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+;; Calculator for GNU Emacs, part II [calc-vec.el]
+;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
+;; Written by Dave Gillespie, [email protected].
+
+;; This file is part of GNU Emacs.
+
+;; GNU Emacs is distributed in the hope that it will be useful,
+;; but WITHOUT ANY WARRANTY. No author or distributor
+;; accepts responsibility to anyone for the consequences of using it
+;; or for whether it serves any particular purpose or works at all,
+;; unless he says so in writing. Refer to the GNU Emacs General Public
+;; License for full details.
+
+;; Everyone is granted permission to copy, modify and redistribute
+;; GNU Emacs, but only under the conditions described in the
+;; GNU Emacs General Public License. A copy of this license is
+;; supposed to have been given to you along with GNU Emacs so you
+;; can know your rights and responsibilities. It should be in a
+;; file named COPYING. Among other things, the copyright notice
+;; and this notice must be preserved on all copies.
+
+
+
+;; This file is autoloaded from calc-ext.el.
+(require 'calc-ext)
+
+(require 'calc-macs)
+
+(defun calc-Need-calc-vec () nil)
+
+
+(defun calc-display-strings (n)
+ (interactive "P")
+ (calc-wrapper
+ (message (if (calc-change-mode 'calc-display-strings n t t)
+ "Displaying vectors of integers as quoted strings."
+ "Displaying vectors of integers normally.")))
+)
+
+
+(defun calc-pack (n)
+ (interactive "P")
+ (calc-wrapper
+ (let* ((nn (if n 1 2))
+ (mode (if n (prefix-numeric-value n) (calc-top-n 1)))
+ (mode (if (and (Math-vectorp mode) (cdr mode)) (cdr mode)
+ (if (integerp mode) mode
+ (error "Packing mode must be an integer or vector of integers"))))
+ (num (calc-pack-size mode))
+ (items (calc-top-list num nn)))
+ (calc-enter-result (+ nn num -1) "pack" (calc-pack-items mode items))))
+)
+
+(defun calc-pack-size (mode)
+ (cond ((consp mode)
+ (let ((size 1))
+ (while mode
+ (or (integerp (car mode)) (error "Vector of integers expected"))
+ (setq size (* size (calc-pack-size (car mode)))
+ mode (cdr mode)))
+ (if (= size 0)
+ (error "Zero dimensions not allowed")
+ size)))
+ ((>= mode 0) mode)
+ (t (or (cdr (assq mode '((-3 . 3) (-13 . 1) (-14 . 3) (-15 . 6))))
+ 2)))
+)
+
+(defun calc-pack-items (mode items)
+ (cond ((consp mode)
+ (if (cdr mode)
+ (let* ((size (calc-pack-size (cdr mode)))
+ (len (length items))
+ (new nil)
+ p row)
+ (while (> len 0)
+ (setq p (nthcdr (1- size) items)
+ row items
+ items (cdr p)
+ len (- len size))
+ (setcdr p nil)
+ (setq new (cons (calc-pack-items (cdr mode) row) new)))
+ (calc-pack-items (car mode) (nreverse new)))
+ (calc-pack-items (car mode) items)))
+ ((>= mode 0)
+ (cons 'vec items))
+ ((= mode -3)
+ (if (and (math-objvecp (car items))
+ (math-objvecp (nth 1 items))
+ (math-objvecp (nth 2 items)))
+ (if (and (math-num-integerp (car items))
+ (math-num-integerp (nth 1 items)))
+ (if (math-realp (nth 2 items))
+ (cons 'hms items)
+ (error "Seconds must be real"))
+ (error "Hours and minutes must be integers"))
+ (math-normalize (list '+
+ (list '+
+ (if (eq calc-angle-mode 'rad)
+ (list '* (car items)
+ '(hms 1 0 0))
+ (car items))
+ (list '* (nth 1 items) '(hms 0 1 0)))
+ (list '* (nth 2 items) '(hms 0 0 1))))))
+ ((= mode -13)
+ (if (math-realp (car items))
+ (cons 'date items)
+ (if (eq (car-safe (car items)) 'date)
+ (car items)
+ (if (math-objvecp (car items))
+ (error "Date value must be real")
+ (cons 'calcFunc-date items)))))
+ ((memq mode '(-14 -15))
+ (let ((p items))
+ (while (and p (math-objvecp (car p)))
+ (or (math-integerp (car p))
+ (error "Components must be integers"))
+ (setq p (cdr p)))
+ (if p
+ (cons 'calcFunc-date items)
+ (list 'date (math-dt-to-date items)))))
+ ((or (eq (car-safe (car items)) 'vec)
+ (eq (car-safe (nth 1 items)) 'vec))
+ (let* ((x (car items))
+ (vx (eq (car-safe x) 'vec))
+ (y (nth 1 items))
+ (vy (eq (car-safe y) 'vec))
+ (z nil)
+ (n (1- (length (if vx x y)))))
+ (and vx vy
+ (/= n (1- (length y)))
+ (error "Vectors must be the same length"))
+ (while (>= (setq n (1- n)) 0)
+ (setq z (cons (calc-pack-items
+ mode
+ (list (if vx (car (setq x (cdr x))) x)
+ (if vy (car (setq y (cdr y))) y)))
+ z)))
+ (cons 'vec (nreverse z))))
+ ((= mode -1)
+ (if (and (math-realp (car items)) (math-realp (nth 1 items)))
+ (cons 'cplx items)
+ (if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
+ (error "Components must be real"))
+ (math-normalize (list '+ (car items)
+ (list '* (nth 1 items) '(cplx 0 1))))))
+ ((= mode -2)
+ (if (and (math-realp (car items)) (math-anglep (nth 1 items)))
+ (cons 'polar items)
+ (if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
+ (error "Components must be real"))
+ (math-normalize (list '* (car items)
+ (if (math-anglep (nth 1 items))
+ (list 'polar 1 (nth 1 items))
+ (list 'calcFunc-exp
+ (list '*
+ (math-to-radians-2
+ (nth 1 items))
+ (list 'polar
+ 1
+ (math-quarter-circle
+ nil)))))))))
+ ((= mode -4)
+ (let ((x (car items))
+ (sigma (nth 1 items)))
+ (if (or (math-scalarp x) (not (math-objvecp x)))
+ (if (or (math-anglep sigma) (not (math-objvecp sigma)))
+ (math-make-sdev x sigma)
+ (error "Error component must be real"))
+ (error "Mean component must be real or complex"))))
+ ((= mode -5)
+ (let ((a (car items))
+ (m (nth 1 items)))
+ (if (and (math-anglep a) (math-anglep m))
+ (if (math-posp m)
+ (math-make-mod a m)
+ (error "Modulus must be positive"))
+ (if (and (math-objectp a) (math-objectp m))
+ (error "Components must be real"))
+ (list 'calcFunc-makemod a m))))
+ ((memq mode '(-6 -7 -8 -9))
+ (let ((lo (car items))
+ (hi (nth 1 items)))
