Combinar las fotografías en una imagen HDR

Elements can easily be extracted from a specific location in a list. For example, this extracts the third element in the list vec.

In[4]:= vec 2, 3, 7, 8, 1, 4 ;

In[5]:= Part vec, 3

Out[5]= 7

The Part function can be abbreviated using a standard input form. In[6]:= vec 3

Out[6]= 7

If you are interested in the elements from more than one location, you can extract them using a list. For example, this picks out the second and fourth elements of vec.

In[7]:= vec 2, 4

Out[7]= 3, 8

For multi-dimensional lists, you have to specify both the sublist and the position of the element in that sublist that you are interested in.

Here is a sample 3 3 matrix that we will work with.

In[8]:= mat Table ai,j, i, 3 , j, 3 MatrixForm

Out[8]//MatrixForm=

a1,1 a1,2 a1,3

a2,1 a2,2 a2,3

a3,1 a3,2 a3,3

This picks out the first part of the second sublist. In[9]:= mat 2, 1

Out[9]= a2,1

For multi-dimensional lists, several options are available to extract subsections of the list. A common operation involves extracting rows or columns from a matrix.

This extracts the entire second column of mat. In[10]:= mat All, 2 MatrixForm

Out[10]//MatrixForm=

a1,2

a2,2

And here is the third row of this matrix. In[11]:= mat 3, All

Out[11]= a3,1, a3,2, a3,3

If you only specify one argument, the second is assumed to be All. In[12]:= mat 3

Out[12]= a3,1, a3,2, a3,3

In addition to being able to extract elements from specific locations in a list, you can extract consecutively placed elements within the list. You can take elements from either the front or the back of a list.

In[13]:= Take 1, 4, 1, 5, 9, 2 , 2

Out[13]= 1, 4

In[14]:= Take 1, 4, 1, 5, 9, 2 , 2

Out[14]= 9, 2

If you take consecutive elements from a list other than from the front and the back, you need to remember that the numbering of positions is different front-to-back and back-to-front.

In[15]:= Take 1, 4, 1, 5, 9, 2 , 2, 4

Out[15]= 4, 1, 5

In[16]:= Take 1, 4, 1, 5, 9, 2 , 5, 3

Out[16]= 4, 1, 5

You can mix both positive and negative indices. In[17]:= Take 1, 4, 1, 5, 9, 2 , 5, 4

Out[17]= 4, 1, 5

You can also take elements in steps. This takes the first through sixth element in incre- ments of 2; that is, it takes every other element.

In[18]:= Take 1, 4, 1, 5, 9, 2 , 1, 6, 2

You can discard elements from a list, keeping the rest. Elements can be removed from either end of the list or from consecutive locations.

In[19]:= Drop 1, 4, 1, 5, 9, 2 , 2 Out[19]= 1, 5, 9, 2 In[20]:= Drop 1, 4, 1, 5, 9, 2 , 1 Out[20]= 1, 4, 1, 5, 9 In[21]:= Drop 1, 4, 1, 5, 9, 2 , 3, 5 Out[21]= 1, 4, 2

You can remove elements at specific locations as well. In[22]:= Delete 1, 4, 1, 5, 9, 2 , 1

Out[22]= 4, 1, 5, 9, 2

In[23]:= Delete 1, 4, 1, 5, 9, 2 , 3 , 4

Out[23]= 1, 4, 9, 2

Certain extractions are used so often that they are given their own functions. In[24]:= First 1, 4, 1, 5, 9, 2 Out[24]= 1 In[25]:= Last 1, 4, 1, 5, 9, 2 Out[25]= 2 In[26]:= Rest 1, 4, 1, 5, 9, 2 Out[26]= 4, 1, 5, 9, 2

Rearranging lists

Every list can be sorted into a canonical order. For lists of numbers or letters, this ordering is usually obvious.

