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| =Assignments= | | =Assignments= |
− | *[[/MD5 attack singlethreaded|MD5 attack singlethreaded]] | + | *[[CoE_Cluster_november_2011/MD5_attack_singlethreaded|MD5 attack singlethreaded]] |
− | *[[/Dell Cluster installation|Dell Cluster Installation]] | + | *[[CoE_Cluster_november_2011/MPI|Programmering med MPI]] |
− | *[[/MPI|Programmering med MPI]]
| + | |
− | *[[/CUDA|Programmering med CUDA]]
| |
| =Results= | | =Results= |
| + | Having investigated CUDA C programming for Nvidia graphics cards and the CUDA architecture, we made some performance measurements using a range of numbers of blocks and threads, executing in parallel. The test program calculated values of the [http://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set ] on a pixel-by-pixel basis. The Mandelbrot Set was a good choice for this test beacuse: |
| + | * It is relatively easy to program (see code listing below) |
| + | * Every pixel has to calculated individually - there is no correlation between values of neighbouring pixels |
| + | * The image can be separated into parts which can be calculated separately and in parallel |
| + | * The time taken to calculate a complete image without parallelization is long enough to allow the performance gains from parallelization to be clearly seen |
| + | * The resulting images are very pretty (if a little strange)! :-) |
| + | |
| + | The results of the benchmarking are here, as an interactive chart (hover your mouse to find out which values are represented by each line, drag to zoom and hide/reveal curves relating to the number of blocks in the legend beneath): |
| + | |
| + | *[http://mars.tekkom.dk/js/cuda_benchmark.htm CUDA Benchmark] (External JavaScript) |
| + | |
| + | Along with the CUDA C programming Guide (see Literature List), the [http://developer.download.nvidia.com/compute/cuda/CUDA_Occupancy_calculator.xls CUDA Occupancy Calculator] provides a good basis for understanding and explaining the results seen. In general, it was found that more than 32 blocks and/or 128 threads per block did not provide noticable performance gains, whereas there were significant performance gains for every step increase below these values. This independent presentation: [[Media:cuda_presentation.ppt]] provides a comprehensive explanation and confirmation of the results we obtained. |
| + | |
| + | [[File:cuda_mandelbrot.png]] |
| + | |
| + | ''Above: Mandelbrot Set drawn in 0,12 seconds, using a single NVidia CUDA capable graphics card (GeForce GTX 460) running 32 blocks and 128 threads in each block. Total image dimension 512 x 512 pixels.'' |
| + | |
| + | For the reasons given above, the Mandelbrot Set was also a good candidate for testing [http://en.wikipedia.org/wiki/Message_Passing_Interface Message Passing Interface - MPI] programming capabilities and strategies. To support graphical output, the final program used a "Master" process which collected calculated values from "Worker" processes and set them together in an X Window. This was a good illustration of the idea that some processes, like Input-Output, have to be run in a serial manner and that perfect parallelization is rarely achievable in practice c.f. [http://en.wikipedia.org/wiki/Amdahl%27s_law Amdahl's Law] |
| + | |
| [[File:mpi_mandelbrot.png]] | | [[File:mpi_mandelbrot.png]] |
| | | |
− | Mandelbrot Set drawn in 1,2 seconds, using a Master-Worker MPI pattern with 16 worker nodes and 1 master node (which collected calculated results from different parts of the image and output them to an X Window). Total image dimension 800 x 800 pixels. | + | ''Above: Mandelbrot Set drawn in 1,2 seconds, using a Master-Worker MPI pattern with 16 worker nodes and 1 master node (which collected calculated results from different parts of the image and output them to an X Window). Total image dimension 800 x 800 pixels.'' |
| + | |
| + | =CUDA Code Listing= |
| | | |
− | [[File:cuda_mandelbrot.png]]
| + | <source lang=c> |
| + | |
| + | // mandelbrot.cu |
| + | |
| + | // Calculate number of iterations required to make each point |
| + | // in Mandelbrot Set diverge and colour the corresponding pixel |
| + | // Tends to work faster with floats rather than doubles - but |
| + | // at the expense of "colour blocking" at lower resolutions |
| + | |
| + | // Paul Saunders |
| + | // Mercantec |
| + | // 03/11-2011 |
| + | |
| + | //#include <stdio.h> |
| + | //#include <stdlib.h> |
| + | //#include <unistd.h> |
| + | |
| + | __device__ inline int calcMandelbrot(const double xPos, const double yPos, const int crunch) |
| + | { |
| + | double y = yPos; |
| + | double x = xPos; |
| + | double yy = y * y; |
| + | double xx = x * x; |
| + | int i = crunch; |
| + | |
| + | while (--i && (xx + yy < 4.0f)) { |
| + | y = x * y * 2.0f + yPos; |
| + | x = xx - yy + xPos; |
| + | yy = y * y; |
| + | xx = x * x; |
| + | } |
| + | return i; |
| + | } // CalcMandelbrot - count down until iterations are used up or until the calculation diverges |
| + | |
| + | __device__ void RGB(int x, int y, unsigned char* m, int step, int iter_count) |
| + | { |
| + | unsigned char *p; |
| + | unsigned int rgb; |
| + | p = ((unsigned char *) (m + step*x)+3*y); |
| + | rgb = *p+((*(p+1))<<8)+((*(p+2))<<16); |
| + | |
| + | rgb = iter_count*2048; |
| + | |
| + | *p = (unsigned char) (rgb&0xff); |
| + | *(p+1) = (unsigned char) ((rgb>>8)&0xff); |
| + | *(p+2) = (unsigned char) ((rgb>>16)&0xff); |
| + | return; |
| + | } //Use calculated iteration count to determine the colour for each pixel |
| | | |
− | Mandelbort Set drawn in 0,12 seconds, using a single NVidia CUDA capable graphics card (GeForce GTX 460) running 32 blocks and 128 threads in each block.
| + | __global__ void Count(unsigned char *img, int rows, int cols, int step, int max_iterations, double centre_x, |
| + | double centre_y, double size, int image_size) |
| + | { |
| + | double rowfac = ((double) rows)/gridDim.x; |
| + | int rowstart = blockIdx.x*rowfac; |
| + | int rowend = (blockIdx.x+1)*rowfac; |
| + | double colfac = ((double) cols)/blockDim.x; |
| + | int colstart = threadIdx.x*colfac; |
| + | int colend = (threadIdx.x+1)*colfac; |
| + | |
| + | double left_edge = centre_x - size/2.0; |
| + | double top_edge = centre_y - size/2.0; |
| + | double pixel_step = size/image_size; |
| + | |
| + | for (int i=rowstart; i<rowend; i++) |
| + | { |
| + | for (int j=colstart; j<colend; j++) |
| + | { |
| + | RGB(i, j, img, step, calcMandelbrot(left_edge + j * pixel_step, top_edge + i * pixel_step, max_iterations)); |
| + | } |
| + | } |
| + | } //Divide calculations between the requested number of blocks and threads, having used the matrix's geometry to |
| + | //determine the values input to the calculation for each pixel |
| | | |
− | <html>
| + | void startCUDA(int blocks, int threads, int iterations, double centre_x, double centre_y, |
− | <head>
| + | double size, unsigned char* img, int rows, int cols, int step, int image_size) |
− | <script type="text/javascript">
| + | { |
− | /* CUDA Benchmarking Mandelbrot Fractal
| + | if (img!=NULL) |
− | * Anders Kjeldsen
| + | { |
− | * Mercantec
| + | dim3 dimBlock(threads, 1, 1); |
− | * 20. April 2012
| + | dim3 dimGrid(blocks, 1, 1); |
− | *
| + | |
− | * Jeg har kørt en CUDA baseret c++ program der beregner tid på hvor
| + | unsigned char *CUDAimg; |
− | * lang tid det tager, at rendere et 512*512 billede med mandelbrot.
| + | cudaMalloc((void**) &CUDAimg, rows*cols*3); |
− | *
| + | cudaMemcpy(CUDAimg, img, rows*cols*3, cudaMemcpyHostToDevice); |
− | * Parameter til programmet for alle resultater på den her graph er:
| + | Count<<<dimGrid, dimBlock>>>(CUDAimg, rows, cols, step, iterations, centre_x, centre_y, size, image_size); |
− | * Real: 0.064000
| + | cudaMemcpy(img, CUDAimg, rows*cols*3, cudaMemcpyDeviceToHost); |
− | * Imag: 0.647000
| + | cudaFree(CUDAimg); |
− | * Size: 0.500000
| + | } |
− | *
| + | } // Allocate sufficient memory for the whole image (@3 bytes per pixel), |
− | * Serveren der har kørt programmet har:
| + | //transfer it to the graphics card (host to device), start the calculation process and, |
− | * GPU: GeForce GTX 460
| + | //when complete, transfer the memory (containing the calculated values) back to the host |
− | * CPU: Intel(R) Core(TM) i7 CPU 950 @ 3.07GHz
| + | </source> |
− | * Den kører piss' hurti'!
