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 vbitandn }
40 { $subsection vbitor }
41 { $subsection vbitxor }
42 { $subsection vlshift }
43 { $subsection vrshift }
45 { $subsection vshuffle }
46 "Inner product and norm:"
49 { $subsection norm-sq }
50 { $subsection normalize }
52 { $subsection distance }
55 { $subsection vsupremum }
56 { $subsection vinfimum }
57 { $subsection trilerp }
58 { $subsection bilerp }
60 { $subsection vnlerp }
61 { $subsection vbilerp } ;
66 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
67 { $description "Negates each element of " { $snippet "u" } "." } ;
70 { $values { "u" "a sequence of numbers" } { "v" "a sequence of non-negative real numbers" } }
71 { $description "Takes the absolute value of each element of " { $snippet "u" } "." } ;
74 { $values { "u" "a sequence of non-negative real numbers" } { "v" "a sequence of non-negative real numbers" } }
75 { $description "Takes the square root of each element of " { $snippet "u" } "." }
76 { $warning "For performance reasons, this does not work with negative inputs, unlike " { $link sqrt } "." } ;
79 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } }
80 { $description "Takes the " { $link floor } " of each element of " { $snippet "u" } "." } ;
83 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } }
84 { $description "Takes the " { $link ceiling } " of each element of " { $snippet "u" } "." } ;
87 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } }
88 { $description "Truncates each element of " { $snippet "u" } "." } ;
91 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
92 { $description "Adds " { $snippet "n" } " to each element of " { $snippet "u" } "." } ;
95 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
96 { $description "Adds " { $snippet "n" } " to each element of " { $snippet "u" } "." } ;
99 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
100 { $description "Subtracts each element of " { $snippet "u" } " from " { $snippet "n" } "." } ;
103 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
104 { $description "Subtracts " { $snippet "n" } " from each element of " { $snippet "u" } "." } ;
107 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
108 { $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
111 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
112 { $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
115 { $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
116 { $description "Divides " { $snippet "n" } " by each element of " { $snippet "u" } "." }
117 { $errors "May throw an error if a division by zero occurs; see " { $link "division-by-zero" } "." } ;
120 { $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
121 { $description "Divides each element of " { $snippet "u" } " by " { $snippet "n" } "." }
122 { $errors "May throw an error if a division by zero occurs; see " { $link "division-by-zero" } "." } ;
125 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
126 { $description "Adds " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
129 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
130 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise." } ;
133 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
134 { $description "Adds and subtracts alternate elements of " { $snippet "v" } " and " { $snippet "u" } " component-wise." }
137 "USING: math.vectors prettyprint ;"
138 "{ 1 2 3 } { 2 3 2 } v+- ."
144 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
145 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise; any components which become negative are set to zero." } ;
148 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
149 { $description "Multiplies " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
152 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
153 { $description "Divides " { $snippet "u" } " by " { $snippet "v" } " component-wise." }
154 { $errors "May throw an error if a division by zero occurs; see " { $link "division-by-zero" } "." } ;
157 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
158 { $description "Creates a sequence where each element is the maximum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
159 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 5 } { -7 6 3 } vmax ." "{ 1 6 5 }" } } ;
162 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
163 { $description "Creates a sequence where each element is the minimum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
164 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 5 } { -7 6 3 } vmin ." "{ -7 2 3 }" } } ;
167 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "x" "a real number" } }
168 { $description "Computes the dot product of two vectors." } ;
171 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
172 { $description "Adds " { $snippet "u" } " and " { $snippet "v" } " component-wise with saturation." }
176 "USING: alien.c-types math.vectors prettyprint specialized-arrays ;"
177 "SPECIALIZED-ARRAY: uchar"
178 "uchar-array{ 100 200 150 } uchar-array{ 70 70 70 } vs+ ."
179 "uchar-array{ 170 255 220 }"
181 "Without saturation:"
183 "USING: alien.c-types math.vectors prettyprint specialized-arrays ;"
184 "SPECIALIZED-ARRAY: uchar"
185 "uchar-array{ 100 200 150 } uchar-array{ 70 70 70 } v+ ."