In[27]:= Sort 3, 1.7, , 4, 22 7

Out[27]= 4, 1.7, 3, 22 7 ,

Mathematica uses the following canonical orderings: numbers are ordered by numeri-

the imaginary part; symbols and strings are ordered alphabetically, powers and products are ordered in a manner corresponding to the terms in a polynomial; expressions are ordered depth-first with shorter expressions coming first.

You can also sort lists according to an ordering function that you can specify. In[28]:= Sort 3, 1.7, , 4, 22 7 , Greater Out[28]= 22 7 , , 3, 1.7, 4

When applied to a nested list, Sort will use the first element of each nested list to determine the order.

In[29]:= Sort 2, c , 7, 9 , e, f, g , 1, 4.5 , x, y, z

Out[29]= 1, 4.5 , 2, c , 7, 9 , e, f, g , x, y, z

The order of the elements in a list can be reversed. In[30]:= Reverse 1, 2, 3, 4, 5

Out[30]= 5, 4, 3, 2, 1

All of the elements can be rotated a specified number of positions to the right or the left. By default RotateLeft (and RotateRight) shifts the list one position to the left (right).

In[31]:= RotateLeft 1, 2, 3, 4, 5

Out[31]= 2, 3, 4, 5, 1

This rotates every element two positions to the right. In[32]:= RotateRight 1, 2, 3, 4, 5 , 2

Out[32]= 4, 5, 1, 2, 3

Partition rearranges list elements to form a nested list. It may use all of the elements and simply divvy up a list. Here we partition the list into nonoverlapping sublists of length two.

In[33]:= Partition 1, 4, 1, 5, 9, 2 , 2

Out[33]= 1, 4 , 1, 5 , 9, 2

You might be interested in only using some of the elements from a list. For example, this takes one-element sublists, with an offset of two; that is, every other one-element sublist.

In[34]:= Partition 1, 4, 1, 5, 9, 2 , 1, 2

Out[34]= 1 , 1 , 9

You can also create overlapping inner lists, consisting of ordered pairs (two-element sublists) whose second element is the first element of the next ordered pair.

In[35]:= Partition 1, 4, 1, 5, 9, 2 , 2, 1

Out[35]= 1, 4 , 4, 1 , 1, 5 , 5, 9 , 9, 2

The Transpose function pairs off the corresponding elements of the inner lists. Its argument is a single list consisting of nested lists.

In[36]:= Transpose 1, 2, 3, 4 , a, b, c, d

Out[36]= 1, a , 2, b , 3, c , 4, d

In[37]:= Transpose 1, 2, 3, 4 , a, b, c, d , i, ii, iii, iv

Out[37]= 1, a, i , 2, b, ii , 3, c, iii , 4, d, iv

For rectangular lists, you might think of Transpose as exchanging the rows and columns of the corresponding matrix.

Elements can be added to the front, the back, or to any specified position in a given list. In[38]:= Append 1, 2, 3, 4 , 5 Out[38]= 1, 2, 3, 4, 5 In[39]:= Prepend 1, 2, 3, 4 , 5 Out[39]= 5, 1, 2, 3, 4 In[40]:= Insert 1, 2, 3, 4 , 5, 3 Out[40]= 1, 2, 5, 3, 4

Elements at specific locations in a list can be replaced with other elements. Here, 5 replaces the element in the second position of the list.

In[41]:= ReplacePart a, b, c, d, e , 5, 2

Out[41]= a, 5, c, d, e

You can flatten a nested list to various extents. You can remove all of the inner braces, creating a linear list of elements.

In[42]:= Flatten 3, 1 , 2, 4 , 5, 3 , 7, 4

You can limit the degree of flattening, removing only some of the inner lists. For example, two inner lists, each having two ordered pairs, can be turned into a single list of four ordered pairs by only flattening down one level deep.

In[43]:= Flatten 3, 1 , 2, 4 , 5, 3 , 7, 4 , 1

Out[43]= 3, 1 , 2, 4 , 5, 3 , 7, 4