Practices - 1, R - rextester

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#R version 3.3.2 
  
# Numbers and Vectors Manipulation
# c(1, 2, 3) is a vector

# x = c(1, 2) and then y = c(x, 0, x)
# then y will be c(1, 2, 0, 1, 2)
# if x is a vector, then min, max, mean, 
# length all work on x and return one value
# sum, prod as well

# Note when all scalar functions above work on 
# multiple variables, they all return one value

# e.g.: x = c(1, 2, 3), y = c(4, 5, 6), z = c(7, 8, 9);
# and max(x, y, z) -> 10;

# Sequence
# seq(from = a, to = b) or seq(start, end, by=steps);
# or seq(length = l, from = a, by = steps)
# and this will return a vector

# rep(x, times = b) will replicate x for n times
# If x is a vector, then rep(x, each = b) will replicate
# each element in x separately for b times.
# e.g.: x = c(1, 2) then rep(x, each=3) -> c(1, 1, 1, 2, 2, 2);

# Logicla operators: &, ||, !...

# NA means missing values and NaN only works for missing numbers
# is.na(x) will tell is x is NA or not and same for is.nan(x);

# Character vectors: \n: newline, \t: tab
# paste(c(str_1, str_2, ...), start:end, sep = string);

# e.g.: paste(c('a', 'b'), 1:5, sep = 'cc'));
#    -> c('acc1', 'bcc2', 'acc3', 'bcc4', 'acc5');

# if x is a vector, then x[conditions applied on element on x]
# will remain elements satisfying that condition
# e.g: x = c(1, 2, 3); y = x[x >= 2] and y = c(2, 3);

# NOTE: in vectors, index start from 1

#y = c('x', 'y')[rep(c(1, 2, 2, 1), times = 4)];
#print (y);

# In this case the vectors in rep can provide the format
# to replicate x and y.
# Here numbers will represent the index of the vector in the front

# x[-(1:5)] means the vectors without the value from index 1 to 5 within x
# And abs(x) will take the abs value of all the value in x

x = c('a', 'b', 'c', 'd', 'e', 'f', 'a', 'b', 'r', 'e');
y = c(1, 2, 3, 1, 2, 9, 4, 4, 6, 2);
z = tapply(y, x, mean);

# To use the tapply function, we need list(a vector) of 
# strings which stand for dimension, and then its level
# will tell you all unique value

# tapply (data, dimension, calculation(including mean, ..))
# Then the result will be a table including data broken
# by the level of the factor

x = c(1, 2, 3, 1, 2, 3, 1, 2, 4, 1, 4, 4);
dim(x) = c(2, 3, 2);

# When assigning c(a, b, c) to dim(v) where v is a long vector
# when print v, it will break down v into c matrixes with a rows and b columns

# Array target
# v = array(start_1:end_1, start_2:end_2, ..., dim = c(numof_rows, numof_cols));
# without the dim, then v will be printed in one long line
#e.g.:

x = array(0, dim = c(3, 4, 1)) # produce 2 3x4 matrixed with all 0
y = array(c(1:8, 2:5), dim = c(4, 2, 4));

# Outer product between two vectors:
# ab = a %o% b or ab = outer (a, b, "*")

f = function(x, y) cos(y)/(1 + x^2); # a function with input x, y and output that formula

a = c(1, 2, 3);
b = c(2, 3, 4);
v = outer(a, b, "*");

# Here outer product means a times the transpose of b
# and inner product means the transpose of b times b

#d = outer(0:9, 0:9);
#fr = table(outer(d, d, "-"));
#plot (as.numeric (names(fr)), fr, type = "h", 
#      xlab = "Determinant", ylab = "Frequency");

# if A is a matrix, then t(A) will return the transpose of A
# and nrow(A) and ncol(A) will return the number of rows and columns of A
# and %*% is the matrix multiplication

# Warning: when multiplying vectors, try not to use %*%

# Solving linear equations and inversion
# A a matrix, x a vector
# b = A %*% x and then solve(A, b) can return x. Here x do not need to be given

# Eigenvalue/Eigenvectors
# Note that this can only be applied to a symmetric matrix

S = array(c(1:3), c(2, 2));

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