| |
− | */
| |
− |
| |
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− | Pa[a].render(c)}),e&&o(N,function(a,b){if(b%2===0&&a<H)Da[a]||(Da[a]=new c),Y=a,q=N[b+1]!==X?N[b+1]:H,Da[a].options={from:R?cb(Y):Y,to:R?cb(q):q,color:e},Da[a].render(),Da[a].isActive=!0}),!B._addedPlotLB)o((u.plotLines||[]).concat(u.plotBands||[]),function(a){k(a)}),B._addedPlotLB=!0;o([Pa,va,Da],function(a){for(var b in a)a[b].isActive?a[b].isActive=!1:(a[b].destroy(),delete a[b])});f&&(g=x+(y?A:0)+T,i=ra-Lb-(y?hb:0)+T,g=I.crispLine([wa,G?x:g,G?i:E,fa,G?sa-Zb:g,G?i:ra-Lb],f),$?$.animate({d:g}):
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− | u.labels,b=this.labelBBox.width,a=b*{left:0,center:0.5,right:1}[a.align]-a.x;return[-a,b-a]},handleOverflow:function(a){var b=!0,c=this.isFirst,d=this.isLast,e=this.label,f=e.x;if(c||d){var g=this.getLabelSides(),h=g[0],g=g[1],i=m.plotLeft,j=i+B.len,k=(a=Pa[N[a+(c?1:-1)]])&&a.label.x+a.getLabelSides()[c?0:1];c&&!ya||d&&ya?f+h<i&&(f=i-h,a&&f+g>k&&(b=!1)):f+g>j&&(f=j-g,a&&f+h<k&&(b=!1));e.x=f}return b},render:function(a,b){var c=this.type,d=this.label,e=this.pos,f=u.labels,g=this.gridLine,h=c?c+"Grid":
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− | "grid",i=c?c+"Tick":"tick",j=u[h+"LineWidth"],k=u[h+"LineColor"],n=u[h+"LineDashStyle"],m=u[i+"Length"],h=u[i+"Width"]||0,l=u[i+"Color"],Y=u[i+"Position"],i=this.mark,q=f.step,ea=b&&Za||ra,qa=!0,o;o=G?Mb(e+Ia,null,null,b)+bb:x+T+(y?(b&&$a||sa)-Zb-x:0);ea=G?ea-Lb+T-(y?hb:0):ea-Mb(e+Ia,null,null,b)-bb;if(j){e=P(e+Ia,j,b);if(g===X){g={stroke:k,"stroke-width":j};if(n)g.dashstyle=n;if(!c)g.zIndex=1;this.gridLine=g=j?I.path(e).attr(g).add(bc):null}!b&&g&&e&&g.animate({d:e})}if(h)Y==="inside"&&(m=-m),y&&
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− | (m=-m),c=I.crispLine([wa,o,ea,fa,o+(G?0:-m),ea+(G?m:0)],h),i?i.animate({d:c}):this.mark=I.path(c).attr({stroke:l,"stroke-width":h}).add(Q);if(d&&!isNaN(o))o=o+f.x-(Ia&&G?Ia*ia*(ya?-1:1):0),ea=ea+f.y-(Ia&&!G?Ia*ia*(ya?1:-1):0),s(f.y)||(ea+=S(d.styles.lineHeight)*0.9-d.getBBox().height/2),Ra&&(ea+=a/(q||1)%Ra*16),d.x=o,d.y=ea,this.isFirst&&!p(u.showFirstLabel,1)||this.isLast&&!p(u.showLastLabel,1)?qa=!1:!Ra&&G&&f.overflow==="justify"&&!this.handleOverflow(a)&&(qa=!1),q&&a%q&&(qa=!1),qa?(d[this.isNew?
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− | "attr":"animate"]({x:d.x,y:d.y}),d.show(),this.isNew=!1):d.hide()},destroy:function(){Jb(this)}};c.prototype={render:function(){var a=this,b=(B.pointRange||0)/2,c=a.options,d=c.label,e=a.label,f=c.width,g=c.to,h=c.from,i=c.value,j,k=c.dashStyle,n=a.svgElem,m=[],l,Y,u=c.color;Y=c.zIndex;var ea=c.events;R&&(h=nb(h),g=nb(g),i=nb(i));if(f){if(m=P(i,f),b={stroke:u,"stroke-width":f},k)b.dashstyle=k}else if(s(h)&&s(g))h=W(h,F-b),g=Ua(g,H+b),j=P(g),(m=P(h))&&j?m.push(j[4],j[5],j[1],j[2]):m=null,b={fill:u};
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− | else return;if(s(Y))b.zIndex=Y;if(n)m?n.animate({d:m},null,n.onGetPath):(n.hide(),n.onGetPath=function(){n.show()});else if(m&&m.length&&(a.svgElem=n=I.path(m).attr(b).add(),ea))for(l in k=function(b){n.on(b,function(c){ea[b].apply(a,[c])})},ea)k(l);if(d&&s(d.text)&&m&&m.length&&A>0&&hb>0){d=K({align:G&&j&&"center",x:G?!j&&4:10,verticalAlign:!G&&j&&"middle",y:G?j?16:10:j?6:-4,rotation:G&&!j&&90},d);if(!e)a.label=e=I.text(d.text,0,0).attr({align:d.textAlign||d.align,rotation:d.rotation,zIndex:Y}).css(d.style).add();
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− | j=[m[1],m[4],p(m[6],m[1])];m=[m[2],m[5],p(m[7],m[2])];l=Sb(j);Y=Sb(m);e.align(d,!1,{x:l,y:Y,width:Ib(j)-l,height:Ib(m)-Y});e.show()}else e&&e.hide();return a},destroy:function(){Jb(this);Gb(ta,this)}};d.prototype={destroy:function(){Jb(this)},setTotal:function(a){this.cum=this.total=a},render:function(a){var b=this.options.formatter.call(this);this.label?this.label.attr({text:b,visibility:ab}):this.label=m.renderer.text(b,0,0).css(this.options.style).attr({align:this.textAlign,rotation:this.options.rotation,
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− | visibility:ab}).add(a)},setOffset:function(a,b){var c=this.isNegative,d=B.translate(this.total,0,0,0,1),e=B.translate(0),e=Ba(d-e),f=m.xAxis[0].translate(this.x)+a,g=m.plotHeight,c={x:U?c?d:d-e:f,y:U?g-f-b:c?g-d-e:g-d,width:U?e:b,height:U?b:e};this.label&&this.label.align(this.alignOptions,null,c).attr({visibility:eb})}};Mb=function(a,b,c,d,e){var f=1,g=0,h=d?jb:ia,d=d?ma:F,e=u.ordinal||R&&e;h||(h=ia);c&&(f*=-1,g=D);ya&&(f*=-1,g-=f*D);b?(ya&&(a=D-a),a=a/h+d,e&&(a=B.lin2val(a))):(e&&(a=B.val2lin(a)),
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− | a=f*(a-d)*h+g+f*Ka);return a};P=function(a,b,c){var d,e,f,a=Mb(a,null,null,c),g=c&&Za||ra,h=c&&$a||sa,i,c=e=z(a+bb);d=f=z(g-a-bb);if(isNaN(a))i=!0;else if(G){if(d=E,f=g-Lb,c<x||c>x+A)i=!0}else if(c=x,e=h-Zb,d<E||d>E+hb)i=!0;return i?null:I.crispLine([wa,c,d,fa,e,f],b||0)};ib=function(){var a=H-F,b=0,c,d;if(t)da?b=na.pointRange:o(B.series,function(a){b=W(b,a.pointRange);d=a.closestPointRange;!a.noSharedTooltip&&s(d)&&(c=s(c)?Ua(c,d):d)}),B.pointRange=b,B.closestPointRange=c;jb=ia;B.translationSlope=
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− | ia=D/(a+b||1);bb=G?x:Lb;Ka=ia*(b/2)};xa.push(B);m[t?"xAxis":"yAxis"].push(B);U&&t&&ya===X&&(ya=!0);L(B,{addPlotBand:k,addPlotLine:k,adjustTickAmount:function(){if(gb&&gb[w]&&!V&&!Va&&!da&&u.alignTicks!==!1){var a=Fa,b=N.length;Fa=gb[w];if(b<Fa){for(;N.length<Fa;)N.push(Cb(N[N.length-1]+Oa));ia*=(b-1)/(Fa-1);H=N[N.length-1]}if(s(a)&&Fa!==a)B.isDirty=!0}},categories:Va,getExtremes:function(){return{min:R?Cb(cb(F)):F,max:R?Cb(cb(H)):H,dataMin:C,dataMax:M,userMin:ba,userMax:ca}},getPlotLinePath:P,getThreshold:function(a){var b=
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− | R?cb(F):F,c=R?cb(H):H;b>a||a===null?a=b:c<a&&(a=c);return Mb(a,0,1,0,1)},isXAxis:t,options:u,plotLinesAndBands:ta,getOffset:function(){var a=B.series.length&&s(F)&&s(H),c=a||p(u.showEmpty,!0),d=0,e,f=0,g=u.title,h=u.labels,i=[-1,1,1,-1][r],j;Q||(Q=I.g("axis").attr({zIndex:7}).add(),bc=I.g("grid").attr({zIndex:u.gridZIndex||1}).add());La=0;if(a||da)o(N,function(a){Pa[a]?Pa[a].addLabel():Pa[a]=new b(a)}),o(N,function(a){if(r===0||r===2||{1:"left",3:"right"}[r]===h.align)La=W(Pa[a].getLabelSize(),La)}),
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− | Ra&&(La+=(Ra-1)*16);else for(j in Pa)Pa[j].destroy(),delete Pa[j];if(g&&g.text){if(!v)v=B.axisTitle=I.text(g.text,0,0,g.useHTML).attr({zIndex:7,rotation:g.rotation||0,align:g.textAlign||{low:"left",middle:"center",high:"right"}[g.align]}).css(g.style).add(),v.isNew=!0;if(c)d=v.getBBox()[G?"height":"width"],f=p(g.margin,G?5:10),e=g.offset;v[c?"show":"hide"]()}T=i*p(u.offset,pa[r]);Ya=p(e,La+f+(r!==2&&La&&i*u.labels[G?"y":"x"]));pa[r]=W(pa[r],Ya+d+i*T)},render:l,setAxisSize:function(){var a=u.offsetLeft||
