Computations

[Mathematical functions | Vectors | Matrices| Apply and sweep]

MATHEMATICAL FUNCTIONS

The following functions apply to either an scalar or to a vector or matrix, element by element

Usual operations functions: a+b, a-b, a*b, a/b, a^b, is a vector with the sum (or whatever) of the coordinates of a and b. To get this in a new vector, we can do d_a+b or d<-a+b. These operation apply to vectors and matrices doing these operation by coordinates.

Trigonometric functions: cos, sin, tan, acos, asin, atan, cosh, sinh, tanh, acosh, asinh, atanh

Exponential functions: gamma, lgamma, exp, log, log10, log(x, base=)

Other mathematical functions: sqrt (square root), abs returns the absolute value,

Truncations and rounding functions:

trunc() returns the integer part.
ceiling() returns the next integer.
round() rounds to the nearets integer. values 1/2 are rounded to the nearest even integer
round(x,,"positive integer")) rounds using the specified number of decimal places.
floor() returns the previous to the next integer.
signif(x,"positive integer")) rounds data to the specified number of significant digits. All the numbers are printed to the same format. 0's are added where necessary.
x%/%y = floor(x/y) returns the integer part of x/y.
x%% y =x- (x%/%y)*y returns x modulus y.

For example,

> trunc(x)
[1] -1 -1 -5  0  0  1  2  2  
> x_c(-1.7,-1.3,-5,.2,.5,1.5,2.3,2.7)
> round(x)
[1] -2 -1 -5  0  0  2  2  3
> floor(x)
[1] -2 -2 -5  0  0  1  2  2
> ceiling(x)
[1] -1 -1 -5  1  1  2  3  
> signif(x,1)
[1] -2.0 -1.0 -5.0  0.2  0.5  2.0  2.0  3.0   
> x_c(-24,-99,82,15)
> x%/%10 
[1] -3 -10  8  1    
> x%%10
[1] 6 1 2 5

OPERATIONS IN VECTORS

The following are operations in one vector giving a number:

sum finds the sum of the all elements of the vector.
prod finds the product of the all elements of the vector.
max finds the maximum of the all elements of the vector.
min finds the minimum of the all elements of the vector.

For example:

> x
[1] -1.7 -1.3 -5.0  0.2  0.5  1.5  2.3  2.7
> sum(x)
[1] -0.8
> prod(x)
[1] -10.29308
> max(x)
[1] 2.7
> min(x)
[1] -5

The following are operations in one vector giving another vector:

cumsum(x) finds the cumulative sums of the all elements of the vector.
diff(x) finds the differences: x[i+1]-x[i] of the elements of the vector.
diff(x,lag="integer") finds ds the differences: x[i+lag]-x[i] of the elements of the vector.
cumprod finds the product of the all elements of the vector.

For example:

> x
[1] -1.7 -1.3 -5.0  0.2  0.5  1.5  2.3  2.7
> cumsum(x)
[1] -1.7 -3.0 -8.0 -7.8 -7.3 -5.8 -3.5 -0.8
> cumpro(x)
Problem: Couldn't find a function definition for "cumpro"
> cumprod(x)
[1]  -1.70000   2.21000 -11.05000  -2.21000  -1.10500  -1.65750  -3.81225
[8] -10.29308
> diff(x)
[1]  0.4 -3.7  5.2  0.3  1.0  0.8  0.4

The following are operations in two vectors giving a number:

crossprod(x,y) finds the crossproduct of x and y.

The following are operations in two vectors giving another vector:

pmax(x,y) finds the maximum of every element of x and y.
pmin(x,y) finds the minimum of every element of x and y.

MATRICES

The following functions apply specifically to matrices:

t(A) finds the transpose of A.
A%*%B multiply the matrices A and B.
diag(A) finds diagonals of A.
crossprod(A,B) finds the cross product of A and B.
outer(A,B) finds the outer product A and B.
svd(A) singular value decomposition.
qr(A) QR decomposition
solve(A,B) finds the solution to the system of equations A %*% X = B.
solve(A) finds the inverse of A.
eigen(A) eigenvalues.
diag(A) find a vector with the diagonals of the matrix A
diag(x) find a matrix with the elements of x in the diagonals
chol(A) Choleski decomposition.
eigen(A) creates an object of mode list with two components: $values and $vectors. Alternatively, eigenvalues could have been obtained using eigen(A)$values, and eigenvectors using eigen(A)$vectors

APPLY AND SWEEP

The function apply allows to use vector commands either by rows or by columns. The first argument of the command apply is the matrix or data frame to which the function will be applied. The second argument gives the dimensions over which the function is to be applied. In the case of a matrix, 1 indicates rows, 2 indicates columns. The third argument gives the name of the function to be applied.

The function sweep(A,integer,a) substract the vector a, by columns if integer=1 and by rows if integer=2, from the matrix A.

> A
      Height Weight
  Tom     42     66
 Fred     40     62
  Sue     42     71
Donna     43     79
  Lee     42     67 
> apply(A,1,mean)
 Tom Fred  Sue Donna  Lee
  54   51 56.5    61 54.5
> apply(A,2,mean)
 Height Weight
   41.8     69   
> a2_c(1:10)
> a2
 [1]  1  2  3  4  5  6  7  8  9 10
> sweep(A,2,a2)
      Height Weight
  Tom     41     64
 Fred     37     58
  Sue     37     65
Donna     36     71
  Lee     33     57 
>  sweep(A,2,a2,"+")
      Height Weight
  Tom     43     68
 Fred     43     66
  Sue     47     77
Donna     50     87
  Lee     51     77
> sweep(A,1,a2,"*")
      Height Weight
  Tom     42    396
 Fred     80    434
  Sue    126    568
Donna    172    711
  Lee    210    670

Comments to: Miguel A. Arcones

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