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Basic definitions

(import (otus algebra))

Vectors

Vector is a one-dimensional array. Vector can be declared using several ways:

• by it's values which can be any applicable number:

> [1 2 3 4 5]
#(1 2 3 4 5)

> [0 -3 3/7 16+4i 7.12 (inexact 7.12) 123456789876543213546576666777757575757444]
#(0 -3 3/7 16+4i 178/25 7.12 123456789876543213546576666777757575757444)

• As a copy of existing vector:

> (define v [1 2 3 4 5])
> (print v)
#(1 2 3 4 5)
> (copy v)
#(1 2 3 4 5)

• As an uninializied vector of N elements.

> (vector 14)
#(0 0 0 0 0 0 0 0 0 0 0 0 0 0)

• As a vector of 0s:

> (zeros 14)
#(0 0 0 0 0 0 0 0 0 0 0 0 0 0)

• As a vector of 1s:

> (ones 42)
#(1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1)

• As a vector of an any applicable same value:

> (fill (vector 17) -33)
#(-33 -33 -33 -33 -33 -33 -33 -33 -33 -33 -33 -33 -33 -33 -33 -33 -33)

Matrices

A matrix is a rectangular array of numbers or a vector of a vectors in other words.

Matrix can be declared using several ways:

• by it's values which can be any applicable number:

> [[1 2 3]
   [4 5 6]
   [7 8 9]]
#(#(1 2 3) #(4 5 6) #(7 8 9))

• As a copy of existing matrix:

> (define v [[1 2 3][4 5 6][7 8 9]])
> (print v)
#(#(1 2 3) #(4 5 6) #(7 8 9))
> (copy v)
#(#(1 2 3) #(4 5 6) #(7 8 9))

• As a matrix of N same vectors.

> (matrix [1 2 3] 4)
#(#(1 2 3) #(1 2 3) #(1 2 3) #(1 2 3))

• As an uninializied matrix of rows*columns elements.

> (matrix 3 4)
#(#(0 0 0 0) #(0 0 0 0) #(0 0 0 0))

• As a matrix of 0s:

> (zeros 3 7)
#(#(0 0 0 0 0 0 0) #(0 0 0 0 0 0 0) #(0 0 0 0 0 0 0))

• As a matrix of 1s:

> (ones 1 3)
#(#(1 1 1))

• As a matrix of an any applicable same value:

> (fill (matrix 2 3) -1)
#(#(-1 -1 -1) #(-1 -1 -1))

• As a matrix with zeros (ones) with same shape of other matrix:

> (define m (matrix 2 5))
> (print m)
#(#(0 0 0 0 0) #(0 0 0 0 0))
> (ones m)
#(#(1 1 1 1 1) #(1 1 1 1 1))