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− | 0,b=u.offsetRight||0;x=p(u.left,O+a);E=p(u.top,J);A=p(u.width,ka-a+b);hb=p(u.height,la);Lb=ra-hb-E;Zb=sa-A-x;D=G?A:hb;B.left=x;B.top=E;B.len=D},setAxisTranslation:ib,setCategories:function(b,c){B.categories=a.categories=Va=b;o(B.series,function(a){a.translate();a.setTooltipPoints(!0)});B.isDirty=!0;p(c,!0)&&m.redraw()},setExtremes:function(a,b,c,d,e){c=p(c,!0);e=L(e,{min:a,max:b});aa(B,"setExtremes",e,function(){ba=a;ca=b;B.isDirtyExtremes=!0;c&&m.redraw(d)})},setScale:function(){var a,b,c,d;ma=F;
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− | za=H;ua=D;D=G?A:hb;d=D!==ua;o(B.series,function(a){if(a.isDirtyData||a.isDirty||a.xAxis.isDirty)c=!0});if(d||c||da||ba!==Aa||ca!==Ca){e();j();Aa=ba;Ca=ca;if(!t)for(a in qa)for(b in qa[a])qa[a][b].cum=qa[a][b].total;if(!B.isDirty)B.isDirty=d||F!==ma||H!==za}},setTickPositions:j,translate:Mb,redraw:function(){ub.resetTracker&&ub.resetTracker();l();o(ta,function(a){a.render()});o(B.series,function(a){a.isDirty=!0})},removePlotBand:n,removePlotLine:n,reversed:ya,setTitle:function(a,b){u.title=K(u.title,
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− | a);v=v.destroy();B.isDirty=!0;p(b,!0)&&m.redraw()},series:[],stacks:qa,destroy:function(){var a;Qa(B);for(a in qa)Jb(qa[a]),qa[a]=null;if(B.stackTotalGroup)B.stackTotalGroup=B.stackTotalGroup.destroy();o([Pa,va,Da,ta],function(a){Jb(a)});o([$,Q,bc,v],function(a){a&&a.destroy()});$=Q=bc=v=null}});for(Sa in Z)ha(B,Sa,Z[Sa]);if(R)B.val2lin=nb,B.lin2val=cb}function d(a){function b(){var c=this.points||Hb(this),d=c[0].series,e;e=[d.tooltipHeaderFormatter(c[0].key)];o(c,function(a){d=a.series;e.push(d.tooltipFormatter&&
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− | d.tooltipFormatter(a)||a.point.tooltipFormatter(d.tooltipOptions.pointFormat))});e.push(a.footerFormat||"");return e.join("")}function c(a,b){l=n?a:(2*l+a)/3;q=n?b:(q+b)/2;t.attr({x:l,y:q});lb=Ba(a-l)>1||Ba(b-q)>1?function(){c(a,b)}:null}function d(){if(!n){var a=m.hoverPoints;t.hide();a&&o(a,function(a){a.setState()});m.hoverPoints=null;n=!0}}var e,f=a.borderWidth,g=a.crosshairs,h=[],i=a.style,j=a.shared,k=S(i.padding),n=!0,l=0,q=0;i.padding=0;var t=I.label("",0,0,null,null,null,a.useHTML).attr({padding:k,
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− | fill:a.backgroundColor,"stroke-width":f,r:a.borderRadius,zIndex:8}).css(i).hide().add();Fa||t.shadow(a.shadow);return{shared:j,refresh:function(f){var i,k,l,q,r={},y=[];l=f.tooltipPos;i=a.formatter||b;var r=m.hoverPoints,v;j&&(!f.series||!f.series.noSharedTooltip)?(q=0,r&&o(r,function(a){a.setState()}),m.hoverPoints=f,o(f,function(a){a.setState(ta);q+=a.plotY;y.push(a.getLabelConfig())}),k=f[0].plotX,q=z(q)/f.length,r={x:f[0].category},r.points=y,f=f[0]):r=f.getLabelConfig();r=i.call(r);e=f.series;
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− | k=p(k,f.plotX);q=p(q,f.plotY);i=z(l?l[0]:U?ka-q:k);k=z(l?l[1]:U?la-k:q);l=j||!e.isCartesian||e.tooltipOutsidePlot||Db(i,k);r===!1||!l?d():(n&&(t.show(),n=!1),t.attr({text:r}),v=a.borderColor||f.color||e.color||"#606060",t.attr({stroke:v}),l=uc(t.width,t.height,O,J,ka,la,{x:i,y:k},p(a.distance,12),U),c(z(l.x),z(l.y)));if(g){g=Hb(g);var R;l=g.length;for(var Z;l--;)if(R=f.series[l?"yAxis":"xAxis"],g[l]&&R)if(R=R.getPlotLinePath(l?p(f.stackY,f.y):f.x,1),h[l])h[l].attr({d:R,visibility:eb});else{Z={"stroke-width":g[l].width||
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− | 1,stroke:g[l].color||"#C0C0C0",zIndex:g[l].zIndex||2};if(g[l].dashStyle)Z.dashstyle=g[l].dashStyle;h[l]=I.path(R).attr(Z).add()}}aa(m,"tooltipRefresh",{text:r,x:i+O,y:k+J,borderColor:v})},hide:d,hideCrosshairs:function(){o(h,function(a){a&&a.hide()})},destroy:function(){o(h,function(a){a&&a.destroy()});t&&(t=t.destroy())}}}function e(a){function b(a){var c,d,e,a=a||ca.event;if(!a.target)a.target=a.srcElement;if(a.originalEvent)a=a.originalEvent;if(a.event)a=a.event;c=a.touches?a.touches.item(0):a;
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− | ya=Ac(D);d=ya.left;e=ya.top;Qb?(d=a.x,c=a.y):(d=c.pageX-d,c=c.pageY-e);return L(a,{chartX:z(d),chartY:z(c)})}function c(a){var b={xAxis:[],yAxis:[]};o(xa,function(c){var d=c.translate,e=c.isXAxis;b[e?"xAxis":"yAxis"].push({axis:c,value:d((U?!e:e)?a.chartX-O:la-a.chartY+J,!0)})});return b}function e(){var a=m.hoverSeries,b=m.hoverPoint;if(b)b.onMouseOut();if(a)a.onMouseOut();vb&&(vb.hide(),vb.hideCrosshairs());ob=null}function f(){if(n){var a={xAxis:[],yAxis:[]},b=n.getBBox(),c=b.x-O,d=b.y-J;k&&(o(xa,
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− | b.setState()}).on("click",function(){var a=function(){b.setVisible()};b.firePointEvent?b.firePointEvent("legendItemClick",null,a):aa(b,"legendItemClick",null,a)}).attr({align:r?"left":"right",zIndex:2}).add(A);if(!k&&o&&o.lineWidth){var u={"stroke-width":o.lineWidth,zIndex:2};if(o.dashStyle)u.dashstyle=o.dashStyle;b.legendLine=I.path([wa,(-h-i)*(r?1:-1),0,fa,-i*(r?1:-1),0]).attr(u).add(A)}if(k)j=I.rect(c=-h-i,e=-11,h,12,2).attr({zIndex:3}).add(A),r||(c+=h);else if(o&&o.marker&&o.marker.enabled)j=
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− | -1?a.replace("/>",' style="display:inline-block;behavior:url(#default#VML);" />'):a.replace('style="','style="display:inline-block;behavior:url(#default#VML);')):a=a.replace("<","<hcv:");return a},text:Eb.prototype.html,path:function(a){return this.createElement("shape").attr({coordsize:"100 100",d:a})},circle:function(a,b,c){return this.symbol("circle").attr({x:a-c,y:b-c,width:2*c,height:2*c})},g:function(a){var b;a&&(b={className:Ia+a,"class":Ia+a});return this.createElement(Ra).attr(b)},image:function(a,
| |
− | b,c,d,e){var f=this.createElement("img").attr({src:a});arguments.length>1&&f.css({left:b,top:c,width:d,height:e});return f},rect:function(a,b,c,d,e,f){if(mb(a))b=a.y,c=a.width,d=a.height,f=a.strokeWidth,a=a.x;var g=this.symbol("rect");g.r=e;return g.attr(g.crisp(f,a,b,W(c,0),W(d,0)))},invertChild:function(a,b){var c=b.style;P(a,{flip:"x",left:S(c.width)-10,top:S(c.height)-10,rotation:-90})},symbols:{arc:function(a,b,c,d,e){var f=e.start,g=e.end,c=e.r||c||d,d=ja(f),h=C(f),i=ja(g),k=C(g),e=e.innerR,
| |
− | j=0.08/c,l=e&&0.25/e||0;if(g-f===0)return["x"];else 2*da-g+f<j?i=-j:g-f<l&&(i=ja(f+l));return["wa",a-c,b-c,a+c,b+c,a+c*d,b+c*h,a+c*i,b+c*k,"at",a-e,b-e,a+e,b+e,a+e*i,b+e*k,a+e*d,b+e*h,"x","e"]},circle:function(a,b,c,d){return["wa",a,b,a+c,b+d,a+c,b+d/2,a+c,b+d/2,"e"]},rect:function(a,b,c,d,e){if(!s(e))return[];var f=a+c,g=b+d,c=Ua(e.r||0,c,d);return[wa,a+c,b,fa,f-c,b,"wa",f-2*c,b,f,b+2*c,f-c,b,f,b+c,fa,f,g-c,"wa",f-2*c,g-2*c,f,g,f,g-c,f-c,g,fa,a+c,g,"wa",a,g-2*c,a+2*c,g,a+c,g,a,g-c,fa,a,b+c,"wa",
