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Introduction to Java Programming and Data Structures, 11E, Y. Daniel Liang

The java. Math class contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

Introduction Java Math class provides several methods to work on math calculations like minmaxavgsincostanroundceilfloorabs. In this article, we will learn about the Java Math class, its basic methods and constructors provided by Java programming language.

Ch 7 maths class 10 java class in Java The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

Unlike some of the numeric methods of class StrictMath, all implementations of the equivalent functions of class Math are not defined to return the bit-for-bit ch 7 maths class 10 java same results.

This relaxation permits better-performing implementations where strict reproducibility is not required. By default, many of the Math methods simply call the equivalent method in StrictMath for their implementation.

Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of Math methods. Such higher-performance implementations still must conform to the specification for Math.

If the size is int or long and the results overflow the range of value, the methods addExactsubtractExactmultiplyExactand toIntExact throw an ArithmeticException. For other arithmetic operations like increment, decrement, divide, absolute value, and negation overflow occur only with a specific minimum or maximum value.

It should be checked against the maximum and minimum value as appropriate. Math class declaration Following is ch 7 maths class 10 java declaration for ch 7 maths class 10 java. Math class public clss class Math extends Object The complete example program of java.

Math class is listed. What is NaN value in Math class? NaN stands for not a number. Nan is produced if a floating-point operation has some input parameters that cause the operation to produce some undefined result. For example, 0. Finding out the square root of a negative number 77 is undefined.

The complete program of NaN value. How to compare NaN values? All numeric operations with NaN as an operand produce NaN math a result. The reason behind this is that NaN is unordered, so a numeric comparison operation involving one or two NaNs returns false.

The inequality operator! The complete program of comparing the NaN values. NaN ; System. Math class methods in Java The java. Math class contains various methods for performing basic numeric operations such as the ch 7 maths class 10 java, cube root, and trigonometric functions. The various java math naths are as follows: 1 Math. This method gives the absolute value of the argument. The argument can be int, double, long and float.

If the argument is positive zero or negative zero, the result is positive zero. If the argument is infinite, the result is positive infinity. If the argument is NaN, the result is NaN. Ch 7 maths class 10 java public static int abs int i public static double abs double d public static float abs float f public static long abs long lng The complete program of java. If the argument is NaN or its absolute value is greater than 1, then the result is NaN.

The results must be semi-monotonic. Syntax public static double acos double a The complete chh of java. If the argument is zero, then the result is a zero with the same sign as the argument.

Syntax javs static double asin double a The complete program of java. Math class usually takes radians as an input which is very much different in real-life applications since angles are usually represented in degrees. Syntax public static double toRadians double deg The complete program of java. The arguments are taken in int, float, double and long.

If clsss provide positive and negative value as an argument, this method will return a positive argument. If we provide both negative values as an argument, the number with the lower magnitude is returned as a result. If the arguments are not clasw number NaN ch 7 maths class 10 java, this method will return NaN.

Syntax public static int max int a, int b public static double max double a, double b public static long max long a, long b public static float max float a, float b The complete program of java. The arguments are taken in int, float, double and long If we provide positive and negative value as an argument, this method will return a negative argument.

If we provide both negative values as an matsh, the number with a higher magnitude is returned as a result. Syntax public static int min int a, int b public static double min double a, double b public static long min long a, long b public static float min float a, float b The complete program of java.

If both first argument and second argument are same then this method will return the second argument. If either argument is a NaN, this method will return NaN. If both arguments are signed zeros, the direction will be unchanged. If start argument a is equal to positive or negative Double. The complete program of java. This method is semantically equivalent to nextAfter d, Double.

If the argument clasd positive infinity, the result is positive infinity. If the argument is zero, the result is Double. It returns the floating-point value adjacent to the user-specified parameter d in the direction of negative infinity.

This method is equivalent to nextAfter d, Double. If the argument is NaN, this method will return NaN. If the argument is Zero and we are dealing with ch 7 maths class 10 java, this method will return Double.