+ (if (and (or (math-anglep lo) (eq (car lo) 'date)
+ (not (math-objvecp lo)))
+ (or (math-anglep hi) (eq (car hi) 'date)
+ (not (math-objvecp hi))))
+ (math-make-intv (+ mode 9) lo hi)
+ (error "Components must be real"))))
+ ((eq mode -10)
+ (if (math-zerop (nth 1 items))
+ (error "Denominator must not be zero")
+ (if (and (math-integerp (car items)) (math-integerp (nth 1 items)))
+ (math-normalize (cons 'frac items))
+ (if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
+ (error "Components must be integers"))
+ (cons 'calcFunc-fdiv items))))
+ ((memq mode '(-11 -12))
+ (if (and (math-realp (car items)) (math-integerp (nth 1 items)))
+ (calcFunc-scf (math-float (car items)) (nth 1 items))
+ (if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
+ (error "Components must be integers"))
+ (math-normalize
+ (list 'calcFunc-scf
+ (list 'calcFunc-float (car items))
+ (nth 1 items)))))
+ (t
+ (error "Invalid packing mode: %d" mode)))
+)
+
+(defun calc-unpack (mode)
+ (interactive "P")
+ (calc-wrapper
+ (let ((calc-unpack-with-type t))
+ (calc-pop-push-record-list 1 "unpk" (calc-unpack-item
+ (and mode
+ (prefix-numeric-value mode))
+ (calc-top)))))
+)
+
+(defun calc-unpack-type (item)
+ (cond ((eq (car-safe item) 'vec)
+ (1- (length item)))
+ ((eq (car-safe item) 'intv)
+ (- (nth 1 item) 9))
+ (t
+ (or (cdr (assq (car-safe item) '( (cplx . -1) (polar . -2)
+ (hms . -3) (sdev . -4) (mod . -5)
+ (frac . -10) (float . -11)
+ (date . -13) )))
+ (error "Argument must be a composite object"))))
+)
+
+(defun calc-unpack-item (mode item)
+ (cond ((not mode)
+ (if (or (and (not (memq (car-safe item) '(frac float cplx polar vec
+ hms date sdev mod
+ intv)))
+ (math-objvecp item))
+ (eq (car-safe item) 'var))
+ (error "Argument must be a composite object or function call"))
+ (if (eq (car item) 'intv)
+ (cdr (cdr item))
+ (cdr item)))
+ ((> mode 0)
+ (let ((dims nil)
+ type new row)
+ (setq item (list item))
+ (while (> mode 0)
+ (setq type (calc-unpack-type (car item))
+ dims (cons type dims)
+ new (calc-unpack-item nil (car item)))
+ (while (setq item (cdr item))
+ (or (= (calc-unpack-type (car item)) type)
+ (error "Inconsistent types or dimensions in vector elements"))
+ (setq new (append new (calc-unpack-item nil (car item)))))
+ (setq item new
+ mode (1- mode)))
+ (if (cdr dims) (setq dims (list (cons 'vec (nreverse dims)))))
+ (cond ((eq calc-unpack-with-type 'pair)
+ (list (car dims) (cons 'vec item)))
+ (calc-unpack-with-type
+ (append item dims))
+ (t item))))
+ ((eq calc-unpack-with-type 'pair)
+ (let ((calc-unpack-with-type nil))
+ (list mode (cons 'vec (calc-unpack-item mode item)))))
+ ((= mode -3)
+ (if (eq (car-safe item) 'hms)
+ (cdr item)
+ (error "Argument must be an HMS form")))
+ ((= mode -13)
+ (if (eq (car-safe item) 'date)
+ (cdr item)
+ (error "Argument must be a date form")))
+ ((= mode -14)
+ (if (eq (car-safe item) 'date)
+ (math-date-to-dt (math-floor (nth 1 item)))
+ (error "Argument must be a date form")))
+ ((= mode -15)
+ (if (eq (car-safe item) 'date)
+ (append (math-date-to-dt (nth 1 item))
+ (and (not (math-integerp (nth 1 item)))
+ (list 0 0 0)))
+ (error "Argument must be a date form")))
+ ((eq (car-safe item) 'vec)
+ (let ((x nil)
+ (y nil)
+ res)
+ (while (setq item (cdr item))
+ (setq res (calc-unpack-item mode (car item))
+ x (cons (car res) x)
+ y (cons (nth 1 res) y)))
+ (list (cons 'vec (nreverse x))
+ (cons 'vec (nreverse y)))))
+ ((= mode -1)
+ (if (eq (car-safe item) 'cplx)
+ (cdr item)
+ (if (eq (car-safe item) 'polar)
+ (cdr (math-complex item))
+ (if (Math-realp item)
+ (list item 0)
+ (error "Argument must be a complex number")))))
+ ((= mode -2)
+ (if (or (memq (car-safe item) '(cplx polar))
+ (Math-realp item))
+ (cdr (math-polar item))
+ (error "Argument must be a complex number")))
+ ((= mode -4)
+ (if (eq (car-safe item) 'sdev)
+ (cdr item)
+ (list item 0)))
+ ((= mode -5)
+ (if (eq (car-safe item) 'mod)
+ (cdr item)
+ (error "Argument must be a modulo form")))
+ ((memq mode '(-6 -7 -8 -9))
+ (if (eq (car-safe item) 'intv)
+ (cdr (cdr item))
+ (list item item)))
+ ((= mode -10)
+ (if (eq (car-safe item) 'frac)
+ (cdr item)
+ (if (Math-integerp item)
+ (list item 1)
+ (error "Argument must be a rational number"))))
+ ((= mode -11)
+ (if (eq (car-safe item) 'float)
+ (list (nth 1 item) (math-normalize (nth 2 item)))
+ (error "Expected a floating-point number")))
+ ((= mode -12)
+ (if (eq (car-safe item) 'float)
+ (list (calcFunc-mant item) (calcFunc-xpon item))
+ (error "Expected a floating-point number")))
+ (t
+ (error "Invalid unpacking mode: %d" mode)))
+)
+(setq calc-unpack-with-type nil)
+
+(defun calc-diag (n)
+ (interactive "P")
+ (calc-wrapper
+ (calc-enter-result 1 "diag" (if n
+ (list 'calcFunc-diag (calc-top-n 1)
+ (prefix-numeric-value n))
+ (list 'calcFunc-diag (calc-top-n 1)))))
+)
+
+(defun calc-ident (n)
+ (interactive "NDimension of identity matrix = ")
+ (calc-wrapper
+ (calc-enter-result 0 "idn" (if (eq n 0)
+ '(calcFunc-idn 1)
+ (list 'calcFunc-idn 1
+ (prefix-numeric-value n)))))
+)
+
+(defun calc-index (n &optional stack)
+ (interactive "NSize of vector = \nP")
+ (calc-wrapper
+ (if (consp stack)
+ (calc-enter-result 3 "indx" (cons 'calcFunc-index (calc-top-list-n 3)))
+ (calc-enter-result 0 "indx" (list 'calcFunc-index
+ (prefix-numeric-value n)))))
+)
+
+(defun calc-build-vector (n)
+ (interactive "NSize of vector = ")
+ (calc-wrapper
+ (calc-enter-result 1 "bldv" (list 'calcFunc-cvec
+ (calc-top-n 1)
+ (prefix-numeric-value n))))
+)
+
+(defun calc-cons (arg)
+ (interactive "P")
+ (calc-wrapper
+ (if (calc-is-hyperbolic)
+ (calc-binary-op "rcns" 'calcFunc-rcons arg)