| |
− | a,b,a+2*c,b+2*c,a,b+c,a+c,b,"x","e"]}}},$a=function(){this.init.apply(this,arguments)},$a.prototype=K(Eb.prototype,w),Xb=$a;var oc,Cc;Fa&&(oc=function(){},Cc=function(){function a(){var a=b.length,d;for(d=0;d<a;d++)b[d]();b=[]}var b=[];return{push:function(c,d){b.length===0&&Hc(d,a);b.push(c)}}}());Xb=$a||oc||Eb;wc.prototype.callbacks=[];var lb=function(){};lb.prototype={init:function(a,b,c){var d=a.chart.counters;this.series=a;this.applyOptions(b,c);this.pointAttr={};if(a.options.colorByPoint){b=
| |
− | a.chart.options.colors;if(!this.options)this.options={};this.color=this.options.color=this.color||b[d.color++];d.wrapColor(b.length)}a.chart.pointCount++;return this},applyOptions:function(a,b){var c=this.series,d=typeof a;this.config=a;if(d==="number"||a===null)this.y=a;else if(typeof a[0]==="number")this.x=a[0],this.y=a[1];else if(d==="object"&&typeof a.length!=="number"){if(L(this,a),this.options=a,a.dataLabels)c._hasPointLabels=!0}else if(typeof a[0]==="string")this.name=a[0],this.y=a[1];if(this.x===
| |
− | X)this.x=b===X?c.autoIncrement():b},destroy:function(){var a=this.series,b=a.chart.hoverPoints,c;a.chart.pointCount--;b&&(this.setState(),Gb(b,this));if(this===a.chart.hoverPoint)this.onMouseOut();a.chart.hoverPoints=null;if(this.graphic||this.dataLabel)Qa(this),this.destroyElements();this.legendItem&&this.series.chart.legend.destroyItem(this);for(c in this)this[c]=null},destroyElements:function(){for(var a="graphic,tracker,dataLabel,group,connector,shadowGroup".split(","),b,c=6;c--;)b=a[c],this[b]&&
| |
− | (this[b]=this[b].destroy())},getLabelConfig:function(){return{x:this.category,y:this.y,key:this.name||this.category,series:this.series,point:this,percentage:this.percentage,total:this.total||this.stackTotal}},select:function(a,b){var c=this,d=c.series.chart,a=p(a,!c.selected);c.firePointEvent(a?"select":"unselect",{accumulate:b},function(){c.selected=a;c.setState(a&&"select");b||o(d.getSelectedPoints(),function(a){if(a.selected&&a!==c)a.selected=!1,a.setState(Ka),a.firePointEvent("unselect")})})},
| |
− | onMouseOver:function(){var a=this.series,b=a.chart,c=b.tooltip,d=b.hoverPoint;if(d&&d!==this)d.onMouseOut();this.firePointEvent("mouseOver");c&&(!c.shared||a.noSharedTooltip)&&c.refresh(this);this.setState(ta);b.hoverPoint=this},onMouseOut:function(){this.firePointEvent("mouseOut");this.setState();this.series.chart.hoverPoint=null},tooltipFormatter:function(a){var b=this.series,c=b.tooltipOptions,d=String(this.y).split("."),d=d[1]?d[1].length:0,e=a.match(/\{(series|point)\.[a-zA-Z]+\}/g),f=/[{\.}]/,
| |
− | g,h,i,k;for(k in e)h=e[k],Ab(h)&&h!==a&&(i=(" "+h).split(f),g={point:this,series:b}[i[1]],i=i[2],g=g===this&&(i==="y"||i==="open"||i==="high"||i==="low"||i==="close")?(c.valuePrefix||c.yPrefix||"")+dc(this[i],p(c.valueDecimals,c.yDecimals,d))+(c.valueSuffix||c.ySuffix||""):g[i],a=a.replace(h,g));return a},update:function(a,b,c){var d=this,e=d.series,f=d.graphic,g,h=e.data,i=h.length,k=e.chart,b=p(b,!0);d.firePointEvent("update",{options:a},function(){d.applyOptions(a);mb(a)&&(e.getAttribs(),f&&f.attr(d.pointAttr[e.state]));
| |
− | for(g=0;g<i;g++)if(h[g]===d){e.xData[g]=d.x;e.yData[g]=d.y;e.options.data[g]=a;break}e.isDirty=!0;e.isDirtyData=!0;b&&k.redraw(c)})},remove:function(a,b){var c=this,d=c.series,e=d.chart,f,g=d.data,h=g.length;Kb(b,e);a=p(a,!0);c.firePointEvent("remove",null,function(){for(f=0;f<h;f++)if(g[f]===c){g.splice(f,1);d.options.data.splice(f,1);d.xData.splice(f,1);d.yData.splice(f,1);break}c.destroy();d.isDirty=!0;d.isDirtyData=!0;a&&e.redraw()})},firePointEvent:function(a,b,c){var d=this,e=this.series.options;
| |
− | (e.point.events[a]||d.options&&d.options.events&&d.options.events[a])&&this.importEvents();a==="click"&&e.allowPointSelect&&(c=function(a){d.select(null,a.ctrlKey||a.metaKey||a.shiftKey)});aa(this,a,b,c)},importEvents:function(){if(!this.hasImportedEvents){var a=K(this.series.options.point,this.options).events,b;this.events=a;for(b in a)ha(this,b,a[b]);this.hasImportedEvents=!0}},setState:function(a){var b=this.plotX,c=this.plotY,d=this.series,e=d.options.states,f=M[d.type].marker&&d.options.marker,
| |
− | g=f&&!f.enabled,h=f&&f.states[a],i=h&&h.enabled===!1,k=d.stateMarkerGraphic,j=d.chart,l=this.pointAttr,a=a||Ka;if(!(a===this.state||this.selected&&a!=="select"||e[a]&&e[a].enabled===!1||a&&(i||g&&!h.enabled))){if(this.graphic)e=f&&this.graphic.symbolName&&l[a].r,this.graphic.attr(K(l[a],e?{x:b-e,y:c-e,width:2*e,height:2*e}:{}));else{if(a){if(!k)e=f.radius,d.stateMarkerGraphic=k=j.renderer.symbol(d.symbol,-e,-e,2*e,2*e).attr(l[a]).add(d.group);k.translate(b,c)}if(k)k[a?"show":"hide"]()}this.state=
| |
− | a}}};var $=function(){};$.prototype={isCartesian:!0,type:"line",pointClass:lb,sorted:!0,pointAttrToOptions:{stroke:"lineColor","stroke-width":"lineWidth",fill:"fillColor",r:"radius"},init:function(a,b){var c,d;d=a.series.length;this.chart=a;this.options=b=this.setOptions(b);this.bindAxes();L(this,{index:d,name:b.name||"Series "+(d+1),state:Ka,pointAttr:{},visible:b.visible!==!1,selected:b.selected===!0});if(Fa)b.animation=!1;d=b.events;for(c in d)ha(this,c,d[c]);if(d&&d.click||b.point&&b.point.events&&
| |
− | b.point.events.click||b.allowPointSelect)a.runTrackerClick=!0;this.getColor();this.getSymbol();this.setData(b.data,!1)},bindAxes:function(){var a=this,b=a.options,c=a.chart,d;a.isCartesian&&o(["xAxis","yAxis"],function(e){o(c[e],function(c){d=c.options;if(b[e]===d.index||b[e]===X&&d.index===0)c.series.push(a),a[e]=c,c.isDirty=!0})})},autoIncrement:function(){var a=this.options,b=this.xIncrement,b=p(b,a.pointStart,0);this.pointInterval=p(this.pointInterval,a.pointInterval,1);this.xIncrement=b+this.pointInterval;
| |
− | return b},getSegments:function(){var a=-1,b=[],c,d=this.points,e=d.length;if(e)if(this.options.connectNulls){for(c=e;c--;)d[c].y===null&&d.splice(c,1);d.length&&(b=[d])}else o(d,function(c,g){c.y===null?(g>a+1&&b.push(d.slice(a+1,g)),a=g):g===e-1&&b.push(d.slice(a+1,g+1))});this.segments=b},setOptions:function(a){var b=this.chart.options,c=b.plotOptions,d=a.data;a.data=null;c=K(c[this.type],c.series,a);c.data=a.data=d;this.tooltipOptions=K(b.tooltip,c.tooltip);return c},getColor:function(){var a=
| |
− | this.chart.options.colors,b=this.chart.counters;this.color=this.options.color||a[b.color++]||"#0000ff";b.wrapColor(a.length)},getSymbol:function(){var a=this.options.marker,b=this.chart,c=b.options.symbols,b=b.counters;this.symbol=a.symbol||c[b.symbol++];if(/^url/.test(this.symbol))a.radius=0;b.wrapSymbol(c.length)},addPoint:function(a,b,c,d){var e=this.data,f=this.graph,g=this.area,h=this.chart,i=this.xData,k=this.yData,j=f&&f.shift||0,l=this.options.data;Kb(d,h);if(f&&c)f.shift=j+1;if(g){if(c)g.shift=