If the argument is Zero and we are dealing with float, this method will return Float. Syntax public static double nextDown double a public static float nextDown float a Ch 7 maths class 10 java complete program of java. The return type of the pow method is double. If the second argument is positive or negative zero, this method will return 1. If the second argument is not a number NaNthis method will return NaN.

If the second argument is 1, this method will return the result the same as the first argument. The default random number always generated between 0 and 1. Returned values are chosen pseudorandomly with approximately uniform javz from that range. When this method is first called, ch 7 maths class 10 java creates a single new pseudorandom-number generator, exactly as if by the expression new java. Note: If you want to a specific range of values, you have to multiply the returned value with the magnitude of the range.

For example, if you want to get a random number between 0 to 20, the resultant address has to be multiplied by 20 to get the desired result. Syntax public static jaths random The complete program of java.

This method is used to return the closest long to the argument, with ties rounding to positive infinity. If the argument is NaN, mathx result is 0. If the argument is negative infinity or any ch 7 maths class 10 java less than or equal to the value of Long.

If the argument is positive infinity or any value greater than or equal to the value of Long. Syntax public static long round double a The complete program of java. Otherwise, the result is the double value closest to the true mathematical square root of the argument value.

If the argument is NaN or less than zero, then the result is NaN. If the argument is positive infinity, then the result is positive infinity. If the argument is positive zero or negative zero, then the result is the same as the argument. Syntax public static double sqrt double x The complete program of java. Mava method returns the natural logarithm base e of a double value as a parameter. If the argument is positive zero or negative zero, then the result is negative infinity.

Syntax public static double log double a The complete program of java. This method returns the base 10 logarithms of a double value. If the argument is Positive value, this method will return the logarithm of a given value.

If the argument is equal to 10n for integer n, this method will return n. If the argument is a Negative value, this method will return NaN. Syntax public static double log10 double a The complete java. This method returns a value between -1 to 1. If the argument is NaN or an infinity, then the result is NaN.

Syntax public static double sin double a The complete program of java. The computed result must be within 1 ulp of the exact result. An ulp of a float or double value is the positive distance between given value and the next value that is larger in magnitude.

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This generator is very fast and has very good random proprieties a very long period of 10 Any other value will be used as a constant. The following basic random distributions are provided: Rndm or Uniform min,max , Gaus mean,sigma , Exp tau , BreitWigner mean,sigma , Landau mean,sigma , Poisson mean , Binomial ntot,prob. You can customize your ROOT session by replacing the random number generator. You can delete gRandom and recreate it with your own.

TRandom2 is another generator, which is also very fast and uses only three words for its state. This variable is set by reading the contents of a.

See Environment Setup below for more information. The behavior of a ROOT session can be tailored with the options in the.

At start-up, ROOT looks for a. If more than one. While in a session, to see current settings, you can do:. For example, if the flag to use true type fonts is set to true in the system.

Removing the UseTTFonts statement in the local. ROOT looks for scripts in the path specified in the. Path variable. You can expand this path to hold your own directories. The rootlogon. C and rootlogoff. C files are scripts loaded and executed at start-up and shutdown. The rootalias. C file is loaded but not executed. It typically contains small utility functions. For example, the rootalias. This allows the user to call the editor from the command line.

You can use the up and down arrow at the command line, to access the previous and next command. It is a text file, and you can edit, cut, and paste from it. You can specify the history file in the system. History option. You can also turn off the command logging in the system. History: -. The first value defines the maximum of lines kept; once it is reached all, the last HistSave lines will be removed.

One can set HistSize to 0 to disable history line management. You can track memory usage and detect leaks by monitoring the number of objects that are created and deleted see TObjectTable. This line will print the list of all active classes and the number of instances for each class.

By comparing consecutive print outs, you can see objects that you forgot to delete. Note that this method cannot show leaks coming from the allocation of non-objects or classes unknown to ROOT. A memory checking system was developed by D. Bertini and M. Ivanov and added in ROOT version 3. To activate the memory checker you can set the resource Root. MemCheck to 1 e. MemCheck: 1 in the.

