chez-scmutils/scmutils/kernel/vectors.scm

#| -*-Scheme-*-

Copyright (C) 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994,
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    2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Massachusetts
    Institute of Technology

This file is part of MIT/GNU Scheme.

MIT/GNU Scheme is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at
your option) any later version.

MIT/GNU Scheme is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with MIT/GNU Scheme; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
USA.

|#

;;;;            Vectors

(declare (usual-integrations))

(define (v:type v) vector-type-tag)
(define (v:type-predicate v) vector-quantity?)

;;; This file makes the identification of the Scheme VECTOR data
;;; type with mathematical n-dimensional vectors.  These are 
;;; interpreted as column vectors by the matrix package.

;;; Thus we inherit the constructors VECTOR and MAKE-VECTOR,
;;; the selectors VECTOR-LENGTH and VECTOR-REF,
;;; the mutator VECTOR-SET!, and zero-based indexing.  
;;; We also get the iterator MAKE-INITIALIZED-VECTOR, 
;;; and the predicate VECTOR?

(define-integrable v:generate make-initialized-vector)
(define-integrable vector:generate make-initialized-vector)
(define-integrable v:dimension vector-length)

(define* ((v:elementwise f) . vectors)
  (assert (and (not (null? vectors))
	       (for-all? vectors vector?)))
  (let ((n (v:dimension (car vectors))))
    (assert (for-all? (cdr vectors)
	      (lambda (m)
		(fix:= (v:dimension m) n))))
    (v:generate
     (vector-length (car vectors))
     (lambda (i)
       (g:apply f
		(map (lambda (v) (vector-ref v i))
		     vectors))))))

(define vector:elementwise v:elementwise)


(define (v:zero? v)
  (vector-forall g:zero? v))

(define (v:make-zero n)
  (make-vector n :zero))

(define (v:zero-like v)
  (v:generate (vector-length v)
	      (lambda (i)
		(g:zero-like (vector-ref v i)))))

(define (literal-vector name dimension)
  (v:generate dimension
	      (lambda (i)
		(string->symbol
		 (string-append (symbol->string name)
				"^"
				(number->string i))))))

(define (v:make-basis-unit n i)	; #(0 0 ... 1 ... 0) n long, 1 in ith position
  (v:generate n (lambda (j) (if (fix:= j i) :one :zero))))

(define (v:basis-unit? v)
  (let ((n (vector-length v)))
    (let lp ((i 0) (ans #f))
      (cond ((fix:= i n) ans)
	    ((g:zero? (vector-ref v i))
	     (lp (fix:+ i 1) ans))
	    ((and (g:one? (vector-ref v i)) (not ans))
	     (lp (fix:+ i 1) i))
	    (else #f)))))


(define (vector=vector v1 v2)
  (vector-forall g:= v1 v2))

(define (vector+vector v1 v2)
  (v:generate (vector-length v1)
    (lambda (i)
      (g:+ (vector-ref v1 i)
	   (vector-ref v2 i)))))
    
(define (vector-vector v1 v2)
  (v:generate (vector-length v1)
    (lambda (i)
      (g:- (vector-ref v1 i)
	   (vector-ref v2 i)))))

(define (v:negate v)
  (v:generate (vector-length v)
    (lambda (i)
      (g:negate (vector-ref v i)))))

(define (v:scale s)
  (lambda (v)
    (v:generate (vector-length v)
      (lambda (i)
	(g:* s (vector-ref v i))))))

(define (scalar*vector s v)
  (v:generate (vector-length v)
    (lambda (i)
      (g:* s (vector-ref v i)))))

(define (vector*scalar v s)
  (v:generate (vector-length v)
    (lambda (i)
      (g:* (vector-ref v i) s))))

(define (vector/scalar v s)
  (v:generate (vector-length v)
    (lambda (i)
      (g:/ (vector-ref v i) s))))

(define (v:inner-product v1 v2)
  (assert (and (vector? v1) (vector? v2))
	  "Not vectors -- INNER-PRODUCT" (list v1 v2))
  (let ((n (v:dimension v1)))
    (assert (fix:= n (v:dimension v2))
	    "Not same dimension -- INNER-PRODUCT" (list v1 v2))
    (let lp ((i 0) (ans :zero))
      (if (fix:= i n)
	  ans
	  (lp (fix:+ i 1)
	      (g:+ ans
		   (g:* (g:conjugate (vector-ref v1 i))
			(vector-ref v2 i))))))))
    
