-! Copyright (C) 2005, 2010, 2018 Slava Pestov, Joe Groff, and Cat Stevens.
+! Copyright (C) 2005, 2010, 2018, 2020 Slava Pestov, Joe Groff, and Cat Stevens.
USING: accessors arrays assocs generic.single formatting locals help.markup help.markup.private help.syntax io
kernel math math.functions math.order math.ratios math.vectors opengl.gl prettyprint
sequences sequences.generalizations urls ;
} { $subsections
main-diagonal
anti-diagonal
+}
+"The following matrix norms are provided in the 𝑙ₚ vector space; these words are equivalent to ∥･∥ₚ for " { $snippet "p = 1, 2, ∞, n" } ", respectively:"
+{ $subsections
+ m-1norm
+ m-infinity-norm
+ frobenius-norm
+ matrix-p-norm-entrywise
+ matrix-p-norm
} ;
! PREDICATE CLASSES
}
} ;
+HELP: >square-matrix
+{ $values { "m" matrix } { "subset" square-matrix } }
+{ $description "Find only the " { $link2 square-matrix "square" } " subset of the input matrix." }
+{ $examples
+ { $example
+ "USING: math.matrices prettyprint ;"
+ "{ { 0 2 4 6 } { 1 3 5 7 } } >square-matrix ."
+ "{ { 0 2 } { 1 3 } }"
+ }
+} ;
+
HELP: matrix-map
{ $values { "matrix" matrix } { "quot" { $quotation ( ... elt -- ... elt' ) } } { "matrix'" matrix } }
{ $description "Apply the quotation to every element of the matrix." }
}
} ;
-HELP: mnorm
-{ $values { "m" matrix } { "m'" matrix } }
-{ $description "Normalize a matrix. Each element from the input matrix is computed as a fraction of the maximum element. The maximum element becomes " { $snippet "1/1" } "." }
-{ $notelist
- $2d-only-note
- { $matrix-scalar-note max abs / }
-}
+HELP: m-1norm
+{ $values { "m" matrix } { "n" number } }
+{ $description "Find the size of a matrix in 𝑙₁ (" { $snippet "L^₁" } ") vector space, usually written ∥･∥₁."
+$nl "This is the matrix norm when " { $snippet "p=1" } ", and is the overall maximum of the sums of the columns." }
+{ $notelist { $equiv-word-note "transpose" m-infinity-norm } }
{ $examples
{ $example
"USING: math.matrices prettyprint ;"
- "{ { 5 9 } { 15 17 } } mnorm ."
- "{ { 5/17 9/17 } { 15/17 1 } }"
+ "{ { 2 -2 1 } { 1 3 -1 } { 2 -4 2 } } m-1norm ."
+ "9"
}
} ;
HELP: m-infinity-norm
-{ $values { "m" matrix } { "n" number } } ;
-
-HELP: m-1norm
-{ $values { "m" matrix } { "n" number } } ;
+{ $values { "m" matrix } { "n" number } }
+{ $description "Find the size of a matrix, in 𝑙∞ (" { $snippet "L^∞" } ") vector space, usually written ∥･∥∞."
+$nl "This is the matrix norm when " { $snippet "p=∞" } ", and is the overall maximum of the sums of the rows." }
+{ $notelist { $equiv-word-note "transpose" m-1norm } }
+{ $examples
+ { $example
+ "USING: math.matrices prettyprint ;"
+ "{ { 2 -2 1 } { 1 3 -1 } { 2 -4 2 } } m-infinity-norm ."
+ "8"
+ }
+} ;
HELP: frobenius-norm
{ $values { "m" matrix } { "n" number } }
-{ $notes "Also known as the Hilbert-Schmidt norm." } ;
+{ $description "Find the size of a matrix in 𝑙₂ (" { $snippet "L^2" } ") vector space, usually written ∥･∥₂ₚ."
+$nl "This is the matrix norm when " { $snippet "p=2" } ", and is the square root of the sums of the squares of all the elements of the matrix." }
+{ $notelist
+ { "This norm is sometimes called the Hilbert-Schmidt norm." }
+ { "Because " $snippet { "p=2" } ", this word could be named " { $snippet "m-2norm" } "." }
+}
+{ $examples
+ { $example
+ "USING: math.matrices prettyprint ;"
+ "{ { 1 1 } { 1 1 } } frobenius-norm ."
+ "2.0"
+ }
+} ;
-HELP: >square-matrix
-{ $values { "m" matrix } { "subset" square-matrix } }
-{ $description "Find only the " { $link2 square-matrix "square" } " subset of the input matrix." }
+{ m-1norm m-infinity-norm frobenius-norm } related-words
+
+HELP: matrix-p-q-norm
+{ $values { "m" matrix } { "p" "positive real number" } { "q" "positive real number" } { "n" "non-negative real number" } }
+{ $description "Find the size of a matrix in " { $snippet "L^p,q" } " vector space."
