Lecture 12

[Music] [Music] hello friends welcome to the course foundations of r software and you may recall that in the last couple of lectures so we have learnt the different aspects of calculations and computation in the r software we have learnt about how to do the calculation with the scalars with data vectors and with built in functions now continuing on the same line another ah very important part of calculation is matrix you know what is the matrix and the rules for matrix operations they are different than the usual mathematical operations so the next question before us is how to handle the matrix in the r software and then how to do various types of calculations and computation related to the matrix well this matrix is very important because when you are going to use the r software for various applications in statistics and other areas many times the input data has to be there in the format of matrix the output data is also many times in the format of metrics so how to understand it how to read it and how you can extract a particular part of the matrix it can be an element it can be a row vector it can be a column vector or it can be a sub matrix then after that there are many operations like as transpose inverse for finding out eigen values etcetera which are very popular when you are trying to use the statistics and other sciences where you want to do the calculations so now in this lecture and in the next couple of lectures my target is that i would like to discuss about the matrices so in this lecture i will try to give you a basic idea that how you can define the matrix inside the r software and then in the forthcoming lectures i will try to take some common popular operations which are related to matrices so let us begin our lecture and try to understand first that how we can handle the matrix in the r software ok so the matrix theory you know that ah matrix theory plays a very important role in doing modeling and other type of things and in r also matrices are important objects in any calculation the first question comes here what is the matrix i believe that you all have a reasonable background in the matrix theory but just for the sake of a quick revision means i can tell you a matrix is a rectangular array in which the values are arranged in rows and columns for example if i say that there is a matrix which has got p rows n n columns right so this looks like this i mean there are rows here one two up two here three rows and then there are here columns one two etcetera and columns and the data is like arranged like 1 2 3 4 5 6 and so on that you know now the values inside this matrix they are the elements of this matrix and an element in the ith row and the g column is denoted by say x i j like this x and the subscript i j ah well that is the notation when we try to do this matrix algebra on the blackboard in the book but when we try to write it down in the say program version means how to write it in the software then a popular notation is like this one x and inside the square brackets you try to write here i n j or i and j they are going to be some values for example i can be any values the value between 1 to n and j can be any value between 1 to p now you can see here that for the first time i am now showing you what is the application of this square bracket and you can recall that at some point of time i had shown you that when we are trying to do the mathematical calculation then we have this type of simple brackets then curly brackets and then say square brackets and these brackets have got some important role in the r software so now this is first place where i can show you that this square bracket has a different role than the mathematical operations so now in case if you try to understand the matrix in a broader way then the element of a matrix can be an object for example a string also but in mathematics we are mostly interested in the matrices which have got some numerical values and whose values are some real numbers right so the first question comes here how can you create a matrix in the r software so we know that whenever we want to create a matrix there are three ingredients which are needed we want to know the total number of rows then total number of columns in the matrix and then we want to know what is the data that has to be arranged in this number of rows and columns and after that many question comes whether you want to arrange the data row wise column wise etcetera so you will try to seek answers for all those questions so the first thing i would like to discuss here that how to create the matrix so in the r software matrix is the command to create a matrix which is m a t r i x and all are given in the lower case alphabets and after that within the parenthesis you have to indicate the basic information that how the matrix has to be created you want to inform the total number of required rows columns and the data so in order to inform the metric that how many rows are going to be there we have a command here n row n r o w and in case if you write n row equal to for example force so this will indicate that there are four rows in the matrix similarly in order to know the number of columns in the matrix we have the command here n c o l and call which means number of columns so if you write here n call is equal to two this will indicate that there are going to be two columns in the matrix now when you have four rows and two columns then you need to have four into two is equal to eight data values which are to be arranged inside the matrix in rows and columns and you know any particular element in the matrix has an address and that address is indicated by the row and column for example i can say the element in the second row and third column so in order to give the input data inside the matrix we have our command here d a t a data and now after this ah you have to write data is equal to but after that you have couple of options that you can give the data in the form of a sequence or individual values or in continuation etcetera but anyway at this moment we have not done many things in the r software so i would try to keep it here very simple and i try to take here 8 values 1 2 3 4 5 6 7 8 and i use the format of data vector so these values are going to be arranged in 4 rows and 2 columns so in case if i try to assign this command in a variable here x and if you try to execute on the r console then x will look like this so you can see here this is indicating the first row let's say r1 then second row i say r2 third row say r3 and fourth row sar4 and these are the columns so this is suppose here column one and this is here column 2. so now you can see here there are 8 positions here where the data has to be placed so now all these values which are given in the data vector they will be placed inside this matrix in these eight values so you can see here how these values are going to be placed the first value if you try to see the data is in this order one two eight so the first value comes