1 USING: help.markup help.syntax math math.functions sequences ;
4 ARTICLE: "math-vectors" "Vector arithmetic"
5 "Any Factor sequence can be used to represent a mathematical vector, however for best performance, the sequences defined by the " { $vocab-link "specialized-arrays" } " and " { $vocab-link "math.vectors.simd" } " vocabularies should be used."
7 "Acting on vectors by a scalar:"
17 "Vector unary operations:"
21 { $subsection vfloor }
22 { $subsection vceiling }
23 { $subsection vtruncate }
24 "Vector/vector binary operations:"
30 "Saturated arithmetic (only on " { $link "specialized-arrays" } "):"
38 { $subsection vbitand }
39 { $subsection vbitor }
40 { $subsection vbitxor }
41 { $subsection vlshift }
42 { $subsection vrshift }
43 "Inner product and norm:"
46 { $subsection norm-sq }
47 { $subsection normalize }
49 { $subsection distance }
52 { $subsection vsupremum }
53 { $subsection vinfimum }
54 { $subsection trilerp }
55 { $subsection bilerp }
57 { $subsection vnlerp }
58 { $subsection vbilerp } ;
63 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
64 { $description "Negates each element of " { $snippet "u" } "." } ;
67 { $values { "u" "a sequence of numbers" } { "v" "a sequence of non-negative real numbers" } }
68 { $description "Takes the absolute value of each element of " { $snippet "u" } "." } ;
71 { $values { "u" "a sequence of non-negative real numbers" } { "v" "a sequence of non-negative real numbers" } }
72 { $description "Takes the square root of each element of " { $snippet "u" } "." }
73 { $warning "For performance reasons, this does not work with negative inputs, unlike " { $link sqrt } "." } ;
76 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } }
77 { $description "Takes the " { $link floor } " of each element of " { $snippet "u" } "." } ;
80 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } }
81 { $description "Takes the " { $link ceiling } " of each element of " { $snippet "u" } "." } ;
84 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } }
85 { $description "Truncates each element of " { $snippet "u" } "." } ;
88 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
89 { $description "Adds " { $snippet "n" } " to each element of " { $snippet "u" } "." } ;
92 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
93 { $description "Adds " { $snippet "n" } " to each element of " { $snippet "u" } "." } ;
96 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
97 { $description "Subtracts each element of " { $snippet "u" } " from " { $snippet "n" } "." } ;
100 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
101 { $description "Subtracts " { $snippet "n" } " from each element of " { $snippet "u" } "." } ;
104 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
105 { $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
108 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
109 { $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
112 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
113 { $description "Divides " { $snippet "n" } " by each element of " { $snippet "u" } "." }
114 { $errors "May throw an error if a division by zero occurs; see " { $link "division-by-zero" } "." } ;
117 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
118 { $description "Divides each element of " { $snippet "u" } " by " { $snippet "n" } "." }
119 { $errors "May throw an error if a division by zero occurs; see " { $link "division-by-zero" } "." } ;
122 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
123 { $description "Adds " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
126 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
127 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise." } ;
130 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
131 { $description "Adds and subtracts alternate elements of " { $snippet "v" } " and " { $snippet "u" } " component-wise." }
134 "USING: math.vectors prettyprint ;"
135 "{ 1 2 3 } { 2 3 2 } v+- ."
141 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
142 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise; any components which become negative are set to zero." } ;
145 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
146 { $description "Multiplies " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
149 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
150 { $description "Divides " { $snippet "u" } " by " { $snippet "v" } " component-wise." }
151 { $errors "May throw an error if a division by zero occurs; see " { $link "division-by-zero" } "." } ;
154 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
155 { $description "Creates a sequence where each element is the maximum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
156 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 5 } { -7 6 3 } vmax ." "{ 1 6 5 }" } } ;
159 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
160 { $description "Creates a sequence where each element is the minimum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
161 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 5 } { -7 6 3 } vmin ." "{ -7 2 3 }" } } ;
164 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "x" "a real number" } }
165 { $description "Computes the dot product of two vectors." } ;
168 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
169 { $description "Adds " { $snippet "u" } " and " { $snippet "v" } " component-wise with saturation." }
173 "USING: math.vectors prettyprint specialized-arrays ;"
174 "SPECIALIZED-ARRAY: uchar"
175 "uchar-array{ 100 200 150 } uchar-array{ 70 70 70 } vs+ ."
176 "uchar-array{ 170 255 220 }"
178 "Without saturation:"
180 "USING: math.vectors prettyprint specialized-arrays ;"
181 "SPECIALIZED-ARRAY: uchar"
182 "uchar-array{ 100 200 150 } uchar-array{ 70 70 70 } v+ ."
183 "uchar-array{ 170 14 220 }"
188 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
189 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise with saturation." } ;
192 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
193 { $description "Multiplies " { $snippet "u" } " and " { $snippet "v" } " component-wise with saturation." } ;
196 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
197 { $description "Takes the bitwise and of " { $snippet "u" } " and " { $snippet "v" } " component-wise." }
198 { $notes "Unlike " { $link bitand } ", this word may be used on a specialized array of floats or doubles, in which case the bitwise representation of the floating point numbers is operated upon." } ;
201 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
202 { $description "Takes the bitwise or of " { $snippet "u" } " and " { $snippet "v" } " component-wise." }
203 { $notes "Unlike " { $link bitor } ", this word may be used on a specialized array of floats or doubles, in which case the bitwise representation of the floating point numbers is operated upon." } ;
206 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
207 { $description "Takes the bitwise exclusive or of " { $snippet "u" } " and " { $snippet "v" } " component-wise." }
208 { $notes "Unlike " { $link bitxor } ", this word may be used on a specialized array of floats or doubles, in which case the bitwise representation of the floating point numbers is operated upon." } ;
211 { $values { "u" "a sequence of integers" } { "n" "a non-negative integer" } { "w" "a sequence of integers" } }
212 { $description "Shifts each element of " { $snippet "u" } " to the left by " { $snippet "n" } " bits." } ;
215 { $values { "u" "a sequence of integers" } { "n" "a non-negative integer" } { "w" "a sequence of integers" } }
216 { $description "Shifts each element of " { $snippet "u" } " to the right by " { $snippet "n" } " bits." } ;
219 { $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
220 { $description "Computes the squared length of a mathematical vector." } ;
223 { $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
224 { $description "Computes the length of a mathematical vector." } ;
227 { $values { "u" "a sequence of numbers, not all zero" } { "v" "a sequence of numbers" } }
228 { $description "Outputs a vector with the same direction as " { $snippet "u" } " but length 1." } ;
231 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
232 { $description "Outputs the Euclidean distance between two vectors." } ;
235 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "axis" "a sequence of 0/1" } { "w" "a sequence of numbers" } }
236 { $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." }
237 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 3 } { 4 5 6 } { 0 1 0 } set-axis ." "{ 1 5 3 }" } } ;
239 { 2map v+ v- v* v/ } related-words
241 { 2reduce v. } related-words
243 { vs+ vs- vs* } related-words