| |
− | j+1;g.isArea=!0}b=p(b,!0);d={series:this};this.pointClass.prototype.applyOptions.apply(d,[a]);i.push(d.x);k.push(this.valueCount===4?[d.open,d.high,d.low,d.close]:d.y);l.push(a);c&&(e[0]?e[0].remove(!1):(e.shift(),i.shift(),k.shift(),l.shift()));this.getAttribs();this.isDirtyData=this.isDirty=!0;b&&h.redraw()},setData:function(a,b){var c=this.points,d=this.options,e=this.initialColor,f=this.chart,g=null;this.xIncrement=null;this.pointRange=this.xAxis&&this.xAxis.categories&&1||d.pointRange;if(s(e))f.counters.color=
| |
− | e;var h=[],i=[],k=a?a.length:[],j=this.valueCount===4;if(k>(d.turboThreshold||1E3)){for(e=0;g===null&&e<k;)g=a[e],e++;if(Bb(g)){g=p(d.pointStart,0);d=p(d.pointInterval,1);for(e=0;e<k;e++)h[e]=g,i[e]=a[e],g+=d;this.xIncrement=g}else if(Fb(g))if(j)for(e=0;e<k;e++)d=a[e],h[e]=d[0],i[e]=d.slice(1,5);else for(e=0;e<k;e++)d=a[e],h[e]=d[0],i[e]=d[1]}else for(e=0;e<k;e++)d={series:this},this.pointClass.prototype.applyOptions.apply(d,[a[e]]),h[e]=d.x,i[e]=j?[d.open,d.high,d.low,d.close]:d.y;this.data=[];this.options.data=
| |
− | a;this.xData=h;this.yData=i;for(e=c&&c.length||0;e--;)c[e]&&c[e].destroy&&c[e].destroy();this.isDirty=this.isDirtyData=f.isDirtyBox=!0;p(b,!0)&&f.redraw(!1)},remove:function(a,b){var c=this,d=c.chart,a=p(a,!0);if(!c.isRemoving)c.isRemoving=!0,aa(c,"remove",null,function(){c.destroy();d.isDirtyLegend=d.isDirtyBox=!0;a&&d.redraw(b)});c.isRemoving=!1},processData:function(a){var b=this.xData,c=this.yData,d=b.length,e=0,f=d,g,h,i=this.xAxis,k=this.options,j=k.cropThreshold,l=this.isCartesian;if(l&&!this.isDirty&&
| |
− | !i.isDirty&&!this.yAxis.isDirty&&!a)return!1;if(l&&this.sorted&&(!j||d>j||this.forceCrop))if(a=i.getExtremes(),i=a.min,j=a.max,b[d-1]<i||b[0]>j)b=[],c=[];else if(b[0]<i||b[d-1]>j){for(a=0;a<d;a++)if(b[a]>=i){e=W(0,a-1);break}for(;a<d;a++)if(b[a]>j){f=a+1;break}b=b.slice(e,f);c=c.slice(e,f);g=!0}for(a=b.length-1;a>0;a--)if(d=b[a]-b[a-1],d>0&&(h===X||d<h))h=d;this.cropped=g;this.cropStart=e;this.processedXData=b;this.processedYData=c;if(k.pointRange===null)this.pointRange=h||1;this.closestPointRange=
| |
− | h},generatePoints:function(){var a=this.options.data,b=this.data,c,d=this.processedXData,e=this.processedYData,f=this.pointClass,g=d.length,h=this.cropStart||0,i,k=this.hasGroupedData,j,l=[],n;if(!b&&!k)b=[],b.length=a.length,b=this.data=b;for(n=0;n<g;n++)i=h+n,k?l[n]=(new f).init(this,[d[n]].concat(Hb(e[n]))):(b[i]?j=b[i]:b[i]=j=(new f).init(this,a[i],d[n]),l[n]=j);if(b&&(g!==(c=b.length)||k))for(n=0;n<c;n++)n===h&&!k&&(n+=g),b[n]&&b[n].destroyElements();this.data=b;this.points=l},translate:function(){this.processedXData||
| |
− | this.processData();this.generatePoints();for(var a=this.chart,b=this.options,c=b.stacking,d=this.xAxis,e=d.categories,f=this.yAxis,g=this.points,h=g.length,i=!!this.modifyValue,k,j=f.series,l=j.length;l--;)if(j[l].visible){l===this.index&&(k=!0);break}for(l=0;l<h;l++){var j=g[l],n=j.x,o=j.y,r=j.low,p=f.stacks[(o<b.threshold?"-":"")+this.stackKey];j.plotX=z(d.translate(n,0,0,0,1)*10)/10;if(c&&this.visible&&p&&p[n]){r=p[n];n=r.total;r.cum=r=r.cum-o;o=r+o;if(k)r=b.threshold;c==="percent"&&(r=n?r*100/
| |
− | n:0,o=n?o*100/n:0);j.percentage=n?j.y*100/n:0;j.stackTotal=n;j.stackY=o}j.yBottom=s(r)?f.translate(r,0,1,0,1):null;i&&(o=this.modifyValue(o,j));j.plotY=typeof o==="number"?z(f.translate(o,0,1,0,1)*10)/10:X;j.clientX=a.inverted?a.plotHeight-j.plotX:j.plotX;j.category=e&&e[j.x]!==X?e[j.x]:j.x}this.getSegments()},setTooltipPoints:function(a){var b=this.chart,c=b.inverted,d=[],b=z((c?b.plotTop:b.plotLeft)+b.plotSizeX),e,f;e=this.xAxis;var g,h,i=[];if(this.options.enableMouseTracking!==!1){if(a)this.tooltipPoints=
| |
− | null;o(this.segments||this.points,function(a){d=d.concat(a)});e&&e.reversed&&(d=d.reverse());a=d.length;for(h=0;h<a;h++){g=d[h];e=d[h-1]?d[h-1]._high+1:0;for(f=g._high=d[h+1]?Ta((g.plotX+(d[h+1]?d[h+1].plotX:b))/2):b;e<=f;)i[c?b-e++:e++]=g}this.tooltipPoints=i}},tooltipHeaderFormatter:function(a){var b=this.tooltipOptions,c=b.xDateFormat||"%A, %b %e, %Y",d=this.xAxis;return b.headerFormat.replace("{point.key}",d&&d.options.type==="datetime"?ac(c,a):a).replace("{series.name}",this.name).replace("{series.color}",
| |
− | this.color)},onMouseOver:function(){var a=this.chart,b=a.hoverSeries;if(Ga||!a.mouseIsDown){if(b&&b!==this)b.onMouseOut();this.options.events.mouseOver&&aa(this,"mouseOver");this.setState(ta);a.hoverSeries=this}},onMouseOut:function(){var a=this.options,b=this.chart,c=b.tooltip,d=b.hoverPoint;if(d)d.onMouseOut();this&&a.events.mouseOut&&aa(this,"mouseOut");c&&!a.stickyTracking&&!c.shared&&c.hide();this.setState();b.hoverSeries=null},animate:function(a){var b=this.chart,c=this.clipRect,d=this.options.animation;
| |
− | d&&!mb(d)&&(d={});if(a){if(!c.isAnimating)c.attr("width",0),c.isAnimating=!0}else c.animate({width:b.plotSizeX},d),this.animate=null},drawPoints:function(){var a,b=this.points,c=this.chart,d,e,f,g,h,i,k,j;if(this.options.marker.enabled)for(f=b.length;f--;)if(g=b[f],d=g.plotX,e=g.plotY,j=g.graphic,e!==X&&!isNaN(e))if(a=g.pointAttr[g.selected?"select":Ka],h=a.r,i=p(g.marker&&g.marker.symbol,this.symbol),k=i.indexOf("url")===0,j)j.animate(L({x:d-h,y:e-h},j.symbolName?{width:2*h,height:2*h}:{}));else if(h>
| |
− | 0||k)g.graphic=c.renderer.symbol(i,d-h,e-h,2*h,2*h).attr(a).add(this.group)},convertAttribs:function(a,b,c,d){var e=this.pointAttrToOptions,f,g,h={},a=a||{},b=b||{},c=c||{},d=d||{};for(f in e)g=e[f],h[f]=p(a[g],b[f],c[f],d[f]);return h},getAttribs:function(){var a=this,b=M[a.type].marker?a.options.marker:a.options,c=b.states,d=c[ta],e,f=a.color,g={stroke:f,fill:f},h=a.points,i=[],k,j=a.pointAttrToOptions,l;a.options.marker?(d.radius=d.radius||b.radius+2,d.lineWidth=d.lineWidth||b.lineWidth+1):d.color=
| |
− | d.color||ma(d.color||f).brighten(d.brightness).get();i[Ka]=a.convertAttribs(b,g);o([ta,"select"],function(b){i[b]=a.convertAttribs(c[b],i[Ka])});a.pointAttr=i;for(f=h.length;f--;){g=h[f];if((b=g.options&&g.options.marker||g.options)&&b.enabled===!1)b.radius=0;e=!1;if(g.options)for(l in j)s(b[j[l]])&&(e=!0);if(e){k=[];c=b.states||{};e=c[ta]=c[ta]||{};if(!a.options.marker)e.color=ma(e.color||g.options.color).brighten(e.brightness||d.brightness).get();k[Ka]=a.convertAttribs(b,i[Ka]);k[ta]=a.convertAttribs(c[ta],
| |