here then the second value then the third value then the fourth value and after this the control goes to the first row in the second column so first four values are inserted in the first column in four rows now after this the fifth value is going to be entered then sixth value is going to be entered then seventh value is going to be entered and then eighth value is going to be entered so now you can see here that this data is entered like this so the data is entered here how column wise that first the data is filled up in the column and then in the rows yes that can be interchanged also so how to get it done these are the questions that we are going to understand in the forthcoming slides so this you can see here this is the screenshot if i just write here like this and then you get here this type of matrix this type of output okay so now if you try to see in this matrix command i have explain you what is the role of n row what is the role of n call and what is the role of data and these data values are written column wise so that is what you have to understand now the next question comes here how do you identify or how do you access a particular value in the matrix so one thing i can share with you that is coming from the matrix theory actually that when i try to write down here x say here 1 2 so this means this is the value in the first row and second column so this one two is indicating like here the position of row and position of column so for example in this matrix which is given here if you try to see in case if i see here x 1 2 so 1 means the first row like i say like this and 2 is the second column so like this so this value at the intersection of these two lines this is the value of x 1 2 which is equal to here 5. so now the same thing i want to do in the r software so for that the question is what type of command are we going to use so in case if you want to access a single element for of a matrix say x because you have to give the matrix a name so here i have given the matrix name as x then inside this square brackets you have to first write the position of the row and then you have to write the position of the column from there you want to access that element for example in case if i want to access the element in the third row and second column then i have to write down here x third row that is r equal to three and column is the second so c is equal to two so now if you try to see here if i try to write down here x three two so what is this value this is here my row number three and this is my here column number two so this value at the intersection is seven so now as soon as you write here x three two and the three two they are separated by comma and then they are written within the square brackets so this value will come out here 7 and this 7 is actually here this 7 and if you try to execute it on the r console also there won't be any problem ok right so before i move further let me try to give this example it on to you on the r console so let me try to define my here matrix here like this you can see x is here matrix n row equal to 4 and call equal 2 etcetera and if you try to enter here then you try to see the value of here x this comes out to be like this so you can see here now the values are entered 1 2 3 4 column wise and then 5 6 seven eight right and in case if you want to access any particular element from here you can write the name of the matrix x and then suppose if i say here four comma two so four comma two will come here eight because this is the fourth row and the second column and this value here is eight and similarly if you try to take here say x two comma four then what will happen do you what you expect this is your here second row and fourth column but where is the fourth column i have only had two column column number one column number two so let us see what r does it will give you error that the subscripts out of bounds that means you are trying to give the value of the column which is not in the range of the the columns which are present in the matrix so rather if you try to write down here something like x two two what does this mean this is the second row and second column so the value here is six so if you try to enter here you will get here the value six and in case if you try to use here some other bracket like x two comma two you can see here this will not work because it cannot understand what this parenthesis is trying to indicate so you have to use only the the square bracket that is going to make the r understand that this is a command for the matrix so now we come back to our slides and try to see some more operations ok so now you have seen that when you are trying to define a matrix in this particular way ah as you have done this data is going to enter column wise that you can see here the data is entered here column y like 1 2 3 4 and then 5 6 7 8 like this so now my objective is that suppose i want to enter this data row wise so how should i control it so when you are trying to enter the data column wise one to it it goes like this one two three four and then it goes to second column five six seven eight but when you want to write down the data in row wise it means that one after this it will be two will be assigned in the second column and then it comes to three and then it will go to 4 then it comes to 5 in the first column and 6 in the second column then 7 comes in the first column and 8 comes in the second column so now how to control it so for that we have here an option which is by row b y r o w this by row this is a logical variable so this can take two possible values one is here true and another here is false so now in case if you write by row is equal to false and try to think for a while what does this mean you are trying to say by row is false that means the data has not to be arranged by rows when the data is not to be arranged in rows then what is the next option the data has to arrange in the columns only so in this case if you try to see here the outcome comes out comes out to be like this data is arranged in the column but what is this mean if you try to compare this command which is not using by row and the second command which is using here the by row when you are trying to use by row then or you are not using the by row it is giving you the same outcome this means when you are not using the option of by row then matrix command is assuming by row equal to false as default that either you give it or not it will always assume that by row is equal to false so now the question comes if you want to arrange your data row wise then what you have to do that is now very obvious simply try to use by row is equal to true and in case if you try to use the same command but now i am using it in a different variable name say here y so matrix command with n row equal to 4 and call equal to 2 and data is the same but by row is equal to now true now you can see the outcome of y so you can see here one is coming here then it goes to two in the second column then the