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n=t("robust-orientation"),i=t("simplicial-complex")},{"robust-orientation":284,"simplicial-complex":295}],298:[function(t,e,r){"use strict";e.exports=function(t,e){var r,a,o,s;if(e[0][0]e[1][0]))return i(e,t);r=e[1],a=e[0]}if(t[0][0]t[1][0]))return-i(t,e);o=t[1],s=t[0]}var l=n(r,a,s),c=n(r,a,o);if(l<0){if(c<=0)return l}else if(l>0){if(c>=0)return l}else if(c)return c;if(l=n(s,o,a),c=n(s,o,r),l<0){if(c<=0)return l}else if(l>0){if(c>=0)return l}else if(c)return c;return a[0]-s[0]};var n=t("robust-orientation");function i(t,e){var r,i,a,o;if(e[0][0]e[1][0])){var s=Math.min(t[0][1],t[1][1]),l=Math.max(t[0][1],t[1][1]),c=Math.min(e[0][1],e[1][1]),u=Math.max(e[0][1],e[1][1]);return lu?s-u:l-u}r=e[1],i=e[0]}t[0][1]0)if(e[0]!==o[1][0])r=t,t=t.right;else{if(l=c(t.right,e))return l;t=t.left}else{if(e[0]!==o[1][0])return t;var l;if(l=c(t.right,e))return l;t=t.left}}return r}function u(t,e,r,n){this.y=t,this.index=e,this.start=r,this.closed=n}function 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p=h.prototype;p.setDistanceLimits=function(t,e){t=t>0?Math.log(t):-1/0,e=e>0?Math.log(e):1/0,e=Math.max(e,t),this.radius.bounds[0][0]=t,this.radius.bounds[1][0]=e},p.getDistanceLimits=function(t){var e=this.radius.bounds[0];return t?(t[0]=Math.exp(e[0][0]),t[1]=Math.exp(e[1][0]),t):[Math.exp(e[0][0]),Math.exp(e[1][0])]},p.recalcMatrix=function(t){this.center.curve(t),this.up.curve(t),this.right.curve(t),this.radius.curve(t),this.angle.curve(t);for(var e=this.computedUp,r=this.computedRight,n=0,i=0,a=0;a<3;++a)i+=e[a]*r[a],n+=e[a]*e[a];var l=Math.sqrt(n),u=0;for(a=0;a<3;++a)r[a]-=e[a]*i/n,u+=r[a]*r[a],e[a]/=l;var f=Math.sqrt(u);for(a=0;a<3;++a)r[a]/=f;var h=this.computedToward;o(h,e,r),s(h,h);var p=Math.exp(this.computedRadius[0]),d=this.computedAngle[0],m=this.computedAngle[1],g=Math.cos(d),v=Math.sin(d),y=Math.cos(m),x=Math.sin(m),b=this.computedCenter,_=g*y,w=v*y,T=x,k=-g*x,A=-v*x,M=y,S=this.computedEye,E=this.computedMatrix;for(a=0;a<3;++a){var L=_*r[a]+w*h[a]+T*e[a];E[4*a+1]=k*r[a]+A*h[a]+M*e[a],E[4*a+2]=L,E[4*a+3]=0}var C=E[1],P=E[5],I=E[9],O=E[2],z=E[6],D=E[10],R=P*D-I*z,F=I*O-C*D,B=C*z-P*O,N=c(R,F,B);R/=N,F/=N,B/=N,E[0]=R,E[4]=F,E[8]=B;for(a=0;a<3;++a)S[a]=b[a]+E[2+4*a]*p;for(a=0;a<3;++a){u=0;for(var j=0;j<3;++j)u+=E[a+4*j]*S[j];E[12+a]=-u}E[15]=1},p.getMatrix=function(t,e){this.recalcMatrix(t);var r=this.computedMatrix;if(e){for(var n=0;n<16;++n)e[n]=r[n];return e}return r};var d=[0,0,0];p.rotate=function(t,e,r,n){if(this.angle.move(t,e,r),n){this.recalcMatrix(t);var i=this.computedMatrix;d[0]=i[2],d[1]=i[6],d[2]=i[10];for(var