Numerical Methods Course Notes Version 0.1 (UCSD Math 174, Fall ...

2.2. USEFUL COMMANDS 15
octave:22> z = 5:(-2):1
z =
5 3 1
octave:23> z = 2:3:11
z =
2 5 8 11
octave:24> z = 2:3:10
z =
2 5 8
2.2 Useful Commands
Here’s a none too complete listing of useful commands in octave:
• help is the most useful command.
• floor(X) returns the largest integer not greater than X. If X is a vector or matrix, it computes
the floor element-wise. This behavior is common in octave: many functions which we normally
think of as applicable to scalars can be applied to matrices, with the result computed elementwise.
• ceil(X) returns the smallest integer not less than X, computed element-wise.
• sin(X), cos(X), tan(X), atan(X), sqrt(X), returns the sine, cosine, tangent, arctangent,
square root of X, computed elementwise.
• exp(X) returns e X , elementwise.
• abs(X) returns |X| , elementwise.
• norm(X) returns the norm of X; if X is a vector, this is the L 2 norm:
‖X‖ 2
=
( ∑
i
X 2 i
) 1/2
,
if X is a matrix, it is the matrix norm subordinate to the L 2 norm.
You can compute other norms with norm(X,p) where p is a number, to get the L p norm, or
with p one of Inf, -Inf, etc.
• zeros(m,n) returns an m × n matrix of all zeros.
• eye(m) returns the m × m identity matrix.
• [m,n] = size(A) returns the number of rows, columns of A.
• length(v) returns the length of vector v, or the larger dimension if v is a matrix.
• diag(v) returns the diagonal matrix with vector v as diagonal. diag(M) returns as a vector,
the diagonal of matrix v. Thus diag(diag(v)) is v for vector v, but diag(diag(M)) is the
diagonal part of matrix M.
• toeplitz(v) returns the Toeplitz matrix associated with vector v. That is
⎡
toeplitz(v) =
⎢
⎣
v(1) v(2) v(3) · · · v(n)
v(2) v(1) v(2) · · · v(n − 1)
v(3) v(2) v(1) · · · v(n − 2)
. . .
. .. .
v(n) v(n − 1) v(n − 2) · · · v(1)
⎤
⎥
⎦