next value comes with the first column it is here three and then it goes to the fourth column which is here four and then it comes with the first column as five then go to the next column as six then it comes to the first column seven and then goes to the next column as eight so you can see here this operation is going like this is row wise assignment of the data so now you can see this is in your control that how you want to assign the data in the matrix and if you try to see here the screenshot that when you are trying to see here there is no option by row is equal to true or false you are not writing anything then the data is this here like this column wise and when you are writing here by row is equal to true then the data here is row wise like this so let me try to show you these operations on the r console also so that you get here more confident so you can see here this is your here matrix x where you have not used any command over here and you can see here this is your here x now in the same command let me try to reduce the phone so that you can see everything on the same scale suppose i make it here 60 so now you can see here that i try to add here by row is equal to false now you can see here the value of here x this is here like this let me reduce the phone size to be like this so that you can see clearly yes now it is clear so you can see here when you are trying to use here by row equal to false then the outcome here and here that is the same but now in case if you try to use here this outcome and you try to make it here true and you try to assign it in a new matrix say y then you can see here y now you can see here when you have biro equal to false then the data is like 1 2 3 4 and when you are trying to use here by or equal to 2 then the data like 1 2 3 4 and so on so that is the difference between the two right ok so now let me come back to our slides and try to see some more operations right so now let us try to consider the same matrix and with then we try to learn some more operations on this matrix x which has four rows and two columns with the data one two eight so this is your column wise arrangement and we try to learn here something here more now whenever you are trying to use a matrix suppose some matrix is given to you and you want to know the information about this matrix so one information in which you are always interested in the dimension of the matrix that how many number of rows are there how many number of columns are there and so on so in order to know the dimension of the matrix we have a command here d i m dim and within the parenthesis if you write down the name of the matrix it will give you the information like is like this 4 comma 2 4 is the number of rows and 2 is the number of columns and in case if you want to know only the number of rows then the command here is n row and parenthesis inside the parenthesis you write the name of the matrix so this will be your here n row and say inside paranthesis x and the answer will come out to be here four why because you can see here in this matrix x you have here one two three four rows and how many columns are there one and here this two so now in order to know the columns of a matrix you simply have to use the command here and call ncol and inside the parenthesis you have to write the variable in which the matrix is saved and it will explain you the number of columns present in the matrix so it is here 2. so you can see here these are not very big operations and similarly if you want to know the mode of the matrix do you remember mode we had done in the earlier lecture where we had numeric character its etcetera and remember this mode was not the mean median mode is a statistical mode so this is going to inform us that how the values in this matrix x are stored so this is you can see here numeric and similarly we have here one more command here attributes so this also provides all the attributes of an object actually so in this case this is a matrix so if you try to write down here attributes x inside the parenthesis then it will give you this type of information which is trying to tell you the dimension of this x which is here 4 and 2 which is four rows and two column and the spelling of this attribute is a double t r i b u t e s in all in lower alphabets lowercase alpha bits small alphabets so this is how you can obtain this type of information now in this matrix there are many other options which are available that how you can handle this matrix so i will not go into all the details but i will request use that you try to see into the help metrics so try to type help and within double quotes type here matrix it will give you all the description metrics as matrix is metrics etc and after that it will give you the usage then the details about different arguments dim names and then after that it will give you this type of detail i have simply taken it from the help which is available in the r right so i will not detail it here because now you know all the things i already have explained you the concept of say s i and s for example if you use here this command s dot matrix so this will simply show you whether the variable here is in the format of matrix or not and in case if you want to convert any number into a matrix then you have to use as dot matrix right so all these things are there i would request you that you please try to look into this help menu and try to read it here and i will try to show you these things on the r console about these two operation dimension and row and call and more attributes so let me try to show you these things on the r console so you can see here now let me try to see here y is our this matrix and if i want to find out the dimension of this here y this is here 4 2. in case if i want to find out the n row in the matrix y you can see here this is here 4 and in case if i want to find out their n call of this y this is here like this 2 and if i try to find out here the mode of y this will be here numeric and if i try to find out the attributes of here y this will be like 4 2. so you can see here getting the information about the matrix is not difficult at all ok so now we come to an end to this lecture this was a very simple short lecture short in terms of the the content of the lecture my idea was that ok this is the first lecture where you are trying to understand the concept of matrix for the first time so i should stop here so that you get some time to do all these operations yourself in the r console it is not difficult the only thing is this you have to settle down these concepts in your mind that how this end row end call data by row etcetera they are going to work once you are familiar with these objects after that i promise you handling with the matrices is very simple and it will be very easy for you to do such operation so you try to have a quick revision try to practice it and i will see you in the next lecture with more details on matrix operation till then good bye [Music] do [Music] [Music] you