+ (calc-binary-op "cons" 'calcFunc-cons arg)))
+)
+
+
+(defun calc-head (arg)
+ (interactive "P")
+ (calc-wrapper
+ (if (calc-is-inverse)
+ (if (calc-is-hyperbolic)
+ (calc-unary-op "rtai" 'calcFunc-rtail arg)
+ (calc-unary-op "tail" 'calcFunc-tail arg))
+ (if (calc-is-hyperbolic)
+ (calc-unary-op "rhed" 'calcFunc-rhead arg)
+ (calc-unary-op "head" 'calcFunc-head arg))))
+)
+
+(defun calc-tail (arg)
+ (interactive "P")
+ (calc-invert-func)
+ (calc-head arg)
+)
+
+(defun calc-vlength (arg)
+ (interactive "P")
+ (calc-wrapper
+ (if (calc-is-hyperbolic)
+ (calc-unary-op "dims" 'calcFunc-mdims arg)
+ (calc-unary-op "len" 'calcFunc-vlen arg)))
+)
+
+(defun calc-arrange-vector (n)
+ (interactive "NNumber of columns = ")
+ (calc-wrapper
+ (calc-enter-result 1 "arng" (list 'calcFunc-arrange (calc-top-n 1)
+ (prefix-numeric-value n))))
+)
+
+(defun calc-vector-find (arg)
+ (interactive "P")
+ (calc-wrapper
+ (let ((func (cons 'calcFunc-find (calc-top-list-n 2))))
+ (calc-enter-result
+ 2 "find"
+ (if arg (append func (list (prefix-numeric-value arg))) func))))
+)
+
+(defun calc-subvector ()
+ (interactive)
+ (calc-wrapper
+ (if (calc-is-inverse)
+ (calc-enter-result 3 "rsvc" (cons 'calcFunc-rsubvec
+ (calc-top-list-n 3)))
+ (calc-enter-result 3 "svec" (cons 'calcFunc-subvec (calc-top-list-n 3)))))
+)
+
+(defun calc-reverse-vector (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "rev" 'calcFunc-rev arg))
+)
+
+(defun calc-mask-vector (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-binary-op "vmsk" 'calcFunc-vmask arg))
+)
+
+(defun calc-expand-vector (arg)
+ (interactive "P")
+ (calc-wrapper
+ (if (calc-is-hyperbolic)
+ (calc-enter-result 3 "vexp" (cons 'calcFunc-vexp (calc-top-list-n 3)))
+ (calc-binary-op "vexp" 'calcFunc-vexp arg)))
+)
+
+(defun calc-sort ()
+ (interactive)
+ (calc-slow-wrapper
+ (if (calc-is-inverse)
+ (calc-enter-result 1 "rsrt" (list 'calcFunc-rsort (calc-top-n 1)))
+ (calc-enter-result 1 "sort" (list 'calcFunc-sort (calc-top-n 1)))))
+)
+
+(defun calc-grade ()
+ (interactive)
+ (calc-slow-wrapper
+ (if (calc-is-inverse)
+ (calc-enter-result 1 "rgrd" (list 'calcFunc-rgrade (calc-top-n 1)))
+ (calc-enter-result 1 "grad" (list 'calcFunc-grade (calc-top-n 1)))))
+)
+
+(defun calc-histogram (n)
+ (interactive "NNumber of bins: ")
+ (calc-slow-wrapper
+ (if calc-hyperbolic-flag
+ (calc-enter-result 2 "hist" (list 'calcFunc-histogram
+ (calc-top-n 2)
+ (calc-top-n 1)
+ (prefix-numeric-value n)))
+ (calc-enter-result 1 "hist" (list 'calcFunc-histogram
+ (calc-top-n 1)
+ (prefix-numeric-value n)))))
+)
+
+(defun calc-transpose (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "trn" 'calcFunc-trn arg))
+)
+
+(defun calc-conj-transpose (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "ctrn" 'calcFunc-ctrn arg))
+)
+
+(defun calc-cross (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-binary-op "cros" 'calcFunc-cross arg))
+)
+
+(defun calc-remove-duplicates (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "rdup" 'calcFunc-rdup arg))
+)
+
+(defun calc-set-union (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-binary-op "unio" 'calcFunc-vunion arg '(vec) 'calcFunc-rdup))
+)
+
+(defun calc-set-intersect (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-binary-op "intr" 'calcFunc-vint arg '(vec) 'calcFunc-rdup))
+)
+
+(defun calc-set-difference (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-binary-op "diff" 'calcFunc-vdiff arg '(vec) 'calcFunc-rdup))
+)
+
+(defun calc-set-xor (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-binary-op "xor" 'calcFunc-vxor arg '(vec) 'calcFunc-rdup))
+)
+
+(defun calc-set-complement (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "cmpl" 'calcFunc-vcompl arg))
+)
+
+(defun calc-set-floor (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "vflr" 'calcFunc-vfloor arg))
+)
+
+(defun calc-set-enumerate (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "enum" 'calcFunc-venum arg))
+)
+
+(defun calc-set-span (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "span" 'calcFunc-vspan arg))
+)
+
+(defun calc-set-cardinality (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "card" 'calcFunc-vcard arg))
+)
+
+(defun calc-unpack-bits (arg)
+ (interactive "P")
+ (calc-wrapper
+ (if (calc-is-inverse)
+ (calc-unary-op "bpck" 'calcFunc-vpack arg)
+ (calc-unary-op "bupk" 'calcFunc-vunpack arg)))
+)
+
+(defun calc-pack-bits (arg)
+ (interactive "P")
+ (calc-invert-func)
+ (calc-unpack-bits arg)
+)
+
+
+(defun calc-rnorm (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "rnrm" 'calcFunc-rnorm arg))
+)
+
+(defun calc-cnorm (arg)
+ (interactive "P")
+ (calc-wrapper
+ (calc-unary-op "cnrm" 'calcFunc-cnorm arg))
+)
+
+(defun calc-mrow (n &optional nn)
+ (interactive "NRow number: \nP")
+ (calc-wrapper
+ (if (consp nn)
+ (calc-enter-result 2 "mrow" (cons 'calcFunc-mrow (calc-top-list-n 2)))
+ (setq n (prefix-numeric-value n))
+ (if (= n 0)
+ (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1)))
+ (if (< n 0)
+ (calc-enter-result 1 "rrow" (list 'calcFunc-mrrow
+ (calc-top-n 1) (- n)))
+ (calc-enter-result 1 "mrow" (list 'calcFunc-mrow
+ (calc-top-n 1) n))))))
+)
+
+(defun calc-mcol (n &optional nn)
+ (interactive "NColumn number: \nP")
+ (calc-wrapper
+ (if (consp nn)
+ (calc-enter-result 2 "mcol" (cons 'calcFunc-mcol (calc-top-list-n 2)))
+ (setq n (prefix-numeric-value n))
+ (if (= n 0)
+ (calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1)))
+ (if (< n 0)
+ (calc-enter-result 1 "rcol" (list 'calcFunc-mrcol
+ (calc-top-n 1) (- n)))
+ (calc-enter-result 1 "mcol" (list 'calcFunc-mcol
+ (calc-top-n 1) n))))))
+)
+
+
+;;;; Vectors.