o=this.computedUp,s=this.computedRight,l=this.computedToward,c=0;c<3;++c)i[4*c]=o[c],i[4*c+1]=s[c],i[4*c+2]=l[c];a(i,i,n,d);for(c=0;c<3;++c)o[c]=i[4*c],s[c]=i[4*c+1];this.up.set(t,o[0],o[1],o[2]),this.right.set(t,s[0],s[1],s[2])}},p.pan=function(t,e,r,n){e=e||0,r=r||0,n=n||0,this.recalcMatrix(t);var 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p=h.prototype;p.setDistanceLimits=function(t,e){t=t>0?Math.log(t):-1/0,e=e>0?Math.log(e):1/0,e=Math.max(e,t),this.radius.bounds[0][0]=t,this.radius.bounds[1][0]=e},p.getDistanceLimits=function(t){var e=this.radius.bounds[0];return t?(t[0]=Math.exp(e[0][0]),t[1]=Math.exp(e[1][0]),t):[Math.exp(e[0][0]),Math.exp(e[1][0])]},p.recalcMatrix=function(t){this.center.curve(t),this.up.curve(t),this.right.curve(t),this.radius.curve(t),this.angle.curve(t);for(var e=this.computedUp,r=this.computedRight,n=0,i=0,a=0;a<3;++a)i+=e[a]*r[a],n+=e[a]*e[a];var l=Math.sqrt(n),u=0;for(a=0;a<3;++a)r[a]-=e[a]*i/n,u+=r[a]*r[a],e[a]/=l;var f=Math.sqrt(u);for(a=0;a<3;++a)r[a]/=f;var h=this.computedToward;o(h,e,r),s(h,h);var p=Math.exp(this.computedRadius[0]),d=this.computedAngle[0],m=this.computedAngle[1],g=Math.cos(d),v=Math.sin(d),y=Math.cos(m),x=Math.sin(m),b=this.computedCenter,_=g*y,w=v*y,T=x,k=-g*x,A=-v*x,M=y,S=this.computedEye,E=this.computedMatrix;for(a=0;a<3;++a){var L=_*r[a]+w*h[a]+T*e[a];E[4*a+1]=k*r[a]+A*h[a]+M*e[a],E[4*a+2]=L,E[4*a+3]=0}var C=E[1],P=E[5],I=E[9],O=E[2],z=E[6],D=E[10],R=P*D-I*z,F=I*O-C*D,B=C*z-P*O,N=c(R,F,B);R/=N,F/=N,B/=N,E[0]=R,E[4]=F,E[8]=B;for(a=0;a<3;++a)S[a]=b[a]+E[2+4*a]*p;for(a=0;a<3;++a){u=0;for(var j=0;j<3;++j)u+=E[a+4*j]*S[j];E[12+a]=-u}E[15]=1},p.getMatrix=function(t,e){this.recalcMatrix(t);var r=this.computedMatrix;if(e){for(var n=0;n<16;++n)e[n]=r[n];return e}return r};var d=[0,0,0];p.rotate=function(t,e,r,n){if(this.angle.move(t,e,r),n){this.recalcMatrix(t);var i=this.computedMatrix;d[0]=i[2],d[1]=i[6],d[2]=i[10];for(var o=this.computedUp,s=this.computedRight,l=this.computedToward,c=0;c<3;++c)i[4*c]=o[c],i[4*c+1]=s[c],i[4*c+2]=l[c];a(i,i,n,d);for(c=0;c<3;++c)o[c]=i[4*c],s[c]=i[4*c+1];this.up.set(t,o[0],o[1],o[2]),this.right.set(t,s[0],s[1],s[2])}},p.pan=function(t,e,r,n){e=e||0,r=r||0,n=n||0,this.recalcMatrix(t);var i=this.computedMatrix,a=(Math.exp(this.computedRadius[0]),i[1]),o=i[5],s=i[9],l=c(a,o,s);a/=l,o/=l,s/=l;var u=i[0],f=i[4],h=i[8],p=u*a+f*o+h*s,d=c(u-=a*p,f-=o*p,h-=s*p),m=(u/=d)*e+a*r,g=(f/=d)*e+o*r,v=(h/=d)*e+s*r;this.center.move(t,m,g,v);var y=Math.exp(this.computedRadius[0]);y=Math.max(1e-4,y+n),this.radius.set(t,Math.log(y))},p.translate=function(t,e,r,n){this.center.move(t,e||0,r||0,n||0)},p.setMatrix=function(t,e,r,n){var a=1;"number"==typeof r&&(a=0|r),(a<0||a>3)&&(a=1);var o=(a+2)%3;e||(this.recalcMatrix(t),e=this.computedMatrix);var s=e[a],l=e[a+4],f=e[a+8];if(n){var h=Math.abs(s),p=Math.abs(l),d=Math.abs(f),m=Math.max(h,p,d);h===m?