Chart 3 Data in Array

Transcription

1 Chart 3 Data in Array 3.1. How to Handle Data in Table Form Create Matrix and Tables 1. Choose an input mode cell where you like to create a table. Next, choose Insert (I) - Table & Matrix (M) - (N). Then you choose Table or Matrix. Input number of rows and columns. In order to make a table, you need frame and diving lines. Check three boxes so that you have frame and dividing lines for the table. Input numbers in the cells of the table. If you like to have a title or item name, input letter or words with quotation marks;. String of letters with quotation marks are treated as a part of a sentence, not variable names. You can assign name to the table by A=... as following example shows. Example In[1]:= Clear A A "sea food" "tuna" "cod" "squid" "price per 100g" Out[2]= sea food, tuna, cod, squid, price per 100g, 500, 100, Present your table in a form of Table You input letters and numbers in the table in the preceding example. However, when you run the Mathematica, the resulting output is horizontally stretched brackets as shown above. This is the default form Mathematica handles tables. In order to present A in a table form, you need extra command. Grid[ table name, Frame->All]. Example In[3]:= Grid A, Frame All Out[3]= sea food tuna cod squid price per 100g How to Take the Numbers out from the Table You can specify the location in the table very much in the same way to specify elements in a matrix. In the following we have a table called A, A A21 A22 A23 By writing A[[1,3]], you specify 1st row 3ird column. You can take out the value in the location of A13. EChart03TableForm-0517.nb 1

2 In[4]:= A21 A22 A23 ; A 1, 3 Out[5]= A13 Example Taking advantage of entries of a table Suppose you have US dollars and euros. These amounts and exchange rates are given in a following table. Let s find Japanese yen value of your foreign currencies. currency exchange rate in yen quantity US dollar euro The answer is equal to We are going to calculate this, using B[[...,...]] where B is name we give to the list shown above. Let s call the table B. Your 200 dollars is located 2nd row 3rd column in table B, for example. You can figure out locations of other numbers. In[6]:= Clear B B "currency" "exchange rate in yen " "quantity" "US dollar" "euro" ; Print "value in Japanese yen ", B 2, 2 B 2, 3 B 3, 2 B 3, 3 value in Japanese yen In the above, we multiplied entries in the 2nd column with those in the 3ird column. Then we sum them up. We can make calculation look neater if we take advantage of ID numbers of the locations in the table. We use index to specify ID number and sigma sign as follows. In the following example, index i changes from 2 to 3. In[9]:= 3 i 2 B i, 2 B i, 3 Out[9]= Substitute values into the Table Suppose you like to have a little more detailed table, adding a column which shows respective values of the currencies. You substitute the values into the added column of the table. In the above table B, the JPY value of US dollars is given by B[[2,2]] B[[ 2,3]] and similarly, by B[[3,2]] B[[ 3,3]] for euros. Let s call new table V. We multiply entry in the 2nd column by the 3rd column. Then substitute the product into the 4th column. Total value is sum of the 2nd and 3rd row of the 4th column. Adding row or column EChart03TableForm-0517.nb 2

3 the first step: Bring the pointer the the right side of the table frame. the second step: Insert(I) - Table/Matrix(M) - Addition of Row or Column; Choose row or column You copy table B and paste it. Then add column. Name it V. You cannot use capital letter C here as a name of the table. Capital letter C means complex number. In[10]:= Clear V ; V "currency" "exchange rate in yen " "quantity" "value in yen" "US dollar" "euro" Out[10]= currency, exchange rate in yen, quantity, value in yen, US dollar, 102, 200,, euro, 140, 150, Let s show the results in the table. You need Grid[..., Frame->All] to show as framed table. Otherwise, output is in the form of brackets. In[11]:= V 2, 4 V 2, 2 V 2, 3 ; V 3, 4 V 3, 2 V 3, 3 ; Grid V, Frame All Print "total value in Japanese yen is equal to ", V 2, 4 V 3, 4 Out[13]= currency exchange rate in yen quantity value in yen US dollar euro total value in Japanese yen is equal to Exercise Random variable X takes values from -20 to 5 with the probabilities given below. Calculate expected value of X. "value of X" "probability" n Expected value is denoted as E[ X ]. Its definition is given by the following; E X i 1p i x i, where x i is the ith value of random variable X and that p i is probability that x i takes place. Random variable is denoted by capital letter and its individual values are in small letters. In[15]:= "value of X" "probability" ; Print "E X ", 6 i 1 A 1, 1 i A 2, 1 i E X 7.5 EChart03TableForm-0517.nb 3

4 3.2. List Arrayed Data Data in array look neat. It is easier to handle data. Particularly it is so as data size becomes larger. We organize data in a form of vector. This vector is called list in Mathematica. Tables and matrices are handled as lists. List Arrayed in Table and Matrix We created table A by inserting and choosing number of columns and rows etc. Although we input A as a table, we have to Grid[ ] to show A as a table. Unless we use command Grid[ A, Frame- >All], output from Mathematica is shown in the form of brackets. Each bracket is the same as vector. As far as Mathematica is concerned, table and matrix are the same thing in different appearances. Table is arranged display of elements with grid lines. Matrix is those with bracket ( ). We can change A, which appeared in the previous section into a form of matrix. In[17]:= ; A Out[17]= A11, A12, A13, A21, A22, A14, A31, A32, A33 Each bracket above looks exactly the same as a vector,which is list of elements. Such a structure by which data is arranged is called list. In other words, Mathematica organize data in a form of list. By taking advantage of lists, we can simplify program. Neater looking program is easier to follow and to prevent errors. Default form of list is the structure of brackets. We can present a list called A in different appearances. We used Row[...] to save space. In[18]:= Print "Default form is as follows; ", A Default form is as follows; A11, A12, A13, A21, A22, A14, A31, A32, A33 In[19]:= Row MatrixForm A, " ", Grid A, Frame All Out[19]= In the above, there are three {... } s inside of the large {... }. The smaller { } s are vectors with three elements. The first vector, { A11, A12, A13 }, corresponds to the first row of the table. And also it corresponds to the first row of the matrix. The same holds true with second and third vectors. Mathematica calls a group of elements list. Vector is list. It is list of elements. Matrix is list whose elements are also lists; { A11, A12, A13 }, for example. Table is also list of list. So A is list of three lists. Let s see what the third element is. It must be a vector. In[20]:= A 3 Out[20]= A31, A32, A33 EChart03TableForm-0517.nb 4

5 Row[{arg1, arg2,...} ] By Row[{...} ], you can show arg1, arg2,... horizontally. You can save space. Arg1, arg2 can be graphs too. In the above example we show matrix and table with empty space between them. Row[ {MatrixForm[A],, Grid[A,Frame All]}] Without empty space, it is not so comfortable to see Elements and Sublist Let s take example of list A again. List A is outer most { }. It has three elements; A[[1]], A[[2]], A[[3]]. Each element A[[ i ]], i=1,2,3 is vector with three elements;{a11, A12, A13 }, for example. Element of the list is also list. We want to organize how to call them. So we call element in the form of list sublist. If the element is number, then it is just an element. A[[1]] is sublist of A and A[[1,3]] is element of A[[1]]. EChart03TableForm-0517.nb 5