(define (v:dot-product v1 v2)
  (assert (and (vector? v1) (vector? v2))
	  "Not vectors -- V:DOT-PRODUCT" (list v1 v2))
  (let ((n (v:dimension v1)))
    (assert (fix:= n (v:dimension v2))
	    "Not same dimension -- V:DOT-PRODUCT" (list v1 v2))
    (let lp ((i 0) (ans :zero))
      (if (fix:= i n)
	  ans
	  (lp (fix:+ i 1)
	      (g:+ ans
		   (g:* (vector-ref v1 i)
			(vector-ref v2 i))))))))


(define (v:square v)
  (v:dot-product v v))

(define (v:cube v)
  (scalar*vector (v:dot-product v v) v))

(define (euclidean-norm v)
  (g:sqrt (v:dot-product v v)))

(define (complex-norm v)
  (g:sqrt (v:inner-product v v)))

(define (maxnorm v)
  (vector-accumulate max g:magnitude :zero v))


(define (v:make-unit v)
  (scalar*vector (g:invert (euclidean-norm v))
		 v))

(define (v:unit? v)
  (g:one? (v:dot-product v v)))


(define (v:conjugate v)
  ((v:elementwise g:conjugate) v))

(define (v:cross-product v w)
  (assert (and (fix:= (vector-length v) 3)
	       (fix:= (vector-length w) 3))
	  "Cross product of non-3-dimensional vectors?"
	  (list v w))
  (let ((v0 (vector-ref v 0))
	(v1 (vector-ref v 1))
	(v2 (vector-ref v 2))
	(w0 (vector-ref w 0))
	(w1 (vector-ref w 1))
	(w2 (vector-ref w 2)))
    (vector (g:- (g:* v1 w2) (g:* v2 w1))
	    (g:- (g:* v2 w0) (g:* v0 w2))
	    (g:- (g:* v0 w1) (g:* v1 w0)))))

(define (general-inner-product addition multiplication :zero)
  (define (ip v1 v2)
    (let ((n (vector-length v1)))
      (if (not (fix:= n (vector-length v2)))
	  (error "Unequal dimensions -- INNER-PRODUCT" v1 v2))
      (if (fix:= n 0)
	  :zero
	  (let loop ((i 1)
		     (ans (multiplication (vector-ref v1 0)
					  (vector-ref v2 0))))
	    (if (fix:= i n)
		ans
		(loop (fix:+ i 1)
		      (addition ans
				(multiplication (vector-ref v1 i)
						(vector-ref v2 i)))))))))
  ip)

(define (v:apply vec args)
  (v:generate (vector-length vec)
    (lambda (i)
      (g:apply (vector-ref vec i) args))))

(define (v:arity v)
  (let ((n (vector-length v)))
    (cond ((fix:= n 0)
	   (error "I don't know the arity of the empty vector"))
	  (else
	   (let lp ((i 1) (a (g:arity (vector-ref v 0))))
	     (if (fix:= i n)
		 a
		 (let ((b (joint-arity a (g:arity (vector-ref v i)))))
		   (if b
		       (lp (+ i 1) b)
		       #f))))))))

(define (v:partial-derivative vector varspecs)
  ((v:elementwise
    (lambda (f)
      (generic:partial-derivative f varspecs)))
   vector))

(define (v:inexact? v)
  (vector-exists g:inexact? v))


(define %kernel-vectors-dummy-1
  (begin
    (assign-operation 'type                v:type            vector?)
    (assign-operation 'type-predicate      v:type-predicate  vector?)
    (assign-operation 'arity               v:arity           vector?)
    (assign-operation 'inexact?            v:inexact?        vector?)

    (assign-operation 'zero-like           v:zero-like       vector?)

    (assign-operation 'zero?               v:zero?           vector?)
    (assign-operation 'negate              v:negate          vector?)
    (assign-operation 'magnitude           complex-norm    vector?)
    (assign-operation 'abs                 euclidean-norm  vector?)
    (assign-operation 'conjugate           v:conjugate       vector?)