You also have to link with libNew. You can also set the resource Root. MemCheckFile to the name of a file. The memory information will be written to that file. The contents of this memcheck. To use this program, you type the shell script command:. If you do not specify the second parameter, a file name is automatically generated for you. If hbookfile is of the form file.

Some HBOOK column-wise ntuples may not be fully converted if the columns are an array of fixed dimension e. In case of row-wise or column-wise ntuples, each column is converted to a branch of a tree. Once you have converted your file, you can look at it and draw histograms or process ntuples using the ROOT command line. An example of session is shown below:. The chapter on trees explains how to read a tree. In case one of the ntuple columns has a variable length e.

Draw "px" will histogram the px column for all tracks in the same histogram. This chapter covers the functionality of the histogram classes.

We begin with an overview of the histogram classes, after which we provide instructions and examples on the histogram features. We have put this chapter ahead of the graphics chapter so that you can begin working with histograms as soon as possible. Some of the examples have graphics commands that may look unfamiliar to you. ROOT supports histograms up to three dimensions. Separate concrete classes are provided for one-dimensional, two-dimensional and three-dimensional classes.

The histogram classes are split into further categories, depending on the set of possible bin values:. ROOT also supports profile histograms, which constitute an elegant replacement of two-dimensional histograms in many cases.

The inter-relation of two measured quantities X and Y can always be visualized with a two-dimensional histogram or scatter-plot. Profile histograms, on the other hand, are used to display the mean value of Y and its RMS for each bin in X. If Y is an unknown but single-valued approximate function of X, it will have greater precision in a profile histogram than in a scatter plot. This means that two-dimensional and three-dimensional histograms are seen as a type of a one-dimensional histogram, in the same way in which multidimensional C arrays are just an abstraction of a one-dimensional contiguous block of memory.

There are several ways in which you can create a histogram object in ROOT. The straightforward method is to use one of the several constructors provided for each concrete class in the histogram hierarchy. Histograms may also be created by:. The histogram classes provide a variety of ways to construct a histogram, but the most common way is to provide the name and title of histogram and for each dimension: the number of bins, the minimum x lower edge of the first bin and the maximum x upper edge of the last bin.

When employing this constructor, you will create a histogram with constant fixed bin width on each axis. For the example above, the interval [0. If you want to create histograms with variable bin widths, ROOT provides another constructor suited for this purpose. Instead of passing the data interval and the number of bins, you have to pass an array single or double precision of bin edges.

Each histogram object contains three TAxis objects: fXaxis , fYaxis, and fZaxis , but for one-dimensional histograms only the X-axis is relevant, while for two-dimensional histograms the X-axis and Y-axis are relevant. See the class TAxis for a description of all the access methods. The bin edges are always stored internally in double precision.

All histogram types support fixed or variable bin sizes. The functions to fill, manipulate, draw, or access histograms are identical in both cases.

At any time, a histogram can be re-binned via the TH1 ::Rebin method. It returns a new histogram with the re-binned contents. If bin errors were stored, they are recomputed during the re-binning. The Fill method computes the bin number corresponding to the given x, y or z argument and increments this bin by the given weight. The Fill method returns the bin number for 1-D histograms or global bin number for 2-D and 3-D histograms.

If TH1 ::Sumw2 has been called before filling, the sum of squares is also stored. By default, the number of bins is computed using the range of the axis. You can change this to re-bin automatically by setting the automatic re-binning option:. Once this is set, the Fill method will automatically extend the axis range to accommodate the new value specified in the Fill argument.

The used method is to double the bin size until the new value fits in the range, merging bins two by two. The TTree ::Draw method extensively uses this automatic binning option when drawing histograms of variables in TTree Byjus Class 4 Maths Question Paper Java with an unknown range. The automatic binning option is supported for 1-D, 2-D and 3-D histograms. During filling, some statistics parameters are incremented to compute the mean value and root mean square with the maximum precision.