+$nl "This is the matrix norm for any " { $snippet "p, q ≥ 1" } ". It is still an entry-wise norm, like " { $link matrix-p-norm-entrywise } "." }
{ $examples
+ "Equivalent to " { $link frobenius-norm } " for " { $snippet "p = q = 2 " } ":"
{ $example
"USING: math.matrices prettyprint ;"
- "{ { 0 2 4 6 } { 1 3 5 7 } } >square-matrix ."
- "{ { 0 2 } { 1 3 } }"
+ "{ { 1 1 } { 1 1 } } 2 2 matrix-p-q-norm ."
+ "2.0"
+ }
+} ;
+
+HELP: matrix-p-norm-entrywise
+{ $values { "m" matrix } { "p" "positive real number" } { "n" "non-negative real number" } }
+{ $description "Find the entry-wise norm of a matrix, in 𝑙ₚ (" { $snippet "L^p" } ") vector space." }
+{ $notes "This word is distinct from a Schatten p-norm, as well as any of " { $links m-1norm frobenius-norm m-infinity-norm } "." }
+{ $examples
+ { $example
+ "USING: math.matrices prettyprint ;"
+ "4 4 1 <matrix> 2 matrix-p-norm-entrywise ."
+ "4.0"
+ }
+} ;
+
+HELP: matrix-p-norm
+{ $values { "m" matrix } { "p" "positive real number" } { "n" "non-negative real number" } }
+{ $description "Find the size of a matrix in 𝑙ₚ (" { $snippet "L^p" } ") vector space, usually written ∥･∥ₚ. For " { $snippet "p ≠ 1, 2, ∞" } ", this is an \"entry-wise\" norm." }
+{ $examples
+ "Calls " { $link m-1norm } ":"
+ { $example
+ "USING: math.matrices prettyprint ;"
+ "4 4 1 <matrix> 1 matrix-p-norm ."
+ "4"
+ }
+ "Falls back to " { $link matrix-p-norm-entrywise } ":"
+ { $example
+ "USING: math.functions math.matrices prettyprint ;"
+ "2 2 3 <matrix> 1.5 matrix-p-norm 7.559 10e-4 ~ ."
+ "t"
+ }
+} ;
+
+{ matrix-p-norm matrix-p-norm-entrywise } related-words
+{ matrix-p-norm matrix-p-q-norm } related-words
+
+HELP: normalize-matrix
+{ $values { "m" matrix } { "m'" matrix } }
+{ $description "Normalize a matrix. Each element from the input matrix is computed as a fraction of the maximum element. The maximum element becomes " { $snippet "1/1" } "." }
+{ $notelist
+ $2d-only-note
+ { $matrix-scalar-note max abs / }
+}
+{ $examples
+ { $example
+ "USING: math.matrices prettyprint ;"
+ "{ { 5 9 } { 15 17 } } normalize-matrix ."
+ "{ { 5/17 9/17 } { 15/17 1 } }"
}
} ;
-! Copyright (C) 2005, 2010, 2018 Slava Pestov, Joe Groff, and Cat Stevens.
+! Copyright (C) 2005, 2010, 2018, 2020 Slava Pestov, Joe Groff, and Cat Stevens.
USING: arrays assocs combinators.short-circuit grouping kernel
math math.statistics sequences sequences.deep tools.test ;
IN: math.matrices
mdot
] unit-test
-
-! TODO: note: merge conflict from HEAD contained the following
-! ------------------------
-! predicates
-
-{ t } [ { } square-matrix? ] unit-test
-{ t } [ { { 1 } } square-matrix? ] unit-test
-{ t } [ { { 1 2 } { 3 4 } } square-matrix? ] unit-test
-{ f } [ { { 1 } { 2 3 } } square-matrix? ] unit-test
-{ f } [ { { 1 2 } } square-matrix? ] unit-test
-
{ 9 }
[ { { 2 -2 1 } { 1 3 -1 } { 2 -4 2 } } m-1norm ] unit-test
{ 2.0 }
[ { { 1 1 } { 1 1 } } frobenius-norm ] unit-test
-! from "intermediate commit"
-! any deep-empty matrix is null
-! it doesn't make any sense for { } to be null while { { } } to be considered nonnull
-{ t } [ {
- { }
- { { } }
- { { { } } }
- { { } { } { } }
- { { { } } { { { } } } }
-} [ null-matrix? ] all?
-] unit-test
-{ f } [ {
- { 1 2 }
- { { 1 2 } }
- { { 1 } { 2 } }
- { { { 1 } } { 2 } { } }
-} [ null-matrix? ] any?