(s=s<0?-1:1,l=f=0):d===m?(f=f<0?-1:1,s=l=0):(l=l<0?-1:1,s=f=0)}else{var g=c(s,l,f);s/=g,l/=g,f/=g}var v,y,x=e[o],b=e[o+4],_=e[o+8],w=x*s+b*l+_*f,T=c(x-=s*w,b-=l*w,_-=f*w),k=l*(_/=T)-f*(b/=T),A=f*(x/=T)-s*_,M=s*b-l*x,S=c(k,A,M);if(k/=S,A/=S,M/=S,this.center.jump(t,q,G,Y),this.radius.idle(t),this.up.jump(t,s,l,f),this.right.jump(t,x,b,_),2===a){var 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i,a,o,s,l,c,u,f,h,p=1,d=r.length,m="";for(a=0;a=0),s.type){case"b":i=parseInt(i,10).toString(2);break;case"c":i=String.fromCharCode(parseInt(i,10));break;case"d":case"i":i=parseInt(i,10);break;case"j":i=JSON.stringify(i,null,s.width?parseInt(s.width):0);break;case"e":i=s.precision?parseFloat(i).toExponential(s.precision):parseFloat(i).toExponential();break;case"f":i=s.precision?parseFloat(i).toFixed(s.precision):parseFloat(i);break;case"g":i=s.precision?String(Number(i.toPrecision(s.precision))):parseFloat(i);break;case"o":i=(parseInt(i,10)>>>0).toString(8);break;case"s":i=String(i),i=s.precision?i.substring(0,s.precision):i;break;case"t":i=String(!!i),i=s.precision?i.substring(0,s.precision):i;break;case"T":i=Object.prototype.toString.call(i).slice(8,-1).toLowerCase(),i=s.precision?i.substring(0,s.precision):i;break;case"u":i=parseInt(i,10)>>>0;break;case"v":i=i.valueOf(),i=s.precision?i.substring(0,s.precision):i;break;case"x":i=(parseInt(i,10)>>>0).toString(16);break;case"X":i=(parseInt(i,10)>>>0).toString(16).toUpperCase()}t.json.test(s.type)?m+=i:(!t.number.test(s.type)||f&&!s.sign?h="":(h=f?"+":"-",i=i.toString().replace(t.sign,"")),c=s.pad_char?"0"===s.pad_char?"0":s.pad_char.charAt(1):" 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6:u.push([t-.5-.25*(-n-r+a+i)/(n-r+i-a),e-.5-.25*(-i-r+a+n)/(i-r+n-a)]);break;case 7:u.push([t-.75-.25*(a+i-2*h)/(i-a),e-.75-.25*(a+n-2*h)/(n-a)]);break;case 8:u.push([t-.75-.25*(-a-i+2*h)/(a-i),e-.75-.25*(-a-n+2*h)/(a-n)]);break;case 9:u.push([t-.5-.25*(n+r+-a-i)/(r-n+a-i),e-.5-.25*(i+r+-a-n)/(r-i+a-n)]);break;case 10:u.push([t-.5-.5*(-n-r-a-i+4*h)/(n-r+a-i),e-.5]);break;case 11:u.push([t-.25-.25*(-a-i+2*h)/(a-i),e-.75-.25*(i+r-2*h)/(r-i)]);break;case 12:u.push([t-.5,e-.5-.5*(-i-r-a-n+4*h)/(i-r+a-n)]);break;case 13:u.push([t-.75-.25*(n+r-2*h)/(r-n),e-.25-.25*(-a-n+2*h)/(a-n)]);break;case 14:u.push([t-.25-.25*(-n-r+2*h)/(n-r),e-.25-.25*(-i-r+2*h)/(i-r)]);break;case 