− | i[ta],k[Ka]);k.select=a.convertAttribs(c.select,i.select,k[Ka])}else k=i;g.pointAttr=k}},destroy:function(){var a=this,b=a.chart,c=a.clipRect,d=/AppleWebKit\/533/.test(kb),e,f,g=a.data||[],h,i,k;aa(a,"destroy");Qa(a);o(["xAxis","yAxis"],function(b){if(k=a[b])Gb(k.series,a),k.isDirty=!0});a.legendItem&&a.chart.legend.destroyItem(a);for(f=g.length;f--;)(h=g[f])&&h.destroy&&h.destroy();a.points=null;if(c&&c!==b.clipRect)a.clipRect=c.destroy();o(["area","graph","dataLabelsGroup","group","tracker"],function(b){a[b]&&
| |
− | (e=d&&b==="group"?"hide":"destroy",a[b][e]())});if(b.hoverSeries===a)b.hoverSeries=null;Gb(b.series,a);for(i in a)delete a[i]},drawDataLabels:function(){var a=this,b=a.options,c=b.dataLabels;if(c.enabled||a._hasPointLabels){var d,e,f=a.points,g,h,i,k=a.dataLabelsGroup,j=a.chart,l=a.xAxis,l=l?l.left:j.plotLeft,n=a.yAxis,n=n?n.top:j.plotTop,t=j.renderer,r=j.inverted,Z=a.type,V=b.stacking,v=Z==="column"||Z==="bar",y=c.verticalAlign===null,q=c.y===null,T=t.fontMetrics(c.style.fontSize),A=T.h,x=T.b,w,
| |
− | ia;v&&(T={top:x,middle:x-A/2,bottom:-A+x},V?(y&&(c=K(c,{verticalAlign:"middle"})),q&&(c=K(c,{y:T[c.verticalAlign]}))):y?c=K(c,{verticalAlign:"top"}):q&&(c=K(c,{y:T[c.verticalAlign]})));k?k.translate(l,n):k=a.dataLabelsGroup=t.g("data-labels").attr({visibility:a.visible?eb:ab,zIndex:6}).translate(l,n).add();h=c;o(f,function(f){w=f.dataLabel;c=h;(g=f.options)&&g.dataLabels&&(c=K(c,g.dataLabels));if(ia=c.enabled){var l=f.barX&&f.barX+f.barW/2||p(f.plotX,-999),n=p(f.plotY,-999),o=c.y===null?f.y>=b.threshold?
| |
− | -A+x:x:c.y;d=(r?j.plotWidth-n:l)+c.x;e=z((r?j.plotHeight-l:n)+o)}if(w&&a.isCartesian&&(!j.isInsidePlot(d,e)||!ia))f.dataLabel=w.destroy();else if(ia){l=c.align;i=c.formatter.call(f.getLabelConfig(),c);Z==="column"&&(d+={left:-1,right:1}[l]*f.barW/2||0);!V&&r&&f.y<0&&(l="right",d-=10);c.style.color=p(c.color,c.style.color,a.color,"black");if(w)w.attr({text:i}).animate({x:d,y:e});else if(s(i))w=f.dataLabel=t[c.rotation?"text":"label"](i,d,e,null,null,null,c.useHTML,!0).attr({align:l,fill:c.backgroundColor,
| |
− | stroke:c.borderColor,"stroke-width":c.borderWidth,r:c.borderRadius,rotation:c.rotation,padding:c.padding,zIndex:1}).css(c.style).add(k).shadow(c.shadow);if(v&&b.stacking&&w)l=f.barX,n=f.barY,o=f.barW,f=f.barH,w.align(c,null,{x:r?j.plotWidth-n-f:l,y:r?j.plotHeight-l-o:n,width:r?f:o,height:r?o:f})}})}},drawGraph:function(){var a=this,b=a.options,c=a.graph,d=[],e,f=a.area,g=a.group,h=b.lineColor||a.color,i=b.lineWidth,k=b.dashStyle,j,l=a.chart.renderer,n=a.yAxis.getThreshold(b.threshold),t=/^area/.test(a.type),
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− | r=[],s=[];o(a.segments,function(c){j=[];o(c,function(d,e){a.getPointSpline?j.push.apply(j,a.getPointSpline(c,d,e)):(j.push(e?fa:wa),e&&b.step&&j.push(d.plotX,c[e-1].plotY),j.push(d.plotX,d.plotY))});c.length>1?d=d.concat(j):r.push(c[0]);if(t){var e=[],f,g=j.length;for(f=0;f<g;f++)e.push(j[f]);g===3&&e.push(fa,j[1],j[2]);if(b.stacking&&a.type!=="areaspline")for(f=c.length-1;f>=0;f--)f<c.length-1&&b.step&&e.push(c[f+1].plotX,c[f].yBottom),e.push(c[f].plotX,c[f].yBottom);else e.push(fa,c[c.length-1].plotX,
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− | n,fa,c[0].plotX,n);s=s.concat(e)}});a.graphPath=d;a.singlePoints=r;if(t)e=p(b.fillColor,ma(a.color).setOpacity(b.fillOpacity||0.75).get()),f?f.animate({d:s}):a.area=a.chart.renderer.path(s).attr({fill:e}).add(g);if(c)Ob(c),c.animate({d:d});else if(i){c={stroke:h,"stroke-width":i};if(k)c.dashstyle=k;a.graph=l.path(d).attr(c).add(g).shadow(b.shadow)}},invertGroups:function(){function a(){var a={width:b.yAxis.len,height:b.xAxis.len};c.attr(a).invert();d&&d.attr(a).invert()}var b=this,c=b.group,d=b.trackerGroup,
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− | e=b.chart;ha(e,"resize",a);ha(b,"destroy",function(){Qa(e,"resize",a)});a();b.invertGroups=a},render:function(){var a=this,b=a.chart,c,d=a.options,e=d.clip!==!1,f=d.animation,g=f&&a.animate,f=g?f&&f.duration||500:0,h=a.clipRect,i=b.renderer;if(!h&&(h=a.clipRect=!b.hasRendered&&b.clipRect?b.clipRect:i.clipRect(0,0,b.plotSizeX,b.plotSizeY+1),!b.clipRect))b.clipRect=h;if(!a.group)c=a.group=i.g("series"),c.attr({visibility:a.visible?eb:ab,zIndex:d.zIndex}).translate(a.xAxis.left,a.yAxis.top).add(b.seriesGroup);
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− | a.drawDataLabels();g&&a.animate(!0);a.getAttribs();a.drawGraph&&a.drawGraph();a.drawPoints();a.options.enableMouseTracking!==!1&&a.drawTracker();b.inverted&&a.invertGroups();e&&!a.hasRendered&&(c.clip(h),a.trackerGroup&&a.trackerGroup.clip(b.clipRect));g&&a.animate();setTimeout(function(){h.isAnimating=!1;if((c=a.group)&&h!==b.clipRect&&h.renderer){if(e)c.clip(a.clipRect=b.clipRect);h.destroy()}},f);a.isDirty=a.isDirtyData=!1;a.hasRendered=!0},redraw:function(){var a=this.chart,b=this.isDirtyData,
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− | c=this.group;c&&(a.inverted&&c.attr({width:a.plotWidth,height:a.plotHeight}),c.animate({translateX:this.xAxis.left,translateY:this.yAxis.top}));this.translate();this.setTooltipPoints(!0);this.render();b&&aa(this,"updatedData")},setState:function(a){var b=this.options,c=this.graph,d=b.states,b=b.lineWidth,a=a||Ka;if(this.state!==a)this.state=a,d[a]&&d[a].enabled===!1||(a&&(b=d[a].lineWidth||b+1),c&&!c.dashstyle&&c.attr({"stroke-width":b},a?0:500))},setVisible:function(a,b){var c=this.chart,d=this.legendItem,
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− | e=this.group,f=this.tracker,g=this.dataLabelsGroup,h,i=this.points,k=c.options.chart.ignoreHiddenSeries;h=this.visible;h=(this.visible=a=a===X?!h:a)?"show":"hide";if(e)e[h]();if(f)f[h]();else if(i)for(e=i.length;e--;)if(f=i[e],f.tracker)f.tracker[h]();if(g)g[h]();d&&c.legend.colorizeItem(this,a);this.isDirty=!0;this.options.stacking&&o(c.series,function(a){if(a.options.stacking&&a.visible)a.isDirty=!0});if(k)c.isDirtyBox=!0;b!==!1&&c.redraw();aa(this,h)},show:function(){this.setVisible(!0)},hide:function(){this.setVisible(!1)},
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− | select:function(a){this.selected=a=a===X?!this.selected:a;if(this.checkbox)this.checkbox.checked=a;aa(this,a?"select":"unselect")},drawTrackerGroup:function(){var a=this.trackerGroup,b=this.chart;if(this.isCartesian){if(!a)this.trackerGroup=a=b.renderer.g().attr({zIndex:this.options.zIndex||1}).add(b.trackerGroup);a.translate(this.xAxis.left,this.yAxis.top)}return a},drawTracker:function(){var a=this,b=a.options,c=[].concat(a.graphPath),d=c.length,e=a.chart,f=e.renderer,g=e.options.tooltip.snap,h=
