12, 0, 0, -1, 0, 0],
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[1, 0, 0, 0, 0, 1, 0],
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[0, 1, 0, 0, 0, 0, 1] ] );
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b = np.array( [ 120, 120, 120, 15, 15] );
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x = np.array( [10, 10, 240, 200, 300, 5, 5] );
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y = np.array( [1, 1, 1, -60, -60 ] );
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s = np.zeros( n );
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s[0] = 2 - 12 * y[0] - 16*y[1] - 30*y[2] -y[3];
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s[1] = 1.5 - 24*y[0] - 16*y[1] - 12*y[2] -y[4];
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s[2] = y[0];
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s[3] = y[1];
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s[4] = y[2];
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s[5] = -y[3];
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s[6] = -y[4];
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alpha = 0.995;
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epsilon = 0.001;
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beta = 0.2;
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num = 0;
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theta = 0;
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print(" iter x1 x2 theta max(xi*si) min(xi*si) mu #");
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while ( True ):
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found = True;
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print("============== iter: %d ============" % (num) );
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maxxs = max( x * s );
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minxs = min( x * s );
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mu = beta * np.dot( x, s) / n;
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print(" %d %lf %lf %lf %lf %lf %lf #" % (num, x[0], x[1], theta, maxxs, minxs, mu) );
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num = num + 1;
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for i in range(n) :
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print("x[%d]: %lf s[%d]: %lf x*s[%d]: %lf " % (i, x[i], i, s[i], i, x[i]*s[i] ) );
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if ( x[i] * s[i] > epsilon ):
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found = False;
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if (found == True ):
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break;
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XSinv = np.zeros( shape=(n,n) );
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for i in range(n) :
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XSinv[i, i] = x[i] / s[i];
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XinvS = np.zeros( shape=(n,n) );
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for i in range(n) :
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XinvS[i, i] = s[i] / x[i];
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muSinvE = np.zeros( n );
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muXinvE = np.zeros( n );
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for i in range(n):
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muXinvE[i] = mu / x[i];
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for i in range(n):
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muSinvE[i] = mu / s[i];
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AXSinvAt = np.dot( np.dot( A, XSinv ), np.transpose(A) );
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dy = np.linalg.solve( AXSinvAt, b - np.dot(A, muSinvE) );
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dx = -x + muSinvE + np.dot( np.dot( XSinv, np.transpose(A) ), dy );
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ds = -s - np.dot( XinvS, dx ) + muXinvE;
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for i in range(n):
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print("dx[%d]: %lf" % (i, dx[i] ) );
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for i in range(m):
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print("dy[%d]: %lf" % (i, dy[i] ) );
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for i in range(n):
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print("ds[%d]: %lf" % (i, ds[i] ) );
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thetax = -1;
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for i in range(n) :
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if (dx[i] < 0 ):
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t = x[i] / (-dx[i]);
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print("t[%d]: %lf" % (i, t) );
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if ( t < thetax or thetax < 0 ):
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thetax = t;
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thetas = -1;
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for i in range(n) :
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if (ds[i] < 0 ):
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t = s[i] / (-ds[i]);
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if ( t < thetas or thetas < 0 ):
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thetas = t;
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theta = min( 1, thetax*alpha, thetas*alpha);
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print("thetax: %lf thetas: %lf theta: %lf" % (thetax, thetas, theta) );
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x = x + theta * dx;
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s = s + theta * ds;
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y = y + theta * dy;
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‎计算机算法设计与分析19-20秋季/Lec8-IPM_CenteringPath2.py‎

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import numpy as np;
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m=5;
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n=7;
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c = np.array( [2, 1.5, 0, 0, 0, 0, 0] );
7+
A = np.array( [ [12, 24, -1, 0, 0, 0, 0],
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[16, 16, 0, -1, 0, 0, 0],
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[30, 12, 0, 0, -1, 0, 0],
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[1, 0, 0, 0, 0, 1, 0],
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[0, 1, 0, 0, 0, 0, 1] ] );
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b = np.array( [ 120, 120, 120, 15, 15] );
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x = np.array( [14, 1, 72, 120, 312, 1, 14] );
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y = np.array( [0.01, 0.01, 0.01, -1, -1 ] );
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s = np.zeros( n );
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s[0] = 2 - 12 * y[0] - 16*y[1] - 30*y[2] -y[3];
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s[1] = 1.5 - 24*y[0] - 16*y[1] - 12*y[2] -y[4];
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s[2] = y[0];
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s[3] = y[1];
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s[4] = y[2];
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s[5] = -y[3];
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s[6] = -y[4];
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alpha = 0.995;
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epsilon = 0.001;
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beta = 0.7;
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num = 0;
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theta = 0;
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print(" iter x1 x2 theta max(xi*si) min(xi*si) mu #");
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while ( True ):
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found = True;
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print("============== iter: %d ============" % (num) );
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maxxs = max( x * s );
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minxs = min( x * s );
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mu = beta * np.dot( x, s) / n;
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print(" %d %lf %lf %lf %lf %lf %lf #" % (num, x[0], x[1], theta, maxxs, minxs, mu) );
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num = num + 1;
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for i in range(n) :
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print("x[%d]: %lf s[%d]: %lf x*s[%d]: %lf " % (i, x[i], i, s[i], i, x[i]*s[i] ) );
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if ( x[i] * s[i] > epsilon ):
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found = False;
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if (found == True ):
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break;
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XSinv = np.zeros( shape=(n,n) );
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for i in range(n) :
55+
XSinv[i, i] = x[i] / s[i];
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XinvS = np.zeros( shape=(n,n) );
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for i in range(n) :
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XinvS[i, i] = s[i] / x[i];
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muSinvE = np.zeros( n );
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muXinvE = np.zeros( n );
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for i in range(n):
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muXinvE[i] = mu / x[i];
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for i in range(n):
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muSinvE[i] = mu / s[i];
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AXSinvAt = np.dot( np.dot( A, XSinv ), np.transpose(A) );
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dy = np.linalg.solve( AXSinvAt, b - np.dot(A, muSinvE) );
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dx = -x + muSinvE + np.dot( np.dot( XSinv, np.transpose(A) ), dy );
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ds = -s - np.dot( XinvS, dx ) + muXinvE;
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for i in range(n):
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print("dx[%d]: %lf" % (i, dx[i] ) );
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for i in range(m):
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print("dy[%d]: %lf" % (i, dy[i] ) );
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for i in range(n):
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print("ds[%d]: %lf" % (i, ds[i] ) );
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thetax = -1;
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for i in range(n) :
84+
if (dx[i] < 0 ):
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t = x[i] / (-dx[i]);
86+
print("t[%d]: %lf" % (i, t) );
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if ( t < thetax or thetax < 0 ):
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thetax = t;
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thetas = -1;
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for i in range(n) :
92+
if (ds[i] < 0 ):
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t = s[i] / (-ds[i]);
94+
if ( t < thetas or thetas < 0 ):
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thetas = t;
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theta = min( 1, thetax*alpha, thetas*alpha);
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print("thetax: %lf thetas: %lf theta: %lf" % (thetax, thetas, theta) );
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x = x + theta * dx;
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s = s + theta * ds;
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y = y + theta * dy;
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