15:u.push([t-.5,e-.5])}},cell:function(t,e,r,n,i,a,o,s,l){i?s.push([t,e]):s.push([e,t])}});return function(t,e){var r=[],i=[];return n(t,r,i,e),{positions:r,cells:i}}}};var o={}},{"ndarray-extract-contour":251,"zero-crossings":318}],303:[function(t,e,r){(function(r){(function(){"use strict";e.exports=function t(e,r,i){i=i||{};var o=a[e];o||(o=a[e]={" ":{data:new Float32Array(0),shape:.2}});var s=o[r];if(!s)if(r.length<=1||!/\d/.test(r))s=o[r]=function(t){for(var e=t.cells,r=t.positions,n=new Float32Array(6*e.length),i=0,a=0,o=0;o0&&(f+=.02);var p=new Float32Array(u),d=0,m=-.5*f;for(h=0;hMath.max(r,n)?i[2]=1:r>Math.max(e,n)?i[0]=1:i[1]=1;for(var a=0,o=0,l=0;l<3;++l)a+=t[l]*t[l],o+=i[l]*t[l];for(l=0;l<3;++l)i[l]-=o/a*t[l];return s(i,i),i}function h(t,e,r,i,a,o,s,l){this.center=n(r),this.up=n(i),this.right=n(a),this.radius=n([o]),this.angle=n([s,l]),this.angle.bounds=[[-1/0,-Math.PI/2],[1/0,Math.PI/2]],this.setDistanceLimits(t,e),this.computedCenter=this.center.curve(0),this.computedUp=this.up.curve(0),this.computedRight=this.right.curve(0),this.computedRadius=this.radius.curve(0),this.computedAngle=this.angle.curve(0),this.computedToward=[0,0,0],this.computedEye=[0,0,0],this.computedMatrix=new Array(16);for(var c=0;c<16;++c)this.computedMatrix[c]=.5;this.recalcMatrix(0)}var p=h.prototype;p.setDistanceLimits=function(t,e){t=t>0?Math.log(t):-1/0,e=e>0?Math.log(e):1/0,e=Math.max(e,t),this.radius.bounds[0][0]=t,this.radius.bounds[1][0]=e},p.getDistanceLimits=function(t){var e=this.radius.bounds[0];return t?(t[0]=Math.exp(e[0][0]),t[1]=Math.exp(e[1][0]),t):[Math.exp(e[0][0]),Math.exp(e[1][0])]},p.recalcMatrix=function(t){this.center.curve(t),this.up.curve(t),this.right.curve(t),this.radius.curve(t),this.angle.curve(t);for(var e=this.computedUp,r=this.computedRight,n=0,i=0,a=0;a<3;++a)i+=e[a]*r[a],n+=e[a]*e[a];var l=Math.sqrt(n),u=0;for(a=0;a<3;++a)r[a]-=e[a]*i/n,u+=r[a]*r[a],e[a]/=l;var f=Math.sqrt(u);for(a=0;a<3;++a)r[a]/=f;var h=this.computedToward;o(h,e,r),s(h,h);var p=Math.exp(this.computedRadius[0]),d=this.computedAngle[0],m=this.computedAngle[1],g=Math.cos(d),v=Math.sin(d),y=Math.cos(m),x=Math.sin(m),b=this.computedCenter,_=g*y,w=v*y,T=x,k=-g*x,A=-v*x,M=y,S=this.computedEye,E=this.computedMatrix;for(a=0;a<3;++a){var L=_*r[a]+w*h[a]+T*e[a];E[4*a+1]=k*r[a]+A*h[a]+M*e[a],E[4*a+2]=L,E[4*a+3]=0}var C=E[1],P=E[5],I=E[9],O=E[2],z=E[6],D=E[10],R=P*D-I*z,F=I*O-C*D,B=C*z-P*O,N=c(R,F,B);R/=N,F/=N,B/=N,E[0]=R,E[4]=F,E[8]=B;for(a=0;a<3;++a)S[a]=b[a]+E[2+4*a]*p;for(a=0;a<3;++a){u=0;for(var j=0;j<3;++j)u+=E[a+4*j]*S[j];E[12+a]=-u}E[15]=1},p.getMatrix=function(t,e){this.recalcMatrix(t);var