107 lines
4.9 KiB
Factor
Executable File
107 lines
4.9 KiB
Factor
Executable File
USING: help.markup help.syntax math sequences ;
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IN: math.vectors
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ARTICLE: "math-vectors" "Vector arithmetic"
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"Any Factor sequence can be used to represent a mathematical vector."
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$nl
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"Acting on vectors by a scalar:"
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{ $subsection vneg }
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{ $subsection v*n }
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{ $subsection n*v }
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{ $subsection v/n }
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{ $subsection n/v }
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"Combining two vectors to form another vector with " { $link 2map } ":"
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{ $subsection v+ }
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{ $subsection v- }
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{ $subsection v* }
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{ $subsection v/ }
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{ $subsection vmax }
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{ $subsection vmin }
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"Inner product and norm:"
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{ $subsection v. }
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{ $subsection norm }
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{ $subsection norm-sq }
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{ $subsection normalize } ;
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ABOUT: "math-vectors"
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HELP: vneg
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{ $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
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{ $description "Negates each element of " { $snippet "u" } "." } ;
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HELP: n*v
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{ $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
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{ $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
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HELP: v*n
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{ $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
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{ $description "Multiplies each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
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HELP: n/v
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{ $values { "n" "a number" } { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } }
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{ $description "Divides " { $snippet "n" } " by each element of " { $snippet "u" } "." } ;
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HELP: v/n
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{ $values { "u" "a sequence of numbers" } { "n" "a number" } { "v" "a sequence of numbers" } }
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{ $description "Divides each element of " { $snippet "u" } " by " { $snippet "n" } "." } ;
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HELP: v+
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{ $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
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{ $description "Adds " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
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HELP: v-
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{ $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
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{ $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise." } ;
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HELP: [v-]
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{ $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
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{ $description "Subtracts " { $snippet "v" } " from " { $snippet "u" } " component-wise; any components which become negative are set to zero." } ;
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HELP: v*
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{ $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
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{ $description "Multiplies " { $snippet "u" } " and " { $snippet "v" } " component-wise." } ;
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HELP: v/
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{ $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "w" "a sequence of numbers" } }
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{ $description "Divides " { $snippet "u" } " by " { $snippet "v" } " component-wise." }
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{ $errors "Throws an error if an integer division by zero occurs." } ;
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HELP: vmax
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{ $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
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{ $description "Creates a sequence where each element is the maximum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
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{ $examples { $example "USE: math.vectors" "{ 1 2 5 } { -7 6 3 } vmax ." "{ 1 6 5 }" } } ;
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HELP: vmin
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{ $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "w" "a sequence of real numbers" } }
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{ $description "Creates a sequence where each element is the minimum of the corresponding elements from " { $snippet "u" } " andd " { $snippet "v" } "." }
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{ $examples { $example "USE: math.vectors" "{ 1 2 5 } { -7 6 3 } vmin ." "{ -7 2 3 }" } } ;
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HELP: v.
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{ $values { "u" "a sequence of real numbers" } { "v" "a sequence of real numbers" } { "x" "a real number" } }
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{ $description "Computes the real-valued dot product." }
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{ $notes
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"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:"
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{ $snippet "0 [ conjugate * + ] 2reduce" }
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} ;
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HELP: norm-sq
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{ $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
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{ $description "Computes the squared length of a mathematical vector." } ;
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HELP: norm
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{ $values { "v" "a sequence of numbers" } { "x" "a non-negative real number" } }
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{ $description "Computes the length of a mathematical vector." } ;
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HELP: normalize
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{ $values { "u" "a sequence of numbers, not all zero" } { "v" "a sequence of numbers" } }
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{ $description "Outputs a vector with the same direction as " { $snippet "u" } " but length 1." } ;
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HELP: set-axis
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{ $values { "u" "a sequence of numbers" } { "v" "a sequence of numbers" } { "axis" "a sequence of 0/1" } { "w" "a sequence of numbers" } }
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{ $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." }
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{ $examples { $example "USE: math.vectors" "{ 1 2 3 } { 4 5 6 } { 0 1 0 } set-axis ." "{ 1 5 3 }" } } ;
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{ 2map v+ v- v* v/ } related-words
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{ 2reduce v. } related-words
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