+
+(defun calcFunc-mdims (m)
+ (or (math-vectorp m)
+ (math-reject-arg m 'vectorp))
+ (cons 'vec (math-mat-dimens m))
+)
+
+
+;;; Apply a function elementwise to vector A. [V X V; N X N] [Public]
+(defun math-map-vec (f a)
+ (if (math-vectorp a)
+ (cons 'vec (mapcar f (cdr a)))
+ (funcall f a))
+)
+
+(defun math-dimension-error ()
+ (calc-record-why "*Dimension error")
+ (signal 'wrong-type-argument nil)
+)
+
+
+;;; Build a vector out of a list of objects. [Public]
+(defun calcFunc-vec (&rest objs)
+ (cons 'vec objs)
+)
+
+
+;;; Build a constant vector or matrix. [Public]
+(defun calcFunc-cvec (obj &rest dims)
+ (math-make-vec-dimen obj dims)
+)
+
+(defun math-make-vec-dimen (obj dims)
+ (if dims
+ (if (natnump (car dims))
+ (if (or (cdr dims)
+ (not (math-numberp obj)))
+ (cons 'vec (copy-sequence
+ (make-list (car dims)
+ (math-make-vec-dimen obj (cdr dims)))))
+ (cons 'vec (make-list (car dims) obj)))
+ (math-reject-arg (car dims) 'fixnatnump))
+ obj)
+)
+
+(defun calcFunc-head (vec)
+ (if (and (Math-vectorp vec)
+ (cdr vec))
+ (nth 1 vec)
+ (calc-record-why 'vectorp vec)
+ (list 'calcFunc-head vec))
+)
+
+(defun calcFunc-tail (vec)
+ (if (and (Math-vectorp vec)
+ (cdr vec))
+ (cons 'vec (cdr (cdr vec)))
+ (calc-record-why 'vectorp vec)
+ (list 'calcFunc-tail vec))
+)
+
+(defun calcFunc-cons (head tail)
+ (if (Math-vectorp tail)
+ (cons 'vec (cons head (cdr tail)))
+ (calc-record-why 'vectorp tail)
+ (list 'calcFunc-cons head tail))
+)
+
+(defun calcFunc-rhead (vec)
+ (if (and (Math-vectorp vec)
+ (cdr vec))
+ (let ((vec (copy-sequence vec)))
+ (setcdr (nthcdr (- (length vec) 2) vec) nil)
+ vec)
+ (calc-record-why 'vectorp vec)
+ (list 'calcFunc-rhead vec))
+)
+
+(defun calcFunc-rtail (vec)
+ (if (and (Math-vectorp vec)
+ (cdr vec))
+ (nth (1- (length vec)) vec)
+ (calc-record-why 'vectorp vec)
+ (list 'calcFunc-rtail vec))
+)
+
+(defun calcFunc-rcons (head tail)
+ (if (Math-vectorp head)
+ (append head (list tail))
+ (calc-record-why 'vectorp head)
+ (list 'calcFunc-rcons head tail))
+)
+
+
+
+;;; Apply a function elementwise to vectors A and B. [O X O O] [Public]
+(defun math-map-vec-2 (f a b)
+ (if (math-vectorp a)
+ (if (math-vectorp b)
+ (let ((v nil))
+ (while (setq a (cdr a))
+ (or (setq b (cdr b))
+ (math-dimension-error))
+ (setq v (cons (funcall f (car a) (car b)) v)))
+ (if a (math-dimension-error))
+ (cons 'vec (nreverse v)))
+ (let ((v nil))
+ (while (setq a (cdr a))
+ (setq v (cons (funcall f (car a) b) v)))
+ (cons 'vec (nreverse v))))
+ (if (math-vectorp b)
+ (let ((v nil))
+ (while (setq b (cdr b))
+ (setq v (cons (funcall f a (car b)) v)))
+ (cons 'vec (nreverse v)))
+ (funcall f a b)))
+)
+
+
+
+;;; "Reduce" a function over a vector (left-associatively). [O X V] [Public]
+(defun math-reduce-vec (f a)
+ (if (math-vectorp a)
+ (if (cdr a)
+ (let ((accum (car (setq a (cdr a)))))
+ (while (setq a (cdr a))
+ (setq accum (funcall f accum (car a))))
+ accum)
+ 0)
+ a)
+)
+
+;;; Reduce a function over the columns of matrix A. [V X V] [Public]
+(defun math-reduce-cols (f a)
+ (if (math-matrixp a)
+ (cons 'vec (math-reduce-cols-col-step f (cdr a) 1 (length (nth 1 a))))
+ a)
+)
+
+(defun math-reduce-cols-col-step (f a col cols)
+ (and (< col cols)
+ (cons (math-reduce-cols-row-step f (nth col (car a)) col (cdr a))
+ (math-reduce-cols-col-step f a (1+ col) cols)))
+)
+
+(defun math-reduce-cols-row-step (f tot col a)
+ (if a
+ (math-reduce-cols-row-step f
+ (funcall f tot (nth col (car a)))
+ col
+ (cdr a))
+ tot)
+)
+
+
+
+(defun math-dot-product (a b)
+ (if (setq a (cdr a) b (cdr b))
+ (let ((accum (math-mul (car a) (car b))))
+ (while (setq a (cdr a) b (cdr b))
+ (setq accum (math-add accum (math-mul (car a) (car b)))))
+ accum)
+ 0)
+)
+
+
+;;; Return the number of elements in vector V. [Public]
+(defun calcFunc-vlen (v)
+ (if (math-vectorp v)
+ (1- (length v))
+ (if (math-objectp v)
+ 0
+ (list 'calcFunc-vlen v)))
+)
+
+;;; Get the Nth row of a matrix.
+(defun calcFunc-mrow (mat n) ; [Public]
+ (if (Math-vectorp n)
+ (math-map-vec (function (lambda (x) (calcFunc-mrow mat x))) n)
+ (if (and (eq (car-safe n) 'intv) (math-constp n))
+ (calcFunc-subvec mat
+ (math-add (nth 2 n) (if (memq (nth 1 n) '(2 3)) 0 1))
+ (math-add (nth 3 n) (if (memq (nth 1 n) '(1 3)) 1 0)))
+ (or (and (integerp (setq n (math-check-integer n)))
+ (> n 0))
+ (math-reject-arg n 'fixposintp))
+ (or (Math-vectorp mat)
+ (math-reject-arg mat 'vectorp))
+ (or (nth n mat)
+ (math-reject-arg n "*Index out of range"))))
+)
+
+(defun calcFunc-subscr (mat n &optional m)
+ (setq mat (calcFunc-mrow mat n))
+ (if m
+ (if (math-num-integerp n)
+ (calcFunc-mrow mat m)
+ (calcFunc-mcol mat m))
+ mat)
+)
+
+;;; Get the Nth column of a matrix.
+(defun math-mat-col (mat n)
+ (cons 'vec (mapcar (function (lambda (x) (elt x n))) (cdr mat)))
+)
+
+(defun calcFunc-mcol (mat n) ; [Public]
+ (if (Math-vectorp n)
+ (calcFunc-trn
+ (math-map-vec (function (lambda (x) (calcFunc-mcol mat x))) n))
+ (if (and (eq (car-safe n) 'intv) (math-constp n))
+ (if (math-matrixp mat)
+ (math-map-vec (function (lambda (x) (calcFunc-mrow x n))) mat)
+ (calcFunc-mrow mat n))
+ (or (and (integerp (setq n (math-check-integer n)))
+ (> n 0))
+ (math-reject-arg n 'fixposintp))
+ (or (Math-vectorp mat)
+ (math-reject-arg mat 'vectorp))
+ (or (if (math-matrixp mat)
+ (and (< n (length (nth 1 mat)))
+ (math-mat-col mat n))
+ (nth n mat))
+ (math-reject-arg n "*Index out of range"))))
+)
+
+;;; Remove the Nth row from a matrix.
+(defun math-mat-less-row (mat n)
+ (if (<= n 0)
+ (cdr mat)
+ (cons (car mat)
+ (math-mat-less-row (cdr mat) (1- n))))
+)
+
+(defun calcFunc-mrrow (mat n) ; [Public]
+ (and (integerp (setq n (math-check-integer n)))
+ (> n 0)
+ (< n (length mat))
+ (math-mat-less-row mat n))
+)
+
+;;; Remove the Nth column from a matrix.