r=this.computedMatrix;if(e){for(var n=0;n<16;++n)e[n]=r[n];return e}return r};var d=[0,0,0];p.rotate=function(t,e,r,n){if(this.angle.move(t,e,r),n){this.recalcMatrix(t);var i=this.computedMatrix;d[0]=i[2],d[1]=i[6],d[2]=i[10];for(var o=this.computedUp,s=this.computedRight,l=this.computedToward,c=0;c<3;++c)i[4*c]=o[c],i[4*c+1]=s[c],i[4*c+2]=l[c];a(i,i,n,d);for(c=0;c<3;++c)o[c]=i[4*c],s[c]=i[4*c+1];this.up.set(t,o[0],o[1],o[2]),this.right.set(t,s[0],s[1],s[2])}},p.pan=function(t,e,r,n){e=e||0,r=r||0,n=n||0,this.recalcMatrix(t);var i=this.computedMatrix,a=(Math.exp(this.computedRadius[0]),i[1]),o=i[5],s=i[9],l=c(a,o,s);a/=l,o/=l,s/=l;var u=i[0],f=i[4],h=i[8],p=u*a+f*o+h*s,d=c(u-=a*p,f-=o*p,h-=s*p),m=(u/=d)*e+a*r,g=(f/=d)*e+o*r,v=(h/=d)*e+s*r;this.center.move(t,m,g,v);var y=Math.exp(this.computedRadius[0]);y=Math.max(1e-4,y+n),this.radius.set(t,Math.log(y))},p.translate=function(t,e,r,n){this.center.move(t,e||0,r||0,n||0)},p.setMatrix=function(t,e,r,n){var a=1;"number"==typeof r&&(a=0|r),(a<0||a>3)&&(a=1);var o=(a+2)%3;e||(this.recalcMatrix(t),e=this.computedMatrix);var s=e[a],l=e[a+4],f=e[a+8];if(n){var h=Math.abs(s),p=Math.abs(l),d=Math.abs(f),m=Math.max(h,p,d);h===m?(s=s<0?-1:1,l=f=0):d===m?(f=f<0?-1:1,s=l=0):(l=l<0?-1:1,s=f=0)}else{var g=c(s,l,f);s/=g,l/=g,f/=g}var v,y,x=e[o],b=e[o+4],_=e[o+8],w=x*s+b*l+_*f,T=c(x-=s*w,b-=l*w,_-=f*w),k=l*(_/=T)-f*(b/=T),A=f*(x/=T)-s*_,M=s*b-l*x,S=c(k,A,M);if(k/=S,A/=S,M/=S,this.center.jump(t,q,G,Y),this.radius.idle(t),this.up.jump(t,s,l,f),this.right.jump(t,x,b,_),2===a){var E=e[1],L=e[5],C=e[9],P=E*x+L*b+C*_,I=E*k+L*A+C*M;v=R<0?-Math.PI/2:Math.PI/2,y=Math.atan2(I,P)}else{var O=e[2],z=e[6],D=e[10],R=O*s+z*l+D*f,F=O*x+z*b+D*_,B=O*k+z*A+D*M;v=Math.asin(u(R)),y=Math.atan2(B,F)}this.angle.jump(t,y,v),this.recalcMatrix(t);var N=e[2],j=e[6],U=e[10],V=this.computedMatrix;i(V,e);var H=V[15],q=V[12]/H,G=V[13]/H,Y=V[14]/H,W=Math.exp(this.computedRadius[0]);this.center.jump(t,q-N*W,G-j*W,Y-U*W)},p.lastT=function(){return Math.max(this.center.lastT(),this.up.lastT(),this.right.lastT(),this.radius.lastT(),this.angle.lastT())},p.idle=function(t){this.center.idle(t),this.up.idle(t),this.right.idle(t),this.radius.idle(t),this.angle.idle(t)},p.flush=function(t){this.center.flush(t),this.up.flush(t),this.right.flush(t),this.radius.flush(t),this.angle.flush(t)},p.setDistance=function(t,e){e>0&&this.radius.set(t,Math.log(e))},p.lookAt=function(t,e,r,n){this.recalcMatrix(t),e=e||this.computedEye,r=r||this.computedCenter;var i=(n=n||this.computedUp)[0],a=n[1],o=n[2],s=c(i,a,o);if(!