f5fa93572d
* Gram-Schmidt using vector type * QR decomposition * Operator 1-norm and maximum norm; stub for 2-norm and angle between subspaces (`matrix-basis-angle') * `matrix-absolute-error' and `matrix-relative-error'; also predicates based on them, such as `matrix-identity?' * Lots of shuffling code about * Types that can have contracts, and an exhaustive test to make sure every value exported by `math/matrix' has a contract when used in untyped code * Some more tests (still needs some)
58 lines
2.2 KiB
Racket
58 lines
2.2 KiB
Racket
#lang typed/racket/base
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(require racket/fixnum
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racket/list
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"matrix-types.rkt"
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"matrix-basic.rkt"
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"matrix-gauss-elim.rkt"
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"utils.rkt"
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"../array/array-indexing.rkt"
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"../array/array-constructors.rkt")
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(provide
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matrix-rank
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matrix-nullity
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matrix-col-space)
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(: matrix-rank : (Matrix Number) -> Index)
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;; Returns the dimension of the column space (equiv. row space) of M
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(define (matrix-rank M)
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(define n (matrix-num-cols M))
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(define-values (_ cols-without-pivot) (matrix-gauss-elim M))
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(assert (- n (length cols-without-pivot)) index?))
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(: matrix-nullity : (Matrix Number) -> Index)
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;; Returns the dimension of the null space of M
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(define (matrix-nullity M)
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(define-values (_ cols-without-pivot)
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(matrix-gauss-elim (ensure-matrix 'matrix-nullity M)))
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(length cols-without-pivot))
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(: maybe-cons-submatrix (All (A) ((Matrix A) Nonnegative-Fixnum Nonnegative-Fixnum (Listof (Matrix A))
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-> (Listof (Matrix A)))))
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(define (maybe-cons-submatrix M j0 j1 Bs)
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(cond [(= j0 j1) Bs]
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[else (cons (submatrix M (::) (:: j0 j1)) Bs)]))
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(: matrix-col-space (All (A) (case-> ((Matrix Real) -> (Matrix Real))
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((Matrix Real) (-> A) -> (U A (Matrix Real)))
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((Matrix Number) -> (Matrix Number))
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((Matrix Number) (-> A) -> (U A (Matrix Number))))))
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(define matrix-col-space
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(case-lambda
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[(M) (matrix-col-space M (λ () (make-array (vector 0 (matrix-num-cols M)) 0)))]
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[(M fail)
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(define n (matrix-num-cols M))
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(define-values (_ wps) (matrix-gauss-elim M))
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(cond [(empty? wps) M]
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[(= (length wps) n) (fail)]
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[else
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(define next-j (first wps))
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(define Bs (maybe-cons-submatrix M 0 next-j empty))
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(let loop ([#{j : Index} next-j] [wps (rest wps)] [Bs Bs])
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(cond [(empty? wps)
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(matrix-augment (reverse (maybe-cons-submatrix M (fx+ j 1) n Bs)))]
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[else
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(define next-j (first wps))
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(loop next-j (rest wps) (maybe-cons-submatrix M (fx+ j 1) next-j Bs))]))])]))
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