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− | a.tracker,i=b.cursor,i=i&&{cursor:i},k=a.singlePoints,j=a.drawTrackerGroup(),l;if(d)for(l=d+1;l--;)c[l]===wa&&c.splice(l+1,0,c[l+1]-g,c[l+2],fa),(l&&c[l]===wa||l===d)&&c.splice(l,0,fa,c[l-2]+g,c[l-1]);for(l=0;l<k.length;l++)d=k[l],c.push(wa,d.plotX-g,d.plotY,fa,d.plotX+g,d.plotY);h?h.attr({d:c}):a.tracker=f.path(c).attr({isTracker:!0,stroke:Gc,fill:Ma,"stroke-linejoin":"bevel","stroke-width":b.lineWidth+2*g,visibility:a.visible?eb:ab}).on(Ga?"touchstart":"mouseover",function(){if(e.hoverSeries!==
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− | a)a.onMouseOver()}).on("mouseout",function(){if(!b.stickyTracking)a.onMouseOut()}).css(i).add(j)}};w=pa($);Ha.line=w;w=pa($,{type:"area"});Ha.area=w;w=pa($,{type:"spline",getPointSpline:function(a,b,c){var d=b.plotX,e=b.plotY,f=a[c-1],g=a[c+1],h,i,k,j;if(c&&c<a.length-1){a=f.plotY;k=g.plotX;var g=g.plotY,l;h=(1.5*d+f.plotX)/2.5;i=(1.5*e+a)/2.5;k=(1.5*d+k)/2.5;j=(1.5*e+g)/2.5;l=(j-i)*(k-d)/(k-h)+e-j;i+=l;j+=l;i>a&&i>e?(i=W(a,e),j=2*e-i):i<a&&i<e&&(i=Ua(a,e),j=2*e-i);j>g&&j>e?(j=W(g,e),i=2*e-j):j<g&&
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− | j<e&&(j=Ua(g,e),i=2*e-j);b.rightContX=k;b.rightContY=j}c?(b=["C",f.rightContX||f.plotX,f.rightContY||f.plotY,h||d,i||e,d,e],f.rightContX=f.rightContY=null):b=[wa,d,e];return b}});Ha.spline=w;w=pa(w,{type:"areaspline"});Ha.areaspline=w;var zb=pa($,{type:"column",tooltipOutsidePlot:!0,pointAttrToOptions:{stroke:"borderColor","stroke-width":"borderWidth",fill:"color",r:"borderRadius"},init:function(){$.prototype.init.apply(this,arguments);var a=this,b=a.chart;b.hasRendered&&o(b.series,function(b){if(b.type===
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− | a.type)b.isDirty=!0})},translate:function(){var a=this,b=a.chart,c=a.options,d=c.stacking,e=c.borderWidth,f=0,g=a.xAxis,h=g.reversed,i={},k,j;$.prototype.translate.apply(a);o(b.series,function(b){if(b.type===a.type&&b.visible&&a.options.group===b.options.group)b.options.stacking?(k=b.stackKey,i[k]===X&&(i[k]=f++),j=i[k]):j=f++,b.columnIndex=j});var b=a.points,g=Ba(g.translationSlope)*(g.ordinalSlope||g.closestPointRange||1),l=g*c.groupPadding,n=(g-2*l)/f,t=c.pointWidth,r=s(t)?(n-t)/2:n*c.pointPadding,
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− | w=Yb(W(p(t,n-2*r),1+2*e)),x=r+(l+((h?f-a.columnIndex:a.columnIndex)||0)*n-g/2)*(h?-1:1),v=a.yAxis.getThreshold(c.threshold),y=p(c.minPointLength,5);o(b,function(b){var f=b.plotY,g=p(b.yBottom,v),h=b.plotX+x,i=Yb(Ua(f,g)),j=Yb(W(f,g)-i),k=a.yAxis.stacks[(b.y<0?"-":"")+a.stackKey];d&&a.visible&&k&&k[b.x]&&k[b.x].setOffset(x,w);Ba(j)<y&&y&&(j=y,i=Ba(i-v)>y?g-y:v-(f<=v?y:0));L(b,{barX:h,barY:i,barW:w,barH:j});b.shapeType="rect";f={x:h,y:i,width:w,height:j,r:c.borderRadius,strokeWidth:e};e%2&&(f.y-=1,
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− | f.height+=1);b.shapeArgs=f;b.trackerArgs=Ba(j)<3&&K(b.shapeArgs,{height:6,y:i-3})})},getSymbol:function(){},drawGraph:function(){},drawPoints:function(){var a=this,b=a.options,c=a.chart.renderer,d,e;o(a.points,function(f){var g=f.plotY;if(g!==X&&!isNaN(g)&&f.y!==null)d=f.graphic,e=f.shapeArgs,d?(Ob(d),d.animate(c.Element.prototype.crisp.apply({},[e.strokeWidth,e.x,e.y,e.width,e.height]))):f.graphic=d=c[f.shapeType](e).attr(f.pointAttr[f.selected?"select":Ka]).add(a.group).shadow(b.shadow)})},drawTracker:function(){var a=
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− | this,b=a.chart,c=b.renderer,d,e,f=+new Date,g=a.options,h=g.cursor,i=h&&{cursor:h},k=a.drawTrackerGroup(),j;o(a.points,function(h){e=h.tracker;d=h.trackerArgs||h.shapeArgs;delete d.strokeWidth;if(h.y!==null)e?e.attr(d):h.tracker=c[h.shapeType](d).attr({isTracker:f,fill:Gc,visibility:a.visible?eb:ab}).on(Ga?"touchstart":"mouseover",function(c){j=c.relatedTarget||c.fromElement;if(b.hoverSeries!==a&&A(j,"isTracker")!==f)a.onMouseOver();h.onMouseOver()}).on("mouseout",function(b){if(!g.stickyTracking&&
| |
− | (j=b.relatedTarget||b.toElement,A(j,"isTracker")!==f))a.onMouseOut()}).css(i).add(h.group||k)})},animate:function(a){var b=this,c=b.points,d=b.options;if(!a)o(c,function(a){var c=a.graphic,a=a.shapeArgs,g=b.yAxis,h=d.threshold;c&&(c.attr({height:0,y:s(h)?g.getThreshold(h):g.translate(g.getExtremes().min,0,1,0,1)}),c.animate({height:a.height,y:a.y},d.animation))}),b.animate=null},remove:function(){var a=this,b=a.chart;b.hasRendered&&o(b.series,function(b){if(b.type===a.type)b.isDirty=!0});$.prototype.remove.apply(a,
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− | arguments)}});Ha.column=zb;w=pa(zb,{type:"bar",init:function(){this.inverted=!0;zb.prototype.init.apply(this,arguments)}});Ha.bar=w;w=pa($,{type:"scatter",sorted:!1,translate:function(){var a=this;$.prototype.translate.apply(a);o(a.points,function(b){b.shapeType="circle";b.shapeArgs={x:b.plotX,y:b.plotY,r:a.chart.options.tooltip.snap}})},drawTracker:function(){for(var a=this,b=a.options.cursor,b=b&&{cursor:b},c=a.points,d=c.length,e;d--;)if(e=c[d].graphic)e.element._i=d;a._hasTracking?a._hasTracking=
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− | !0:a.group.attr({isTracker:!0}).on(Ga?"touchstart":"mouseover",function(b){a.onMouseOver();if(b.target._i!==X)c[b.target._i].onMouseOver()}).on("mouseout",function(){if(!a.options.stickyTracking)a.onMouseOut()}).css(b)}});Ha.scatter=w;w=pa(lb,{init:function(){lb.prototype.init.apply(this,arguments);var a=this,b;L(a,{visible:a.visible!==!1,name:p(a.name,"Slice")});b=function(){a.slice()};ha(a,"select",b);ha(a,"unselect",b);return a},setVisible:function(a){var b=this.series.chart,c=this.tracker,d=this.dataLabel,
| |
− | e=this.connector,f=this.shadowGroup,g;g=(this.visible=a=a===X?!this.visible:a)?"show":"hide";this.group[g]();if(c)c[g]();if(d)d[g]();if(e)e[g]();if(f)f[g]();this.legendItem&&b.legend.colorizeItem(this,a)},slice:function(a,b,c){var d=this.series.chart,e=this.slicedTranslation;Kb(c,d);p(b,!0);a=this.sliced=s(a)?a:!this.sliced;a={translateX:a?e[0]:d.plotLeft,translateY:a?e[1]:d.plotTop};this.group.animate(a);this.shadowGroup&&this.shadowGroup.animate(a)}});w=pa($,{type:"pie",isCartesian:!1,pointClass:w,
| |
− | pointAttrToOptions:{stroke:"borderColor","stroke-width":"borderWidth",fill:"color"},getColor:function(){this.initialColor=this.chart.counters.color},animate:function(){var a=this;o(a.points,function(b){var c=b.graphic,b=b.shapeArgs,d=-da/2;c&&(c.attr({r:0,start:d,end:d}),c.animate({r:b.r,start:b.start,end:b.end},a.options.animation))});a.animate=null},setData:function(){$.prototype.setData.apply(this,arguments);this.processData();this.generatePoints()},translate:function(){this.generatePoints();var a=
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− | 0,b=-0.25,c=this.options,d=c.slicedOffset,e=d+c.borderWidth,f=c.center.concat([c.size,c.innerSize||0]),g=this.chart,h=g.plotWidth,i=g.plotHeight,k,j,l,n=this.points,p=2*da,r,s=Ua(h,i),w,v,y,q=c.dataLabels.distance,f=Vb(f,function(a,b){return(w=/%$/.test(a))?[h,i,s,s][b]*S(a)/100:a});this.getX=function(a,b){l=oa.asin((a-f[1])/(f[2]/2+q));return f[0]+(b?-1:1)*ja(l)*(f[2]/2+q)};this.center=f;o(n,function(b){a+=b.y});o(n,function(c){r=a?c.y/a:0;k=z(b*p*1E3)/1E3;b+=r;j=z(b*p*1E3)/1E3;c.shapeType="arc";