(s<1e-6)){i/=s,a/=s,o/=s;var l=e[0]-r[0],f=e[1]-r[1],h=e[2]-r[2],p=c(l,f,h);if(!(p<1e-6)){l/=p,f/=p,h/=p;var d=this.computedRight,m=d[0],g=d[1],v=d[2],y=i*m+a*g+o*v,x=c(m-=y*i,g-=y*a,v-=y*o);if(!(x<.01&&(x=c(m=a*h-o*f,g=o*l-i*h,v=i*f-a*l))<1e-6)){m/=x,g/=x,v/=x,this.up.set(t,i,a,o),this.right.set(t,m,g,v),this.center.set(t,r[0],r[1],r[2]),this.radius.set(t,Math.log(p));var b=a*v-o*g,_=o*m-i*v,w=i*g-a*m,T=c(b,_,w),k=i*l+a*f+o*h,A=m*l+g*f+v*h,M=(b/=T)*l+(_/=T)*f+(w/=T)*h,S=Math.asin(u(k)),E=Math.atan2(M,A),L=this.angle._state,C=L[L.length-1],P=L[L.length-2];C%=2*Math.PI;var I=Math.abs(C+2*Math.PI-E),O=Math.abs(C-E),z=Math.abs(C-2*Math.PI-E);I0?r.pop():new ArrayBuffer(t)}function d(t){return new Uint8Array(p(t),0,t)}function m(t){return new Uint16Array(p(2*t),0,t)}function g(t){return new Uint32Array(p(4*t),0,t)}function v(t){return new Int8Array(p(t),0,t)}function y(t){return new Int16Array(p(2*t),0,t)}function x(t){return new 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\ No newline at end of file diff --git a/src/algo2_testing.ipynb b/src/algo2_testing.ipynb index bd4b836..268bca1 100644 --- a/src/algo2_testing.ipynb +++ b/src/algo2_testing.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -29,41 +29,37 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 86, "metadata": {}, "outputs": [], "source": [ - "def Arnoldi(A, v, m): # defined ad algorithm 2 in the paper\n", + "def Arnoldi(A, v, m): \n", " beta = norm(v)\n", - " print(\"A\")\n", - " v = v/beta\n", - " print(\"B\")\n", - " h = sp.sparse.lil_matrix((m,m))\n", - " print(\"C\")\n", + " v = v/beta \n", + " h = sp.sparse.lil_matrix((m,m)) \n", "\n", " for j in range(m):\n", - " w = A.dot(v)\n", - " print(\"D\")\n", + " w = A @ v \n", " for i in range(j):\n", - " h[i,j] = v.T.dot(w)\n", - " print(\"E\")\n", - " w = w - h[i,j]*v[i]\n", - " print(\"F\")\n", + " tmp = v.T @ w \n", + " h[i,j] = tmp[0,0]\n", + " w = w - h[i,j]*v \n", + " h[j,j-1] = norm(w) \n", "\n", - " h[j+1,j] = norm(w)\n", - " print(\"G\")\n", - "\n", - " if h[j+1,j] == 0:\n", - " print(\"The algorithm didn't converge\")\n", + " if h[j,j-1] == 0: \n", + " print(\"Arnoldi breakdown\")\n", " m = j\n", - " v[m+1] = 0\n", + " v = 0\n", " break\n", " else:\n", - " print(\"H\")\n", - " v[j+1] = w**h[j+1,j] # THIS IS WRONG, I DON'T KNOW HOW TO FIX IT. ERROR \" matrix is not square\"\n", - " print(\"I\")\n", - "\n", - " return v, h, m, beta, j" + " v = w/h[j,j-1] \n", + " \n", + " print(\"Arnoldi finished\\n\")\n", + " print(\"h is \", h.shape)\n", + " print(\"v is \", v.shape)\n", + " print(\"m is \", m)\n", + " print(\"beta is \", beta)\n", + " return v, h, m, beta, j # this