Vector products: Difference between revisions

=={{header|Ksh}}==

<lang ksh>

#!/bin/ksh

# Vector products

# # dot product (a scalar quantity) A • B = a1b1 + a2b2 + a3b3 + ...

# # cross product (a vector quantity) A x B = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)

# # scalar triple product (a scalar quantity) A • (B x C)

# # vector triple product (a vector quantity) A x (B x C)

# # Variables:

#

typeset -a A=( 3 4 5 )

typeset -a B=( 4 3 5 )

typeset -a C=( -5 -12 -13 )

# # Functions:

#

# # Function _dotprod(vec1, vec2) - Return the (scalar) dot product of 2 vectors

#

function _dotprod {

typeset _vec1 ; nameref _vec1="$1" # Input vector 1

typeset _vec2 ; nameref _vec2="$2" # Input vector 2

typeset _i ; typeset -si _i

typeset _dotp ; integer _dotp=0

for ((_i=0; _i<${#_vec1[*]}; _i++)); do

(( _dotp+=(_vec1[_i] * _vec2[_i]) ))

done

echo ${_dotp}

}

# # Function _crossprod(vec1, vec2, vec) - Return the (vector) cross product of 2 vectors

#

function _crossprod {

typeset _vec1 ; nameref _vec1="$1" # Input vector 1

typeset _vec2 ; nameref _vec2="$2" # Input vector 2

typeset _vec3 ; nameref _vec3="$3" # Output vector

_vec3+=( $(( _vec1[1]*_vec2[2] - _vec1[2]*_vec2[1] )) )

_vec3+=( $(( _vec1[2]*_vec2[0] - _vec1[0]*_vec2[2] )) )

_vec3+=( $(( _vec1[0]*_vec2[1] - _vec1[1]*_vec2[0] )) )

}

# # Function _scal3prod(vec1, vec2, vec3) - Return the (scalar) scalar triple product of 3 vectors

#

function _scal3prod {

typeset _vec1 ; nameref _vec1="$1" # Input vector 1

typeset _vec2 ; nameref _vec2="$2" # Input vector 2

typeset _vec3 ; nameref _vec3="$3" # Input vector 3

typeset _vect ; typeset -a _vect # temp vector

_crossprod _vec2 _vec3 _vect # (B x C)

echo $(_dotprod _vec1 _vect) # A • (B x C)

}

# # Function _vect3prod(vec1, vec2, vec3, vec) - Return the (vector) vector triple product of 3 vectors

#

function _vect3prod {

typeset _vec1 ; nameref _vec1="$1" # Input vector 1

typeset _vec2 ; nameref _vec2="$2" # Input vector 2

typeset _vec3 ; nameref _vec3="$3" # Input vector 3

typeset _vec4 ; nameref _vec4="$4" # Output vector

typeset _vect ; typeset -a _vect # temp vector

_crossprod _vec2 _vec3 _vect # (B x C)

_crossprod _vec1 _vect _vec4 # A x (B x C)

}

######

# main #

######

print "The dot product A • B = $(_dotprod A B)"

typeset -a arr

_crossprod A B arr

print "The cross product A x B = ( ${arr[@]} )"

print "The scalar triple product A • (B x C) = $(_scal3prod A B C)"

typeset -m crossprod=arr ; typeset -a arr

_vect3prod A B C arr

print "The vector triple product A x (B x C) = ( ${arr[@]} )"

</lang>

{{out}}<pre>

The dot product A • B = 49

The cross product A x B = ( 5 5 -7 )

The scalar triple product A • (B x C) = 6

The vector triple product A x (B x C) = ( -267 204 -3 )</pre>