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− | c.shapeArgs={x:f[0],y:f[1],r:f[2]/2,innerR:f[3]/2,start:k,end:j};l=(j+k)/2;c.slicedTranslation=Vb([ja(l)*d+g.plotLeft,C(l)*d+g.plotTop],z);v=ja(l)*f[2]/2;y=C(l)*f[2]/2;c.tooltipPos=[f[0]+v*0.7,f[1]+y*0.7];c.labelPos=[f[0]+v+ja(l)*q,f[1]+y+C(l)*q,f[0]+v+ja(l)*e,f[1]+y+C(l)*e,f[0]+v,f[1]+y,q<0?"center":l<p/4?"left":"right",l];c.percentage=r*100;c.total=a});this.setTooltipPoints()},render:function(){this.getAttribs();this.drawPoints();this.options.enableMouseTracking!==!1&&this.drawTracker();this.drawDataLabels();
| |
− | this.options.animation&&this.animate&&this.animate();this.isDirty=!1},drawPoints:function(){var a=this.chart,b=a.renderer,c,d,e,f=this.options.shadow,g,h;o(this.points,function(i){d=i.graphic;h=i.shapeArgs;e=i.group;g=i.shadowGroup;if(f&&!g)g=i.shadowGroup=b.g("shadow").attr({zIndex:4}).add();if(!e)e=i.group=b.g("point").attr({zIndex:5}).add();c=i.sliced?i.slicedTranslation:[a.plotLeft,a.plotTop];e.translate(c[0],c[1]);g&&g.translate(c[0],c[1]);d?d.animate(h):i.graphic=b.arc(h).attr(L(i.pointAttr[Ka],
| |
− | {"stroke-linejoin":"round"})).add(i.group).shadow(f,g);i.visible===!1&&i.setVisible(!1)})},drawDataLabels:function(){var a=this.data,b,c=this.chart,d=this.options.dataLabels,e=p(d.connectorPadding,10),f=p(d.connectorWidth,1),g,h,i=p(d.softConnector,!0),k=d.distance,j=this.center,l=j[2]/2,j=j[1],n=k>0,t=[[],[]],r,s,w,v,y=2,q;if(d.enabled){$.prototype.drawDataLabels.apply(this);o(a,function(a){a.dataLabel&&t[a.labelPos[7]<da/2?0:1].push(a)});t[1].reverse();v=function(a,b){return b.y-a.y};for(a=t[0][0]&&
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− | t[0][0].dataLabel&&t[0][0].dataLabel.getBBox().height;y--;){var x=[],A=[],z=t[y],E=z.length,C;for(q=j-l-k;q<=j+l+k;q+=a)x.push(q);w=x.length;if(E>w){h=[].concat(z);h.sort(v);for(q=E;q--;)h[q].rank=q;for(q=E;q--;)z[q].rank>=w&&z.splice(q,1);E=z.length}for(q=0;q<E;q++){b=z[q];h=b.labelPos;b=9999;for(s=0;s<w;s++)g=Ba(x[s]-h[1]),g<b&&(b=g,C=s);if(C<q&&x[q]!==null)C=q;else for(w<E-q+C&&x[q]!==null&&(C=w-E+q);x[C]===null;)C++;A.push({i:C,y:x[C]});x[C]=null}A.sort(v);for(q=0;q<E;q++){b=z[q];h=b.labelPos;
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− | g=b.dataLabel;s=A.pop();r=h[1];w=b.visible===!1?ab:eb;C=s.i;s=s.y;if(r>s&&x[C+1]!==null||r<s&&x[C-1]!==null)s=r;r=this.getX(C===0||C===x.length-1?r:s,y);g.attr({visibility:w,align:h[6]})[g.moved?"animate":"attr"]({x:r+d.x+({left:e,right:-e}[h[6]]||0),y:s+d.y});g.moved=!0;if(n&&f)g=b.connector,h=i?[wa,r+(h[6]==="left"?5:-5),s,"C",r,s,2*h[2]-h[4],2*h[3]-h[5],h[2],h[3],fa,h[4],h[5]]:[wa,r+(h[6]==="left"?5:-5),s,fa,h[2],h[3],fa,h[4],h[5]],g?(g.animate({d:h}),g.attr("visibility",w)):b.connector=g=this.chart.renderer.path(h).attr({"stroke-width":f,
| |
− | stroke:d.connectorColor||b.color||"#606060",visibility:w,zIndex:3}).translate(c.plotLeft,c.plotTop).add()}}}},drawTracker:zb.prototype.drawTracker,getSymbol:function(){}});Ha.pie=w;L(Highcharts,{Chart:wc,dateFormat:ac,pathAnim:La,getOptions:function(){return Ea},hasBidiBug:Qc,numberFormat:dc,Point:lb,Color:ma,Renderer:Xb,SVGRenderer:Eb,VMLRenderer:$a,CanVGRenderer:oc,seriesTypes:Ha,setOptions:function(a){$b=K($b,a.xAxis);kc=K(kc,a.yAxis);a.xAxis=a.yAxis=X;Ea=K(Ea,a);vc();return Ea},Series:$,addEvent:ha,
| |
− | removeEvent:Qa,createElement:Aa,discardElement:Tb,css:P,each:o,extend:L,map:Vb,merge:K,pick:p,splat:Hb,extendClass:pa,placeBox:uc,product:"Highcharts",version:"2.2.1"})})();
| |
− | (function(){function x(a){for(var b=a.length;b--;)typeof a[b]==="number"&&(a[b]=Math.round(a[b])-0.5);return a}var f=Highcharts,y=f.Chart,z=f.addEvent,B=f.removeEvent,r=f.createElement,u=f.discardElement,t=f.css,s=f.merge,k=f.each,n=f.extend,C=Math.max,h=document,D=window,A=h.documentElement.ontouchstart!==void 0,v=f.getOptions();n(v.lang,{downloadPNG:"Download PNG image",downloadJPEG:"Download JPEG image",downloadPDF:"Download PDF document",downloadSVG:"Download SVG vector image",exportButtonTitle:"Export to raster or vector image",
| |
− | printButtonTitle:"Print the chart"});v.navigation={menuStyle:{border:"1px solid #A0A0A0",background:"#FFFFFF"},menuItemStyle:{padding:"0 5px",background:"none",color:"#303030",fontSize:A?"14px":"11px"},menuItemHoverStyle:{background:"#4572A5",color:"#FFFFFF"},buttonOptions:{align:"right",backgroundColor:{linearGradient:[0,0,0,20],stops:[[0.4,"#F7F7F7"],[0.6,"#E3E3E3"]]},borderColor:"#B0B0B0",borderRadius:3,borderWidth:1,height:20,hoverBorderColor:"#909090",hoverSymbolFill:"#81A7CF",hoverSymbolStroke:"#4572A5",
| |
− | symbolFill:"#E0E0E0",symbolStroke:"#A0A0A0",symbolX:11.5,symbolY:10.5,verticalAlign:"top",width:24,y:10}};v.exporting={type:"image/png",url:"http://export.highcharts.com/",width:800,buttons:{exportButton:{symbol:"exportIcon",x:-10,symbolFill:"#A8BF77",hoverSymbolFill:"#768F3E",_id:"exportButton",_titleKey:"exportButtonTitle",menuItems:[{textKey:"downloadPNG",onclick:function(){this.exportChart()}},{textKey:"downloadJPEG",onclick:function(){this.exportChart({type:"image/jpeg"})}},{textKey:"downloadPDF",
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| =Slides= | | =Slides= |
{{#img: image=Super-computer-artw.jpg | page=Linux Cluster til Center of Excelence/Beskrivelse til CoE West | width=200px | title=Linux Supercomputer projekt }}
Having investigated CUDA C programming for Nvidia graphics cards and the CUDA architecture, we made some performance measurements using a range of numbers of blocks and threads, executing in parallel. The test program calculated values of the Mandelbrot Set on a pixel-by-pixel basis. The Mandelbrot Set was a good choice for this test beacuse:
The results of the benchmarking are here, as an interactive chart (hover your mouse to find out which values are represented by each line, drag to zoom and hide/reveal curves relating to the number of blocks in the legend beneath):
For the reasons given above, the Mandelbrot Set was also a good candidate for testing Message Passing Interface - MPI programming capabilities and strategies. To support graphical output, the final program used a "Master" process which collected calculated values from "Worker" processes and set them together in an X Window. This was a good illustration of the idea that some processes, like Input-Output, have to be run in a serial manner and that perfect parallelization is rarely achievable in practice c.f. Amdahl's Law