is not the output required in the paper, I should return the matrix V and the matrix H\n" ] }, { @@ -75,20 +71,33 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 82, "metadata": {}, "outputs": [], "source": [ - "A = sp.sparse.rand(100,100, density=0.5, format='lil')\n", - "v = sp.sparse.rand(100,1, density=0.5, format='lil')\n", - "m = 100" + "m = 100\n", + "A = sp.sparse.rand(m,m, density=0.5, format='lil')\n", + "v = sp.sparse.rand(m,1, density=0.5, format='lil')" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 87, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Arnoldi finished\n", + "\n", + "h is (100, 100)\n", + "v is (100, 1)\n", + "m is 100\n", + "beta is 1.0\n" + ] + } + ], "source": [ "v, h, m, beta, j = Arnoldi(A, v, m)" ] diff --git a/src/main.py b/src/main.py index 12d430c..3858d39 100755 --- a/src/main.py +++ b/src/main.py @@ -113,7 +113,7 @@ class Utilities: def transition_matrix(P, v, d): print("Creating the transition matrix...") - Pt = P + v.dot(d.T) + Pt = P + v @ (d.T) print("Transition matrix created\n") return Pt @@ -154,7 +154,7 @@ class Algorithms: start_time = time.time() print("STARTING ALGORITHM 1...") - u = Pt.dot(v) - v + u = Pt @ v - v mv = 1 # number of matrix-vector multiplications r = sp.sparse.lil_matrix((n,1)) Res = sp.sparse.lil_matrix((len(a),1)) @@ -169,7 +169,7 @@ class Algorithms: x = r + v while max(Res) > tau and mv < max_mv: - u = Pt*u + u = Pt @ u mv += 1 for i in range(len(a)): @@ -193,26 +193,28 @@ class Algorithms: return mv, x, r, total_time # Refers to Algorithm 2 in the paper, it's needed to implement the algorithm 4. It doesn't work yet. Refer to the file testing.ipynb for more details. This function down here is just a place holder for now - def Arnoldi(A, v, m): - beta = norm(v) - v = v/beta - h = sp.sparse.lil_matrix((m,m)) - - for j in range(1,m): - w = A.dot(v) - for i in range(1,j): - h[i,j] = v.T.dot(w) - w = w - h[i,j]*v - - h[j+i,j] = norm(w) - - if h[j+1,j] == 0: - m = j - v[m+1] = 0 - break - else: - v[j+1] = w/h[j+1,j] - return v, h, m, beta, j +def Arnoldi(A, v, m): + beta = norm(v) + v = v/beta + h = sp.sparse.lil_matrix((m,m)) + + for j in range(m): + w = A @ v + for i in range(j): + tmp = v.T @ w + h[i,j] = tmp[0,0] + w = w - h[i,j]*v + h[j,j-1] = norm(w) + + if h[j,j-1] == 0: + print("Arnoldi breakdown") + m = j + v = 0 + break + else: + v = w/h[j,j-1] + return v, h, m, beta, j # this is not the output required in the paper, I should return the matrix V and the matrix H + # pandas dataframe to store the results df = pd.DataFrame(columns=['alpha', 'products m-v', 'tau', 'time'])