TH1 ::FillRandom can be used to randomly fill a histogram using the contents of an existing TF1 function or another TH1 histogram for all dimensions. For example, the following two statements create and fill a histogram 10 times with a default Gaussian distribution of mean 0 and sigma 1 :.

TH1 ::GetRandom can be used to get a random number distributed according the contents of a histogram. To fill a histogram following the distribution in an existing histogram you can use the second signature of TH1 ::FillRandom. Next code snipped assumes that h is an existing histogram TH1. The distribution contained in the histogram h1 TH1 is integrated over the channel contents. It is normalized to one. The second parameter indicates how many random numbers are generated.

You can see below an example of the TH1 ::GetRandom method which can be used to get a random number distributed according the contents of a histogram. The Add , Divide and Multiply methods also exist to add, divide or multiply a histogram by a function.

Histograms objects not pointers TH1F h1 can be multiplied by a constant using:. If a histogram has associated error bars TH1 ::Sumw2 has been called , the resulting error bars are also computed assuming independent histograms.

In case of divisions, binomial errors are also supported. When you call the Draw method of a histogram TH1 ::Draw for the first time, it creates a THistPainter object and saves a pointer to painter as a data member of the histogram. The THistPainter class specializes in the drawing of histograms. It allows logarithmic axes x, y, z when the CONT drawing option is using. The THistPainter class is separated from the histogram so that one can have histograms without the graphics overhead, for example in a batch program.

When a displayed histogram is filled again, you do not have to call the Draw method again. The image is refreshed the next time the pad is updated. A pad is updated after one of these three actions:. By default, the TH1 ::Draw clears the pad before drawing the new image of the histogram. You can use the "SAME" option to leave the previous display intact and superimpose the new histogram. The same histogram can be drawn with different graphics options in different pads.

When a displayed histogram is deleted, its image is automatically removed from the pad. To create a copy of the histogram when drawing it, you can use TH1 ::DrawClone. This will clone the histogram and allow you to change and delete the original one without affecting the clone. You can use TH1 ::DrawNormalized to draw a normalized copy of a histogram. A clone of this histogram is normalized to norm and drawn with option.

A pointer to the normalized histogram is returned. The contents of the histogram copy are scaled such that the new sum of weights excluding under and overflow is equal to norm.

Note that the returned normalized histogram is not added to the list of histograms in the current directory in memory.

The kCanDelete bit is set for the returned object. If a pad containing this copy is cleared, the histogram will be automatically deleted.

Histograms use the current style gStyle , which is the global object of class TStyle. To change the current style for histograms, the TStyle class provides a multitude of methods ranging from setting the fill color to the axis tick marks. Here are a few examples:. When you change the current style and would like to propagate the change to a previously created histogram you can call TH1 ::UseCurrentStyle.

You will need to call UseCurrentStyle on each histogram. When reading many histograms from a file and you wish to update them to the current style, you can use gROOT ::ForceStyle and all histograms read after this call will be updated to use the current style. When a histogram is automatically created as a result of a TTree ::Draw , the style of the histogram is inherited from the tree attributes and the current style is ignored.

The tree attributes are the ones set in the current TStyle at the time the tree was created. To visualize it without errors use HIST together with the required option e. By default, the histogram is drawn in low resolution in case the number of bins is greater than the number of pixels in the current pad.

Use it when superposing many histograms on the same picture. Most options can be concatenated without spaces or commas, for example, if h is a histogram pointer:. The options are not case sensitive. You can also set the default drawing option with TH1 ::SetOption. To see the current option use TH1 ::GetOption. By default, 2D histograms are drawn as scatter plots. For each cell i,j a number of points proportional to the cell content are drawn.

A maximum of points per cell are drawn. If the maximum is above contents are normalized to The ARR option shows the gradient between adjacent cells. For each cell i,j an arrow is drawn. The orientation of the arrow follows the cell gradient. For each cell i,j a box is drawn with surface proportional to contents. The size of the box is proportional to the absolute value of the cell contents.

The cells with negative contents are drawn with an X on top of the boxes. A sunken button is drawn for negative values, a raised one for positive values. Note that for all options, the line and fill attributes of the histogram are used for the errors or errors contours.