+(defun math-mat-less-col (mat n)
+ (cons 'vec (mapcar (function (lambda (x) (math-mat-less-row x n)))
+ (cdr mat)))
+)
+
+(defun calcFunc-mrcol (mat n) ; [Public]
+ (and (integerp (setq n (math-check-integer n)))
+ (> n 0)
+ (if (math-matrixp mat)
+ (and (< n (length (nth 1 mat)))
+ (math-mat-less-col mat n))
+ (math-mat-less-row mat n)))
+)
+
+(defun calcFunc-getdiag (mat) ; [Public]
+ (if (math-square-matrixp mat)
+ (cons 'vec (math-get-diag-step (cdr mat) 1))
+ (calc-record-why 'square-matrixp mat)
+ (list 'calcFunc-getdiag mat))
+)
+
+(defun math-get-diag-step (row n)
+ (and row
+ (cons (nth n (car row))
+ (math-get-diag-step (cdr row) (1+ n))))
+)
+
+(defun math-transpose (mat) ; [Public]
+ (let ((m nil)
+ (col (length (nth 1 mat))))
+ (while (> (setq col (1- col)) 0)
+ (setq m (cons (math-mat-col mat col) m)))
+ (cons 'vec m))
+)
+
+(defun calcFunc-trn (mat)
+ (if (math-vectorp mat)
+ (if (math-matrixp mat)
+ (math-transpose mat)
+ (math-col-matrix mat))
+ (if (math-numberp mat)
+ mat
+ (math-reject-arg mat 'matrixp)))
+)
+
+(defun calcFunc-ctrn (mat)
+ (calcFunc-conj (calcFunc-trn mat))
+)
+
+(defun calcFunc-pack (mode els)
+ (or (Math-vectorp els) (math-reject-arg els 'vectorp))
+ (if (and (Math-vectorp mode) (cdr mode))
+ (setq mode (cdr mode))
+ (or (integerp mode) (math-reject-arg mode 'fixnump)))
+ (condition-case err
+ (if (= (calc-pack-size mode) (1- (length els)))
+ (calc-pack-items mode (cdr els))
+ (math-reject-arg els "*Wrong number of elements"))
+ (error (math-reject-arg els (nth 1 err))))
+)
+
+(defun calcFunc-unpack (mode thing)
+ (or (integerp mode) (math-reject-arg mode 'fixnump))
+ (condition-case err
+ (cons 'vec (calc-unpack-item mode thing))
+ (error (math-reject-arg thing (nth 1 err))))
+)
+
+(defun calcFunc-unpackt (mode thing)
+ (let ((calc-unpack-with-type 'pair))
+ (calcFunc-unpack mode thing))
+)
+
+(defun calcFunc-arrange (vec cols) ; [Public]
+ (setq cols (math-check-fixnum cols t))
+ (if (math-vectorp vec)
+ (let* ((flat (math-flatten-vector vec))
+ (mat (list 'vec))
+ next)
+ (if (<= cols 0)
+ (nconc mat flat)
+ (while (>= (length flat) cols)
+ (setq next (nthcdr cols flat))
+ (setcdr (nthcdr (1- cols) flat) nil)
+ (setq mat (nconc mat (list (cons 'vec flat)))
+ flat next))
+ (if flat
+ (setq mat (nconc mat (list (cons 'vec flat)))))
+ mat)))
+)
+
+(defun math-flatten-vector (vec) ; [L V]
+ (if (math-vectorp vec)
+ (apply 'append (mapcar 'math-flatten-vector (cdr vec)))
+ (list vec))
+)
+
+(defun calcFunc-vconcat (a b)
+ (math-normalize (list '| a b))
+)
+
+(defun calcFunc-vconcatrev (a b)
+ (math-normalize (list '| b a))
+)
+
+(defun calcFunc-append (v1 v2)
+ (if (and (math-vectorp v1) (math-vectorp v2))
+ (append v1 (cdr v2))
+ (list 'calcFunc-append v1 v2))
+)
+
+(defun calcFunc-appendrev (v1 v2)
+ (calcFunc-append v2 v1)
+)
+
+
+;;; Copy a matrix. [Public]
+(defun math-copy-matrix (m)
+ (if (math-vectorp (nth 1 m))
+ (cons 'vec (mapcar 'copy-sequence (cdr m)))
+ (copy-sequence m))
+)
+
+;;; Convert a scalar or vector into an NxN diagonal matrix. [Public]
+(defun calcFunc-diag (a &optional n)
+ (and n (not (integerp n))
+ (setq n (math-check-fixnum n)))
+ (if (math-vectorp a)
+ (if (and n (/= (length a) (1+ n)))
+ (list 'calcFunc-diag a n)
+ (if (math-matrixp a)
+ (if (and n (/= (length (elt a 1)) (1+ n)))
+ (list 'calcFunc-diag a n)
+ a)
+ (cons 'vec (math-diag-step (cdr a) 0 (1- (length a))))))
+ (if n
+ (cons 'vec (math-diag-step (make-list n a) 0 n))
+ (list 'calcFunc-diag a)))
+)
+
+(defun calcFunc-idn (a &optional n)
+ (if n
+ (if (math-vectorp a)
+ (math-reject-arg a 'numberp)
+ (calcFunc-diag a n))
+ (if (integerp calc-matrix-mode)
+ (calcFunc-idn a calc-matrix-mode)
+ (list 'calcFunc-idn a)))
+)
+
+(defun math-mimic-ident (a m)
+ (if (math-square-matrixp m)
+ (calcFunc-idn a (1- (length m)))
+ (if (math-vectorp m)
+ (if (math-zerop a)
+ (cons 'vec (mapcar (function (lambda (x)
+ (if (math-vectorp x)
+ (math-mimic-ident a x)
+ a)))
+ (cdr m)))
+ (math-dimension-error))
+ (calcFunc-idn a)))
+)
+
+(defun math-diag-step (a n m)
+ (if (< n m)
+ (cons (cons 'vec
+ (nconc (make-list n 0)
+ (cons (car a)
+ (make-list (1- (- m n)) 0))))
+ (math-diag-step (cdr a) (1+ n) m))
+ nil)
+)
+
+;;; Create a vector of consecutive integers. [Public]
+(defun calcFunc-index (n &optional start incr)
+ (if (math-messy-integerp n)
+ (math-float (calcFunc-index (math-trunc n) start incr))
+ (and (not (integerp n))
+ (setq n (math-check-fixnum n)))
+ (let ((vec nil))
+ (if start
+ (progn
+ (if (>= n 0)
+ (while (>= (setq n (1- n)) 0)
+ (setq vec (cons start vec)
+ start (math-add start (or incr 1))))
+ (while (<= (setq n (1+ n)) 0)
+ (setq vec (cons start vec)
+ start (math-mul start (or incr 2)))))
+ (setq vec (nreverse vec)))
+ (if (>= n 0)
+ (while (> n 0)
+ (setq vec (cons n vec)
+ n (1- n)))
+ (let ((i -1))
+ (while (>= i n)
+ (setq vec (cons i vec)
+ i (1- i))))))
+ (cons 'vec vec)))
+)
+
+;;; Find an element in a vector.
+(defun calcFunc-find (vec x &optional start)
+ (setq start (if start (math-check-fixnum start t) 1))
+ (if (< start 1) (math-reject-arg start 'posp))
+ (setq vec (nthcdr start vec))
+ (let ((n start))
+ (while (and vec (not (Math-equal x (car vec))))
+ (setq n (1+ n)
+ vec (cdr vec)))
+ (if vec n 0))
+)
+
+;;; Return a subvector of a vector.
+(defun calcFunc-subvec (vec start &optional end)
+ (setq start (math-check-fixnum start t)
+ end (math-check-fixnum (or end 0) t))
+ (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
+ (let ((len (1- (length vec))))
+ (if (<= start 0)
+ (setq start (+ len start 1)))
+ (if (<= end 0)
+ (setq end (+ len end 1)))
+ (if (or (> start len)
+ (<= end start))
+ '(vec)
+ (setq vec (nthcdr start vec))
+ (if (<= end len)
+ (let ((chop (nthcdr (- end start 1) (setq vec (copy-sequence vec)))))
+ (setcdr chop nil)))
+ (cons 'vec vec)))
+)
+
+;;; Remove a subvector from a vector.
