1 USING: help.markup help.syntax math sequences ;
4 ARTICLE: "math-vectors" "Vector arithmetic"
5 "Any Factor sequence can be used to represent a mathematical vector."
7 "Acting on vectors by a scalar:"
13 "Combining two vectors to form another vector with " { $link 2map } ":"
20 "Inner product and norm:"
23 { $subsection norm-sq }
24 { $subsection normalize } ;
29 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
30 { $description "Negates each element of " { $snippet "u" } "." } ;
33 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
34 { $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
37 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
38 { $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
41 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
42 { $description "Divides " { $snippet "n" } " by each element of " { $snippet "u" } "." } ;
45 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
46 { $description "Divides each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
49 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
50 { $description "Adds " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
53 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
54 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise." } ;
57 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
58 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise; any components which become negative are set to zero." } ;
61 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
62 { $description "Multiplies " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
65 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
66 { $description "Divides " { $snippet "u" } " by " { $snippet "v" } " component-wise." }
67 { $errors "Throws an error if an integer division by zero occurs." } ;
70 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
71 { $description "Creates a sequence where each element is the maximum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
72 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 5 } { -7 6 3 } vmax ." "{ 1 6 5 }" } } ;
75 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
76 { $description "Creates a sequence where each element is the minimum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
77 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 5 } { -7 6 3 } vmin ." "{ -7 2 3 }" } } ;
80 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "x" "a real number" } }
81 { $description "Computes the real-valued dot product." }
83 "This word can also take complex number sequences as input, however mathematically it will compute the wrong result. The complex-valued dot product is defined differently:"
84 { $snippet "0 [ conjugate * + ] 2reduce" }
88 { $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
89 { $description "Computes the squared length of a mathematical vector." } ;
92 { $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
93 { $description "Computes the length of a mathematical vector." } ;
96 { $values { "u" "a sequence of numbers, not all zero" } { "v" "a sequence of numbers" } }
97 { $description "Outputs a vector with the same direction as " { $snippet "u" } " but length 1." } ;
100 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "axis" "a sequence of 0/1" } { "w" "a sequence of numbers" } }
101 { $description "Using " { $snippet "w" } " as a template, creates a new sequence containing corresponding elements from " { $snippet "u" } " in place of 0, and corresponding elements from " { $snippet "v" } " in place of 1." }
102 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 3 } { 4 5 6 } { 0 1 0 } set-axis ." "{ 1 5 3 }" } } ;
104 { 2map v+ v- v* v/ } related-words
106 { 2reduce v. } related-words