186 "uchar-array{ 170 14 220 }"
191 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
192 { $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise with saturation." } ;
195 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
196 { $description "Multiplies " { $snippet "u" } " and " { $snippet "v" } " component-wise with saturation." } ;
199 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
200 { $description "Takes the bitwise and of " { $snippet "u" } " and " { $snippet "v" } " component-wise." }
201 { $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." } ;
204 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
205 { $description "Takes the bitwise and-not of " { $snippet "u" } " and " { $snippet "v" } " component-wise, where " { $snippet "x and-not y" } " is defined as " { $snippet "not(x) and y" } "." }
206 { $notes "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." } ;
209 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
210 { $description "Takes the bitwise or of " { $snippet "u" } " and " { $snippet "v" } " component-wise." }
211 { $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." } ;
214 { $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
215 { $description "Takes the bitwise exclusive or of " { $snippet "u" } " and " { $snippet "v" } " component-wise." }
216 { $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." } ;
219 { $values { "u" "a sequence of integers" } { "n" "a non-negative integer" } { "w" "a sequence of integers" } }
220 { $description "Shifts each element of " { $snippet "u" } " to the left by " { $snippet "n" } " bits." }
221 { $notes "Undefined behavior will result if " { $snippet "n" } " is negative." } ;
224 { $values { "u" "a sequence of integers" } { "n" "a non-negative integer" } { "w" "a sequence of integers" } }
225 { $description "Shifts each element of " { $snippet "u" } " to the right by " { $snippet "n" } " bits." }
226 { $notes "Undefined behavior will result if " { $snippet "n" } " is negative." } ;
229 { $values { "u" "a SIMD array" } { "n" "a non-negative integer" } { "w" "a SIMD array" } }
230 { $description "Shifts the entire SIMD array to the left by " { $snippet "n" } " bytes. This word may only be used in a context where the compiler can statically infer that the input is a SIMD array." } ;
233 { $values { "u" "a SIMD array" } { "n" "a non-negative integer" } { "w" "a SIMD array" } }
234 { $description "Shifts the entire SIMD array to the right by " { $snippet "n" } " bytes. This word may only be used in a context where the compiler can statically infer that the input is a SIMD array." } ;
237 { $values { "u" "a SIMD array" } { "n" "a non-negative integer" } { "v" "a SIMD array" } }
238 { $description "Outputs a new SIMD array of the same type as " { $snippet "u" } " where every element is equal to the " { $snippet "n" } "th element of " { $snippet "u" } "." }
241 "USING: alien.c-types math.vectors math.vectors.simd" "prettyprint ;"
243 "int-4{ 69 42 911 13 } 2 vbroadcast ."
244 "int-4{ 911 911 911 911 }"
249 { $values { "u" "a SIMD array" } { "perm" "an array of integers" } { "v" "a SIMD array" } }
250 { $description "Permutes the elements of a SIMD array. Duplicate entries are allowed in the permutation." }
253 "USING: alien.c-types math.vectors math.vectors.simd" "prettyprint ;"
255 "int-4{ 69 42 911 13 } { 1 3 2 3 } vshuffle ."
256 "int-4{ 42 13 911 13 }"
261 { $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
262 { $description "Computes the squared length of a mathematical vector." } ;
265 { $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
266 { $description "Computes the length of a mathematical vector." } ;
269 { $values { "u" "a sequence of numbers, not all zero" } { "v" "a sequence of numbers" } }
270 { $description "Outputs a vector with the same direction as " { $snippet "u" } " but length 1." } ;
273 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
274 { $description "Outputs the Euclidean distance between two vectors." } ;
277 { $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "axis" "a sequence of 0/1" } { "w" "a sequence of numbers" } }
278 { $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." }
279 { $examples { $example "USING: math.vectors prettyprint ;" "{ 1 2 3 } { 4 5 6 } { 0 1 0 } set-axis ." "{ 1 5 3 }" } } ;
281 { 2map v+ v- v* v/ } related-words
283 { 2reduce v. } related-words
285 { vs+ vs- vs* } related-words