+(defun calcFunc-rsubvec (vec start &optional end)
+ (setq start (math-check-fixnum start t)
+ end (math-check-fixnum (or end 0) t))
+ (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
+ (let ((len (1- (length vec))))
+ (if (<= start 0)
+ (setq start (+ len start 1)))
+ (if (<= end 0)
+ (setq end (+ len end 1)))
+ (if (or (> start len)
+ (<= end start))
+ vec
+ (let ((tail (nthcdr end vec))
+ (chop (nthcdr (1- start) (setq vec (copy-sequence vec)))))
+ (setcdr chop nil)
+ (append vec tail))))
+)
+
+;;; Reverse the order of the elements of a vector.
+(defun calcFunc-rev (vec)
+ (if (math-vectorp vec)
+ (cons 'vec (reverse (cdr vec)))
+ (math-reject-arg vec 'vectorp))
+)
+
+;;; Compress a vector according to a mask vector.
+(defun calcFunc-vmask (mask vec)
+ (if (math-numberp mask)
+ (if (math-zerop mask)
+ '(vec)
+ vec)
+ (or (math-vectorp mask) (math-reject-arg mask 'vectorp))
+ (or (math-constp mask) (math-reject-arg mask 'constp))
+ (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
+ (or (= (length mask) (length vec)) (math-dimension-error))
+ (let ((new nil))
+ (while (setq mask (cdr mask) vec (cdr vec))
+ (or (math-zerop (car mask))
+ (setq new (cons (car vec) new))))
+ (cons 'vec (nreverse new))))
+)
+
+;;; Expand a vector according to a mask vector.
+(defun calcFunc-vexp (mask vec &optional filler)
+ (or (math-vectorp mask) (math-reject-arg mask 'vectorp))
+ (or (math-constp mask) (math-reject-arg mask 'constp))
+ (or (math-vectorp vec) (math-reject-arg vec 'vectorp))
+ (let ((new nil)
+ (fvec (and filler (math-vectorp filler))))
+ (while (setq mask (cdr mask))
+ (if (math-zerop (car mask))
+ (setq new (cons (or (if fvec
+ (car (setq filler (cdr filler)))
+ filler)
+ (car mask)) new))
+ (setq vec (cdr vec)
+ new (cons (or (car vec) (car mask)) new))))
+ (cons 'vec (nreverse new)))
+)
+
+
+;;; Compute the row and column norms of a vector or matrix. [Public]
+(defun calcFunc-rnorm (a)
+ (if (and (Math-vectorp a)
+ (math-constp a))
+ (if (math-matrixp a)
+ (math-reduce-vec 'math-max (math-map-vec 'calcFunc-cnorm a))
+ (math-reduce-vec 'math-max (math-map-vec 'math-abs a)))
+ (calc-record-why 'vectorp a)
+ (list 'calcFunc-rnorm a))
+)
+
+(defun calcFunc-cnorm (a)
+ (if (and (Math-vectorp a)
+ (math-constp a))
+ (if (math-matrixp a)
+ (math-reduce-vec 'math-max
+ (math-reduce-cols 'math-add-abs a))
+ (math-reduce-vec 'math-add-abs a))
+ (calc-record-why 'vectorp a)
+ (list 'calcFunc-cnorm a))
+)
+
+(defun math-add-abs (a b)
+ (math-add (math-abs a) (math-abs b))
+)
+
+
+;;; Sort the elements of a vector into increasing order.
+(defun calcFunc-sort (vec) ; [Public]
+ (if (math-vectorp vec)
+ (cons 'vec (sort (copy-sequence (cdr vec)) 'math-beforep))
+ (math-reject-arg vec 'vectorp))
+)
+
+(defun calcFunc-rsort (vec) ; [Public]
+ (if (math-vectorp vec)
+ (cons 'vec (nreverse (sort (copy-sequence (cdr vec)) 'math-beforep)))
+ (math-reject-arg vec 'vectorp))
+)
+
+(defun calcFunc-grade (grade-vec)
+ (if (math-vectorp grade-vec)
+ (let* ((len (1- (length grade-vec))))
+ (cons 'vec (sort (cdr (calcFunc-index len)) 'math-grade-beforep)))
+ (math-reject-arg grade-vec 'vectorp))
+)
+
+(defun calcFunc-rgrade (grade-vec)
+ (if (math-vectorp grade-vec)
+ (let* ((len (1- (length grade-vec))))
+ (cons 'vec (nreverse (sort (cdr (calcFunc-index len))
+ 'math-grade-beforep))))
+ (math-reject-arg grade-vec 'vectorp))
+)
+
+(defun math-grade-beforep (i j)
+ (math-beforep (nth i grade-vec) (nth j grade-vec))
+)
+
+
+;;; Compile a histogram of data from a vector.
+(defun calcFunc-histogram (vec wts &optional n)
+ (or n (setq n wts wts 1))
+ (or (Math-vectorp vec)
+ (math-reject-arg vec 'vectorp))
+ (if (Math-vectorp wts)
+ (or (= (length vec) (length wts))
+ (math-dimension-error)))
+ (or (natnump n)
+ (math-reject-arg n 'fixnatnump))
+ (let ((res (make-vector n 0))
+ (vp vec)
+ (wvec (Math-vectorp wts))
+ (wp wts)
+ bin)
+ (while (setq vp (cdr vp))
+ (setq bin (car vp))
+ (or (natnump bin)
+ (setq bin (math-floor bin)))
+ (and (natnump bin)
+ (< bin n)
+ (aset res bin (math-add (aref res bin)
+ (if wvec (car (setq wp (cdr wp))) wts)))))
+ (cons 'vec (append res nil)))
+)
+
+
+;;; Set operations.