The parameter dx is a percentage of bin width for errors along X. For each cell i,j a box is drawn with a color proportional to the cell content. The color table used is defined in the current style gStyle. The default number of contour levels is 20 equidistant levels. It can be changed with TH1 ::SetContour. For one given contour, more than one disjoint poly-line may be generated.

Here we show how to access the first graph in the list. The tutorial macro earth. C uses these four options and produces the following picture:. In a lego plot, the cell contents are drawn as 3D boxes, with the height of the box proportional to the cell content. A lego plot can be represented in several coordinate systems; the default system is Cartesian coordinates.

With TStyle ::SetPalette the color palette can be changed. We suggest you use palette 1 with the call:. In a surface plot, cell contents are represented as a mesh. The height of the mesh is proportional to the cell content. A surface plot can be represented in several coordinate systems. The following picture uses SURF1. If there is not enough space on the right side, you can increase the size of the right margin by calling TPad ::SetRightMargin.

The attributes used to display the palette axis values are taken from the Z axis of the object. For example, you can set the labels size on the palette axis with:. You can set the color palette with TStyle ::SetPalette , e. For example, the option COL draws a 2-D histogram with cells represented by a box filled with a color index, which is a function of the cell content. If the cell content is N, the color index used will be the color number in colors1324.

If the maximum cell content is greater than ncolors , all cell contents are scaled to ncolors. This palette is recommended for pads, labels. It defines:. The color numbers specified in this palette can be viewed by selecting the menu entry Colors in the View menu of the canvas menu bar. A TPaletteAxis object is used to display the color palette when drawing 2D histograms. It is added to the histogram list of functions.

It can be retrieved and its attributes can be changed with:. The palette can be interactively moved and resized. The context menu can be used to set the axis attributes. For example, to draw the 2-D histogram h2 using all default attributes except the viewing angles, one can do:.

Operators can be put in any order in the option and must be separated by a space " ". No space characters should be put in an operator. All the available operators are described below. The following tables summarize all the possible combinations of both groups:.

Next example sets line color to 2, line type to 1 and line width to 2. Note that if pa is not specified, the histogram line attributes are used:. Sometimes the displayed region is rather large. When displaying all channels the pictures become very dense and complicated. It is very difficult to understand the overall shape of data. Only the channels coinciding with given nodes are displayed.

Allowed values are 0, 90, and degrees. Note that the X and Y axis are always linear. For sophisticated shading Light, Height and LightHeight Display Modes Groups the color palette starts from the basic pen color see pa function.

There is a predefined number of color levels Color in every level is calculated by adding the increments of the r , g , b components to the previous level.

Using this function one can change the color increments between two neighboring color levels. The function does not apply on the Simple Display Modes Group. The default values are: 1,1,1. When the level of a component reaches the limit value one can choose either smooth transition by decreasing the limit value or a sharp modulo transition continuing with 0 value.

This allows various visual effects. One can choose from the following set of the algorithms:. This function does not apply on Simple display modes group. Default value is 0. In Light and LightHeight display modes groups the color palette is calculated according to the fictive light source position in 3-d space. This function does not apply for Simple and Height display modes groups.

Default is: lp ,, The surface picture is composed of triangles. The edges of the neighboring triangles can be smoothed shaded. The shadow can be painted as well. The function does not apply on Simple display modes group. The possible values for shading are:. The function does not apply on other display modes groups and display modes.

Default value is: b 0. This function applies only on for the Contours display mode. One can change the width between horizontal slices and thus their density. Default value: cw For LightHeight display modes group one can change the weight between both shading algorithms. The function does not apply on other display modes groups. Default value is lhw 0.

In addition to the surface drawn using any above given algorithm one can display channel marks. One can control the color as well as the width, height in pixels and the style of the marks. The possible styles are:. In addition to the surface drawn using any above given algorithm one can display grid using the color parameter.