    (assign-operation '=           vector=vector       vector? vector?)
    (assign-operation '+           vector+vector       vector? vector?)
    (assign-operation '-           vector-vector       vector? vector?)

    (assign-operation '*           scalar*vector       scalar? vector?)
    (assign-operation '*           vector*scalar       vector? scalar?)

    (assign-operation '/           vector/scalar       vector? scalar?)

;;; subsumed by s:dot-product
;;; (assign-operation 'dot-product v:dot-product   vector? vector?)

    (assign-operation 'cross-product v:cross-product   vector? vector?)

    (assign-operation 'dimension v:dimension  vector?)))


#| ;;; Should be subsumed by deriv:pd in deriv.scm.
(assign-operation 'partial-derivative
		  v:partial-derivative
		  vector? any?)
|#

#| ;;; Should be subsumed by s:apply in structs.scm.
(assign-operation 'apply       v:apply           vector? any?)
|#

;;; Abstract vectors generalize vector quantities.

(define (abstract-vector symbol)
  (make-literal vector-type-tag symbol))

(define (av:arity v)
  ;; Default is vector of numbers.
  (get-property v 'arity *at-least-zero*))

(define (av:zero-like v)
  (let ((z (abstract-vector (list 'zero-like v))))
    (add-property! z 'zero #t)
    z))

(define* (make-vector-combination operator #:optional reverse?)
  (if (default-object? reverse?)
      (lambda operands 
	(make-combination vector-type-tag
			  operator operands))
      (lambda operands 
	(make-combination vector-type-tag
			  operator (reverse operands)))))

(define %kernel-vectors-dummy-2
  (begin
    (assign-operation 'type           v:type             abstract-vector?)
    (assign-operation 'type-predicate v:type-predicate   abstract-vector?)
    (assign-operation 'arity          av:arity           abstract-vector?)

    (assign-operation 'inexact? (has-property? 'inexact) abstract-vector?)

    (assign-operation 'zero-like      av:zero-like       abstract-vector?)

    (assign-operation 'zero?    (has-property? 'zero)    abstract-vector?)

    (assign-operation
     'negate     (make-vector-combination 'negate)     abstract-vector?)
    (assign-operation
     'magnitude  (make-vector-combination 'magnitude)  abstract-vector?)
    (assign-operation
     'abs        (make-vector-combination 'abs)        abstract-vector?)
    (assign-operation
     'conjugate  (make-vector-combination 'conjugate)  abstract-vector?)
    #|
    (assign-operation
    'derivative (make-vector-combination 'derivative) abstract-vector?)
    |#

                                        ;(assign-operation '= vector=vector abstract-vector? abstract-vector?)
    (assign-operation
     '+  (make-vector-combination '+) abstract-vector? abstract-vector?)
    (assign-operation
     '+  (make-vector-combination '+) vector?          abstract-vector?)
    (assign-operation
     '+  (make-vector-combination '+ 'r)       abstract-vector? vector?)
    
    (assign-operation
     '-  (make-vector-combination '-) abstract-vector? abstract-vector?)
    (assign-operation
     '-  (make-vector-combination '-) vector?          abstract-vector?)
    (assign-operation
     '-  (make-vector-combination '-) abstract-vector? vector?)
    
    (assign-operation
     '*  (make-numerical-combination '*)    abstract-vector? abstract-vector?)
    (assign-operation
     '*  (make-numerical-combination '*)    vector?          abstract-vector?)
    (assign-operation
     '*  (make-numerical-combination '* 'r) abstract-vector? vector?)
    (assign-operation
     '*  (make-vector-combination '*)       scalar?          abstract-vector?)
    (assign-operation
     '*  (make-vector-combination '* 'r)    abstract-vector? scalar?)
    
    (assign-operation
     '/  (make-vector-combination '/)       abstract-vector? scalar?)


    (assign-operation
     'dot-product (make-vector-combination 'dot-product)
     abstract-vector? abstract-vector?)

    (assign-operation 'partial-derivative
                      (make-vector-combination 'partial-derivative)
                      abstract-vector? any?)))

;;; I don't know what to do here -- GJS.  This is part of the literal
;;; function problem.

;(assign-operation 'apply  v:apply              abstract-vector? any?)