+
+(defun calcFunc-vunion (a b)
+ (if (Math-objectp a)
+ (setq a (list 'vec a))
+ (or (math-vectorp a) (math-reject-arg a 'vectorp)))
+ (if (Math-objectp b)
+ (setq b (list b))
+ (or (math-vectorp b) (math-reject-arg b 'vectorp))
+ (setq b (cdr b)))
+ (calcFunc-rdup (append a b))
+)
+
+(defun calcFunc-vint (a b)
+ (if (and (math-simple-set a) (math-simple-set b))
+ (progn
+ (setq a (cdr (calcFunc-rdup a)))
+ (setq b (cdr (calcFunc-rdup b)))
+ (let ((vec (list 'vec)))
+ (while (and a b)
+ (if (math-beforep (car a) (car b))
+ (setq a (cdr a))
+ (if (Math-equal (car a) (car b))
+ (setq vec (cons (car a) vec)
+ a (cdr a)))
+ (setq b (cdr b))))
+ (nreverse vec)))
+ (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a)
+ (calcFunc-vcompl b))))
+)
+
+(defun calcFunc-vdiff (a b)
+ (if (and (math-simple-set a) (math-simple-set b))
+ (progn
+ (setq a (cdr (calcFunc-rdup a)))
+ (setq b (cdr (calcFunc-rdup b)))
+ (let ((vec (list 'vec)))
+ (while a
+ (while (and b (math-beforep (car b) (car a)))
+ (setq b (cdr b)))
+ (if (and b (Math-equal (car a) (car b)))
+ (setq a (cdr a)
+ b (cdr b))
+ (setq vec (cons (car a) vec)
+ a (cdr a))))
+ (nreverse vec)))
+ (calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) b)))
+)
+
+(defun calcFunc-vxor (a b)
+ (if (and (math-simple-set a) (math-simple-set b))
+ (progn
+ (setq a (cdr (calcFunc-rdup a)))
+ (setq b (cdr (calcFunc-rdup b)))
+ (let ((vec (list 'vec)))
+ (while (or a b)
+ (if (and a
+ (or (not b)
+ (math-beforep (car a) (car b))))
+ (setq vec (cons (car a) vec)
+ a (cdr a))
+ (if (and a (Math-equal (car a) (car b)))
+ (setq a (cdr a))
+ (setq vec (cons (car b) vec)))
+ (setq b (cdr b))))
+ (nreverse vec)))
+ (let ((ca (calcFunc-vcompl a))
+ (cb (calcFunc-vcompl b)))
+ (calcFunc-vunion (calcFunc-vcompl (calcFunc-vunion ca b))
+ (calcFunc-vcompl (calcFunc-vunion a cb)))))
+)
+
+(defun calcFunc-vcompl (a)
+ (setq a (math-prepare-set a))
+ (let ((vec (list 'vec))
+ (prev '(neg (var inf var-inf)))
+ (closed 2))
+ (while (setq a (cdr a))
+ (or (and (equal (nth 2 (car a)) '(neg (var inf var-inf)))
+ (memq (nth 1 (car a)) '(2 3)))
+ (setq vec (cons (list 'intv
+ (+ closed
+ (if (memq (nth 1 (car a)) '(0 1)) 1 0))
+ prev
+ (nth 2 (car a)))
+ vec)))
+ (setq prev (nth 3 (car a))
+ closed (if (memq (nth 1 (car a)) '(0 2)) 2 0)))
+ (or (and (equal prev '(var inf var-inf))
+ (= closed 0))
+ (setq vec (cons (list 'intv (+ closed 1)
+ prev '(var inf var-inf))
+ vec)))
+ (math-clean-set (nreverse vec)))
+)
+
+(defun calcFunc-vspan (a)
+ (setq a (math-prepare-set a))
+ (if (cdr a)
+ (let ((last (nth (1- (length a)) a)))
+ (math-make-intv (+ (logand (nth 1 (nth 1 a)) 2)
+ (logand (nth 1 last) 1))
+ (nth 2 (nth 1 a))
+ (nth 3 last)))
+ '(intv 2 0 0))
+)
+
+(defun calcFunc-vfloor (a &optional always-vec)
+ (setq a (math-prepare-set a))
+ (let ((vec (list 'vec)) (p a) (prev nil) b mask)
+ (while (setq p (cdr p))
+ (setq mask (nth 1 (car p))
+ a (nth 2 (car p))
+ b (nth 3 (car p)))
+ (and (memq mask '(0 1))
+ (not (math-infinitep a))
+ (setq mask (logior mask 2))
+ (math-num-integerp a)
+ (setq a (math-add a 1)))
+ (setq a (math-ceiling a))
+ (and (memq mask '(0 2))
+ (not (math-infinitep b))
+ (setq mask (logior mask 1))
+ (math-num-integerp b)
+ (setq b (math-sub b 1)))
+ (setq b (math-floor b))
+ (if (and prev (Math-equal (math-sub a 1) (nth 3 prev)))
+ (setcar (nthcdr 3 prev) b)
+ (or (Math-lessp b a)
+ (setq vec (cons (setq prev (list 'intv mask a b)) vec)))))
+ (setq vec (nreverse vec))
+ (math-clean-set vec always-vec))
+)
+
+(defun calcFunc-vcard (a)
+ (setq a (calcFunc-vfloor a t))
+ (or (math-constp a) (math-reject-arg a "*Set must be finite"))
+ (let ((count 0))
+ (while (setq a (cdr a))
+ (if (eq (car-safe (car a)) 'intv)
+ (setq count (math-add count (math-sub (nth 3 (car a))
+ (nth 2 (car a))))))
+ (setq count (math-add count 1)))
+ count)
+)
+
+(defun calcFunc-venum (a)
+ (setq a (calcFunc-vfloor a t))
+ (or (math-constp a) (math-reject-arg a "*Set must be finite"))
+ (let ((p a) next)
+ (while (cdr p)
+ (setq next (cdr p))
+ (if (eq (car-safe (nth 1 p)) 'intv)
+ (setcdr p (nconc (cdr (calcFunc-index (math-add
+ (math-sub (nth 3 (nth 1 p))
+ (nth 2 (nth 1 p)))
+ 1)
+ (nth 2 (nth 1 p))))
+ (cdr (cdr p)))))
+ (setq p next))
+ a)
+)
+
+(defun calcFunc-vpack (a)
+ (setq a (calcFunc-vfloor a t))
+ (if (and (cdr a)
+ (math-negp (if (eq (car-safe (nth 1 a)) 'intv)
+ (nth 2 (nth 1 a))
+ (nth 1 a))))
+ (math-reject-arg (nth 1 a) 'posp))
+ (let ((accum 0))
+ (while (setq a (cdr a))
+ (if (eq (car-safe (car a)) 'intv)
+ (if (equal (nth 3 (car a)) '(var inf var-inf))
+ (setq accum (math-sub accum
+ (math-power-of-2 (nth 2 (car a)))))
+ (setq accum (math-add accum
+ (math-sub
+ (math-power-of-2 (1+ (nth 3 (car a))))
+ (math-power-of-2 (nth 2 (car a)))))))
+ (setq accum (math-add accum (math-power-of-2 (car a))))))
+ accum)
+)
+
+(defun calcFunc-vunpack (a &optional w)
+ (or (math-num-integerp a) (math-reject-arg a 'integerp))
+ (if w (setq a (math-clip a w)))
+ (if (math-messy-integerp a) (setq a (math-trunc a)))
+ (let* ((calc-number-radix 2)
+ (neg (math-negp a))
+ (aa (if neg (math-sub -1 a) a))
+ (str (if (eq aa 0)
+ ""
+ (if (consp aa)
+ (math-format-bignum-binary (cdr aa))
+ (math-format-binary aa))))
+ (zero (if neg ?1 ?0))
+ (one (if neg ?0 ?1))
+ (len (length str))
+ (vec (list 'vec))
+ (pos (1- len)) pos2)
+ (while (>= pos 0)
+ (if (eq (aref str pos) zero)
+ (setq pos (1- pos))
+ (setq pos2 pos)
+ (while (and (>= pos 0) (eq (aref str pos) one))
+ (setq pos (1- pos)))
+ (setq vec (cons (if (= pos (1- pos2))
+ (- len pos2 1)
+ (list 'intv 3 (- len pos2 1) (- len pos 2)))
+ vec))))
+ (if neg
+ (setq vec (cons (list 'intv 2 len '(var inf var-inf)) vec)))
+ (math-clean-set (nreverse vec)))
+)
+
+(defun calcFunc-rdup (a)
+ (if (math-simple-set a)
+ (progn
+ (and (Math-objectp a) (setq a (list 'vec a)))
+ (or (math-vectorp a) (math-reject-arg a 'vectorp))
+ (setq a (sort (copy-sequence (cdr a)) 'math-beforep))
+ (let ((p a))
+ (while (cdr p)
+ (if (Math-equal (car p) (nth 1 p))
+ (setcdr p (cdr (cdr p)))
+ (setq p (cdr p)))))
+ (cons 'vec a))
+ (math-clean-set (math-prepare-set a)))
+)
+
+(defun math-prepare-set (a)
+ (if (Math-objectp a)
+ (setq a (list 'vec a))
+ (or (math-vectorp a) (math-reject-arg a 'vectorp))
+ (setq a (cons 'vec (sort (copy-sequence (cdr a)) 'math-beforep))))
+ (let ((p a) res)
+
+ ;; Convert all elements to non-empty intervals.
+ (while (cdr p)
+ (if (eq (car-safe (nth 1 p)) 'intv)
+ (if (math-intv-constp (nth 1 p))
+ (if (and (memq (nth 1 (nth 1 p)) '(0 1 2))
+ (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p))))
+ (setcdr p (cdr (cdr p)))
+ (setq p (cdr p)))
+ (math-reject-arg (nth 1 p) 'constp))
+ (or (Math-anglep (nth 1 p))
+ (eq (car (nth 1 p)) 'date)
+ (equal (nth 1 p) '(var inf var-inf))
+ (equal (nth 1 p) '(neg (var inf var-inf)))
+ (math-reject-arg (nth 1 p) 'realp))
+ (setcar (cdr p) (list 'intv 3 (nth 1 p) (nth 1 p)))
+ (setq p (cdr p))))
+
+ ;; Combine redundant intervals.