-] unit-test
+{ 10e-8 }
+[
+ 5.4772255
+ { { 1 2 } { 3 4 } } frobenius-norm
+] unit-test~
-{ t } [ 10 dup <zero-matrix> zero-matrix? ] unit-test
-{ t } [ 10 10 15 <simple-eye> zero-matrix? ] unit-test
-{ t } [ 0 dup <zero-matrix> null-matrix? ] unit-test
-{ f } [ 0 dup <zero-matrix> zero-matrix? ] unit-test
-{ f } [ 4 <identity-matrix> zero-matrix? ] unit-test
+{ 10e-6 }
+[
+ 36.94590
+ { { 1 2 } { 4 8 } { 16 32 } } frobenius-norm
+] unit-test~
-{ t } [ { } regular-matrix? ] unit-test
-{ t } [ { { } } regular-matrix? ] unit-test
-{ t } [ { { 1 2 } } regular-matrix? ] unit-test
-{ t } [ { { 1 2 } { 3 4 } } regular-matrix? ] unit-test
-{ t } [ { { 1 } { 3 } } regular-matrix? ] unit-test
-{ f } [ { { 1 2 } { 3 } } regular-matrix? ] unit-test
-{ f } [ { { 1 } { 3 2 } } regular-matrix? ] unit-test
-! TODO: note: lines since last HEAD comment were deleted in "fix more code and add more rigorous tests"
+! equivalent to frobenius for p = q = 2
+{ 2.0 }
+[ { { 1 1 } { 1 1 } } 2 2 matrix-p-q-norm ] unit-test
+
+{ 10e-7 }
+[
+ 33.456466
+ { { 1 2 } { 4 8 } { 16 32 } } 3 matrix-p-norm-entrywise
+] unit-test~
+
+{ { { -1 0 } { 0 0 } } }
+[ { { -2 0 } { 0 0 } } normalize-matrix ] unit-test
+
+{ { { -1 0 } { 0 1/2 } } }
+[ { { -2 0 } { 0 1 } } normalize-matrix ] unit-test
+
+{ t }
+[ 3 3 <zero-matrix> dup normalize-matrix = ] unit-test
! diagonals
-! Copyright (C) 2005, 2010, 2018 Slava Pestov, Joe Groff, and Cat Stevens.
+! Copyright (C) 2005, 2010, 2018, 2020 Slava Pestov, Joe Groff, and Cat Stevens.
! See http://factorcode.org/license.txt for BSD license.
USING: accessors arrays classes.singleton columns combinators
combinators.short-circuit combinators.smart formatting fry
grouping kernel locals math math.bits math.functions math.order
math.private math.ranges math.statistics math.vectors
-math.vectors.private sequences sequences.deep sequences.private
-slots.private summary ;
+math.vectors.private sequences sequences.deep sequences.extras
+sequences.private slots.private summary ;
IN: math.matrices
! defined here because of issue #1943
: mmin ( m -- n ) [ 1/0. ] dip [ [ min ] each ] each ;
: mmax ( m -- n ) [ -1/0. ] dip [ [ max ] each ] each ;
-: mnorm ( m -- m' ) dup mmax abs m/n ;
-: m-infinity-norm ( m -- n ) [ [ abs ] map-sum ] map supremum ;
-: m-1norm ( m -- n ) flip m-infinity-norm ;
-: frobenius-norm ( m -- n ) [ [ sq ] map-sum ] map-sum sqrt ;
+
+: m-infinity-norm ( m -- n )
+ dup zero-matrix? [ drop 0. ] [
+ [ [ abs ] map-sum ] map supremum
+ ] if ;
+
+: m-1norm ( m -- n )
+ dup zero-matrix? [ drop 0. ] [
+ flip m-infinity-norm
+ ] if ;
+
+: frobenius-norm ( m -- n )
+ dup zero-matrix? [ drop 0. ] [
+ [ [ sq ] map-sum ] map-sum sqrt
+ ] if ;
+
+ALIAS: hilbert-schmidt-norm frobenius-norm
+
+:: matrix-p-q-norm ( m p q -- n )
+ m dup zero-matrix? [ drop 0. ] [
+ [ [ sq ] map-sum q p / ^ ] map-sum q recip ^
+ ] if ;
+
+: matrix-p-norm-entrywise ( m p -- n )
+ dup zero-matrix? [ 2drop 0. ] [
+ [ flatten1 V{ } like ] dip p-norm-default
+ ] if ;
+
+: matrix-p-norm ( m p -- n )
+ dup zero-matrix? [ 2drop 0. ] [
+ {
+ { [ dup 1 = ] [ drop m-1norm ] }
+ { [ dup 2 = ] [ drop frobenius-norm ] }
+ { [ dup fp-infinity? ] [ drop m-infinity-norm ] }
+ [ matrix-p-norm-entrywise ]
+ } cond
+ ] if ;
+
+: normalize-matrix ( m -- m' )
+ dup zero-matrix? [ ] [
+ dup mabs mmax m/n
+ ] if ;
! well-defined for square matrices; but works on nonsquare too
: main-diagonal ( matrix -- seq )
projects / factor.git / commitdiff