The parameter enable can be set to:. By default a 3D scatter plot is drawn. Using a TCutG object, it is possible to draw a 2D histogram sub-range.

Up to 16 cuts may be specified in the cut string delimited by "[.. Currently only the following drawing options are sensitive to the cuts option: col , box , scat , hist , lego , surf and cartesian coordinates only.

The following script creates two histograms; the second histogram is the bins integral of the first one. It shows a procedure to draw the two histograms in the same pad and it draws the scale of the second histogram using a new vertical axis on the right side.

By default, a histogram drawing includes the statistics box. The parameter option can contain:. With the option "same" , the statistic box is not redrawn. With the option "sames" , it is re-drawn. If it hides the previous statistics box, you can change its position with the next lines where h is the histogram pointer :.

See the description of these classes for the list of options. The TPad ::SetTicks method specifies the type of tick marks on the axis.

Use TPad ::SetTicks tx,ty to set these options. See also the methods of TAxis that set specific axis attributes. If multiple color-filled histograms are drawn on the same pad, the fill area may hide the axis tick marks. One can force the axis redrawing over all the histograms by calling:. Because the axis title is an attribute of the axis, you have to get the axis first and then call TAxis ::SetTitle.

The histogram title and the axis titles can be any TLatex string. The titles are part of the persistent histogram. For example if you wanted to write E with a subscript T you could use this:. It is also possible to specify the histogram title and the axis titles at creation time. This makes an identical copy of the original histogram including all associated errors and functions:.

The following statements create a ROOT file and store a histogram on the file. Because TH1 derives from TNamed , the key identifier on the file is the histogram name:. The parameter option is a character string that specifies:. Bin the KS distances in a histogram, and then take the integral of all the KS values above the value obtained from the original data to Monte Carlo distribution. The function returns the integral. TH1 ::Smooth - smoothes the bin contents of a 1D histogram.

TH1 ::GetMean int axis - returns the mean value along axis. TH1 ::GetStdDev int axis - returns the sigma distribution along axis. Then h3 is created and filled with the asymmetry between h1 and h2 ; h1 and h2 are left intact. TH1 ::Reset - resets the bin contents and errors of a histogram. By default, histogram statistics are computed at fill time using the unbinned data used to update the bin content.

See the documentation on THGetStats. This is useful if you want to keep track of the mean and standard deviation of the dataset you are visualizing with the histogram, but it can lead to some unintuitive results. For example, suppose you have a histogram with one bin between 0 and , then you fill it with a Gaussian dataset with mean 20 and standard deviation Next, zoom in on the Gaussian:.

What happened? Well, GetMean and GetStdDev and many other TH1 functions return the statistics for bins in range Ncert Book Solution For Class 10th Maths Java ; this is because the histogram only stores the contents of its bins, not the coordinates of the values used to fill it. This remains true even if you zoom out:. To mark the X axis as having no range, you can call.

If you want ROOT to consistently return the statistics of the binned dataset stored in the histogram and not those of the dataset used to fill it, you can call THResetStats. This will delete the statistics originally calculated at fill time and replace them with those calculated from the bins; note that you cannot later retrieve the original statistics�they are lost.

Continuing the example above,. If you fill the histogram again, the statistics will be a mix of binned and unbinned:. By default, a histogram axis is drawn with its numeric bin labels. One can specify alphanumeric labels instead. This can always be done before or after filling. Bin labels will be automatically drawn with the histogram. You change that and draw the value of char[0] as an integer by adding an arithmetic operation to the expression as shown below.

When using the options 2 or 3 above, the labels are automatically added to the list THashList of labels for a given axis. By default, an axis is drawn with the order of bins corresponding to the filling sequence. It is possible to reorder the axis alphabetically or by increasing or decreasing values.

When using the option second above, new labels are added by doubling the current number of bins in case one label does not exist yet. When the filling is terminated, it is possible to trim the number of bins to match the number of active labels by calling:.

Here axis may be X, Y, or Z. This operation is automatic when using TTree ::Draw. The THStack does not own the objects in the list.