+ (setq p a)
+ (while (cdr (cdr p))
+ (if (or (memq (setq res (math-compare (nth 3 (nth 1 p))
+ (nth 2 (nth 2 p))))
+ '(-1 2))
+ (and (eq res 0)
+ (memq (nth 1 (nth 1 p)) '(0 2))
+ (memq (nth 1 (nth 2 p)) '(0 1))))
+ (setq p (cdr p))
+ (setq res (math-compare (nth 3 (nth 1 p)) (nth 3 (nth 2 p))))
+ (setcdr p (cons (list 'intv
+ (+ (logand (logior (nth 1 (nth 1 p))
+ (if (Math-equal
+ (nth 2 (nth 1 p))
+ (nth 2 (nth 2 p)))
+ (nth 1 (nth 2 p))
+ 0))
+ 2)
+ (logand (logior (if (memq res '(1 0 2))
+ (nth 1 (nth 1 p)) 0)
+ (if (memq res '(-1 0 2))
+ (nth 1 (nth 2 p)) 0))
+ 1))
+ (nth 2 (nth 1 p))
+ (if (eq res 1)
+ (nth 3 (nth 1 p))
+ (nth 3 (nth 2 p))))
+ (cdr (cdr (cdr p))))))))
+ a
+)
+
+(defun math-clean-set (a &optional always-vec)
+ (let ((p a) res)
+ (while (cdr p)
+ (if (and (eq (car-safe (nth 1 p)) 'intv)
+ (Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p))))
+ (setcar (cdr p) (nth 2 (nth 1 p))))
+ (setq p (cdr p)))
+ (if (and (not (cdr (cdr a)))
+ (eq (car-safe (nth 1 a)) 'intv)
+ (not always-vec))
+ (nth 1 a)
+ a))
+)
+
+(defun math-simple-set (a)
+ (or (and (Math-objectp a)
+ (not (eq (car-safe a) 'intv)))
+ (and (Math-vectorp a)
+ (progn
+ (while (and (setq a (cdr a))
+ (not (eq (car-safe (car a)) 'intv))))
+ (null a))))
+)
+
+
+
+
+;;; Compute a right-handed vector cross product. [O O O] [Public]
+(defun calcFunc-cross (a b)
+ (if (and (eq (car-safe a) 'vec)
+ (= (length a) 4))
+ (if (and (eq (car-safe b) 'vec)
+ (= (length b) 4))
+ (list 'vec
+ (math-sub (math-mul (nth 2 a) (nth 3 b))
+ (math-mul (nth 3 a) (nth 2 b)))
+ (math-sub (math-mul (nth 3 a) (nth 1 b))
+ (math-mul (nth 1 a) (nth 3 b)))
+ (math-sub (math-mul (nth 1 a) (nth 2 b))
+ (math-mul (nth 2 a) (nth 1 b))))
+ (math-reject-arg b "*Three-vector expected"))
+ (math-reject-arg a "*Three-vector expected"))
+)
+
+
+
+
+
+(defun math-read-brackets (space-sep close)
+ (and space-sep (setq space-sep (not (math-check-for-commas))))
+ (math-read-token)
+ (while (eq exp-token 'space)
+ (math-read-token))
+ (if (or (equal exp-data close)
+ (eq exp-token 'end))
+ (progn
+ (math-read-token)
+ '(vec))
+ (let ((save-exp-pos exp-pos)
+ (save-exp-old-pos exp-old-pos)
+ (save-exp-token exp-token)
+ (save-exp-data exp-data)
+ (vals (let ((exp-keep-spaces space-sep))
+ (if (or (equal exp-data "\\dots")
+ (equal exp-data "\\ldots"))
+ '(vec (neg (var inf var-inf)))
+ (catch 'syntax (math-read-vector))))))
+ (if (stringp vals)
+ (if space-sep
+ (let ((error-exp-pos exp-pos)
+ (error-exp-old-pos exp-old-pos)
+ vals2)
+ (setq exp-pos save-exp-pos
+ exp-old-pos save-exp-old-pos
+ exp-token save-exp-token
+ exp-data save-exp-data)
+ (let ((exp-keep-spaces nil))
+ (setq vals2 (catch 'syntax (math-read-vector))))
+ (if (and (not (stringp vals2))
+ (or (assoc exp-data '(("\\ldots") ("\\dots") (";")))
+ (equal exp-data close)
+ (eq exp-token 'end)))
+ (setq space-sep nil
+ vals vals2)
+ (setq exp-pos error-exp-pos
+ exp-old-pos error-exp-old-pos)
+ (throw 'syntax vals)))
+ (throw 'syntax vals)))
+ (if (or (equal exp-data "\\dots")
+ (equal exp-data "\\ldots"))
+ (progn
+ (math-read-token)
+ (setq vals (if (> (length vals) 2)
+ (cons 'calcFunc-mul (cdr vals)) (nth 1 vals)))
+ (let ((exp2 (if (or (equal exp-data close)
+ (equal exp-data ")")
+ (eq exp-token 'end))
+ '(var inf var-inf)
+ (math-read-expr-level 0))))
+ (setq vals
+ (list 'intv
+ (if (equal exp-data ")") 2 3)
+ vals
+ exp2)))
+ (if (not (or (equal exp-data close)
+ (equal exp-data ")")
+ (eq exp-token 'end)))
+ (throw 'syntax "Expected `]'")))
+ (if (equal exp-data ";")
+ (let ((exp-keep-spaces space-sep))
+ (setq vals (cons 'vec (math-read-matrix (list vals))))))
+ (if (not (or (equal exp-data close)
+ (eq exp-token 'end)))
+ (throw 'syntax "Expected `]'")))
+ (or (eq exp-token 'end)
+ (math-read-token))
+ vals))
+)
+
+(defun math-check-for-commas (&optional balancing)
+ (let ((count 0)
+ (pos (1- exp-pos)))
+ (while (and (>= count 0)
+ (setq pos (string-match
+ (if balancing "[],[{}()<>]" "[],[{}()]")
+ exp-str (1+ pos)))
+ (or (/= (aref exp-str pos) ?,) (> count 0) balancing))
+ (cond ((memq (aref exp-str pos) '(?\[ ?\{ ?\( ?\<))
+ (setq count (1+ count)))
+ ((memq (aref exp-str pos) '(?\] ?\} ?\) ?\>))
+ (setq count (1- count)))))
+ (if balancing
+ pos
+ (and pos (= (aref exp-str pos) ?,))))
+)
+
+(defun math-read-vector ()
+ (let* ((val (list (math-read-expr-level 0)))
+ (last val))
+ (while (progn
+ (while (eq exp-token 'space)
+ (math-read-token))
+ (and (not (eq exp-token 'end))
+ (not (equal exp-data ";"))
+ (not (equal exp-data close))
+ (not (equal exp-data "\\dots"))
+ (not (equal exp-data "\\ldots"))))
+ (if (equal exp-data ",")
+ (math-read-token))
+ (while (eq exp-token 'space)
+ (math-read-token))
+ (let ((rest (list (math-read-expr-level 0))))
+ (setcdr last rest)
+ (setq last rest)))
+ (cons 'vec val))
+)
+
+(defun math-read-matrix (mat)
+ (while (equal exp-data ";")
+ (math-read-token)
+ (while (eq exp-token 'space)
+ (math-read-token))
+ (setq mat (nconc mat (list (math-read-vector)))))
+ mat
+)
+