By default, THStack ::Draw draws the histograms stacked as shown in the left pad in the picture above. If the option "nostack" is used, the histograms are superimposed as if they were drawn one at a time using the "same" draw option. The right pad in this picture illustrates the THStack drawn with the "nostack" option. TH2Poly is a 2D Histogram class allowing to define polygonal bins of arbitrary shape.

TH2PolyBin is a very simple class containing the vertices and contents of the polygonal bin as well as several related functions. Bins are defined using one of the AddBin methods. The bin definition should be done before filling. Profile histograms are in many cases an elegant replacement of two-dimensional histograms. The relationship of two quantities X and Y can be visualized by a two-dimensional histogram or a scatter-plot; its representation is not particularly satisfactory, except for sparse data.

If Y is an unknown [but single-valued] function of X, it can be displayed by a profile histogram with much better precision than by a scatter-plot. The following shows the contents [capital letters] and the values shown in the graphics [small letters] of the elements for bin j.

When you fill a profile histogram with TProfile. Fill x,y :. In the special case where s[j] is zero, when there is only one entry per bin, e[j] is computed from the average of the s[j] for all bins.

This approximation is used to keep the bin during a fit operation. The TProfile constructor takes up to eight arguments. The first five parameters are similar to TH1D constructor. All values of y are accepted at filling time. To fill a profile histogram, you must use TProfile ::Fill function.

Note that when filling the profile histogram the method TProfile ::Fill checks if the variable y is between fYmin and fYmax. If a minimum or maximum value is set for the Y scale before filling, then all values below ylow or above yup will be discarded. Setting the minimum or maximum value for the Y scale before filling has the same effect as calling the special TProfile constructor above where ylow and yup are specified.

The last parameter is the build option. If a bin has N data points all with the same value Y, which is the case when dealing with integers, the spread in Y for that bin is zero, and the uncertainty assigned is also zero, and the bin is ignored in making subsequent fits. That it is only in the case where the Y variable is some sort of counting statistics, following a Poisson distribution.

This is the default case. An example is an ADC measurement. The next figure shows the graphic output of this simple example of a profile histogram. This will draw the outline of the TProfile. To create a regular histogram from a profile histogram, use the method TProfile ::ProjectionX. The 'prof' and 'profs' options in the TTree ::Draw method generate a profile histogram TProfile , given a two dimensional expression in the tree, or a TProfile2D given a three dimensional expression.

Note that you can specify 'prof' or 'profs' : 'prof' generates a TProfile with error on the mean, 'profs' generates a TProfile with error on the spread. It is in many cases an elegant replacement of a three-dimensional histogram. The relationship of three measured quantities X, Y and Z can be visualized by a three-dimensional histogram or scatter-plot; its representation is not particularly satisfactory, except for sparse data. If Z is an unknown but single-valued function of X,Y , it can be displayed with a TProfile2D with better precision than by a scatter-plot.

The following shows the cumulated contents capital letters and the values displayed small letters of the elements for cell i,j. When you fill a profile histogram with TProfile2D. Fill x,y,z :. In the special case where s[i,j] is zero, when there is only one entry per cell, e[i,j] is computed from the average of the s[i,j] for all cells.

This approximation is used to keep the cell during a fit operation. The TPie class allows to create a Pie Chart representation of a one dimensional data set. A statement that the information in the notice is accurate, and under penalty of perjury, that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

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The answer has to discuss how such a trend impacts general public opinion, especially of the younger generation. Question 5 Class 10th Hindi Kritika Chapter 2.

The question is about the efforts by the sculptor for reinstating the nose. Some of the measures included procuring the stone to repair the nose. As no information could be found from government files, the sculptor himself travelled to a hilly state to inspect different quarries. These solutions have been drafted to follow the examination format, making it easy for the student to get used to the question frame.

The language that has been used in this solution is easy to understand so as to help students remember better. Answers to these questions provided here are to the point and ensure to unravel the meaning hidden in each sentence.

Byjus Maths Class 9 Question Paper Analysis Used Boat Motor Qualification