1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
|
<HTML>
<TITLE>vector Specification Sheet</TITLE>
<H1>vector Specification Sheet</H1>
<HR>
Computer Algebra Kit (c) 1993,99 by Comp.Alg.Objects. All Rights Reserved.<P>
<H1>Vector</H1>
<B>Inherits from:</B> CAObject<P>
<B>Maturity Index:</B> Relatively mature<P>
<H2>Class Description</H2>
A vector consists of a number of <I>scalars</I> that can be arbitrary Computer Algebra Kit objects, but they currently have to be either floating-point or elements of a field (see <B>inField</B>) or elements of an integral domain (see <B>inIntegralDomain</B>).<P>
There are methods to access, insert and remove scalars. It's also possible to place or replace a scalar directly at a given index. See the documentation on <B>eachScalar</B> to access the scalar at a given index.<P>
<B>Note:</B> Vector objects are meant for computational tasks. They are no substitute for List or Collection objects, that are better suited for the purpose of storing objects.<P>
<H2>Method types</H2>
<H3><B>Creation</B></H3>
<UL>
<LI><A HREF="#1">collection:</A></LI>
<LI><A HREF="#4">scalarZero:numScalars:</A></LI>
<LI><A HREF="#5">copy</A></LI>
<LI><A HREF="#6">deepCopy</A></LI>
<LI><A HREF="#7">clear</A></LI>
</UL>
<H3><B>Identity</B></H3>
<UL>
<LI><A HREF="#13">scalarZero</A></LI>
<LI><A HREF="#14">numScalars</A></LI>
<LI><A HREF="#43">hash</A></LI>
<LI><A HREF="#44">isEqual:</A></LI>
</UL>
<H3><B>Insertion Scalars</B></H3>
<UL>
<LI><A HREF="#16">insertScalar:</A></LI>
<LI><A HREF="#17">insertScalar:at:</A></LI>
</UL>
<H3><B>Removing Scalars</B></H3>
<UL>
<LI><A HREF="#18">removeScalar</A></LI>
<LI><A HREF="#19">removeScalarAt:</A></LI>
<LI><A HREF="#20">freeScalarAt:</A></LI>
</UL>
<H3><B>Placing and Replacing</B></H3>
<UL>
<LI><A HREF="#21">placeScalar:at:</A></LI>
<LI><A HREF="#22">replaceScalarAt:with:</A></LI>
<LI><A HREF="#23">asCollection</A></LI>
<LI><A HREF="#24">asNumerical</A></LI>
<LI><A HREF="#25">asModp:</A></LI>
<LI><A HREF="#27">onCommonDenominator:</A></LI>
</UL>
<H3><B>Accessing Scalars</B></H3>
<UL>
<LI><A HREF="#30">eachScalar</A></LI>
<LI><A HREF="#31">floatValueAt:</A></LI>
<LI><A HREF="#32">intValueAt:</A></LI>
</UL>
<H3><B>Addition</B></H3>
<UL>
<LI><A HREF="#33">zero</A></LI>
<LI><A HREF="#46">isZero</A></LI>
<LI><A HREF="#48">isOpposite:</A></LI>
<LI><A HREF="#50">negate</A></LI>
<LI><A HREF="#54">double</A></LI>
<LI><A HREF="#58">add:</A></LI>
<LI><A HREF="#60">subtract:</A></LI>
<LI><A HREF="#34">addScalar:at:</A></LI>
<LI><A HREF="#35">subtractScalar:at:</A></LI>
</UL>
<H3><B>Scalar Multiplication</B></H3>
<UL>
<LI><A HREF="#62">multiplyScalar:</A></LI>
<LI><A HREF="#64">divideScalar:</A></LI>
</UL>
<H3><B>Multiplication</B></H3>
<UL>
<LI><A HREF="#36">dotSquare</A></LI>
<LI><A HREF="#37">dotMultiply:</A></LI>
<LI><A HREF="#38">multiplyLeftMatrix:</A></LI>
</UL>
<H3><B>Printing</B></H3>
<UL>
<LI><A HREF="#42">printOn:</A></LI>
</UL>
<H2>Methods</H2>
<H3><A NAME="1">collection:</A></H3>
<BLOCKQUOTE>+<B>collection</B>:<I>aCltn</I></BLOCKQUOTE>
Creates a vector containing references to the scalars from <I>aCltn</I>. The collection must not be empty. You remain responsible for freeing the collection.<P>
<H3><A NAME="4">scalarZero:numScalars:</A></H3>
<BLOCKQUOTE>+<B>scalarZero</B>:<I>aScalarZero</I><B>numScalars</B>:(int)<I>numScalars</I></BLOCKQUOTE>
Creates a new vector with <I>numScalars</I> zero scalars.<P>
<H3><A NAME="5">copy</A></H3>
<BLOCKQUOTE>-<B>copy</B></BLOCKQUOTE>
Returns a new vector. <P>
<H3><A NAME="6">deepCopy</A></H3>
<BLOCKQUOTE>-<B>deepCopy</B></BLOCKQUOTE>
Returns a new vector. Sends <B>deepCopy</B> messages to the scalars in the vector.<P>
<H3><A NAME="7">clear</A></H3>
<BLOCKQUOTE>-<B>clear</B></BLOCKQUOTE>
Sends <B>free</B> messages to the scalars in the vector.<P>
<H3><A NAME="13">scalarZero</A></H3>
<BLOCKQUOTE>-<B>scalarZero</B></BLOCKQUOTE>
Returns the zero scalar element. You may not free or modify the object returned by this method.<P>
<H3><A NAME="14">numScalars</A></H3>
<BLOCKQUOTE>- (int)<B>numScalars</B></BLOCKQUOTE>
Returns the number of scalar objects in the vector. Returns 0 if the vector is empty. The first scalar in the vector is at index 0, the last scalar at <I>numScalars</I> minus one.<P>
<H3><A NAME="16">insertScalar:</A></H3>
<BLOCKQUOTE>-<B>insertScalar</B>:<I>aScalar</I></BLOCKQUOTE>
Inserts <I>aScalar</I> as first entry and returns <B>self</B>. The object <I>aScalar</I> belongs to the vector after insertion, and is not necessarily copied. To insert a scalar, the reference count of the vector should be equal to one.<P>
<H3><A NAME="17">insertScalar:at:</A></H3>
<BLOCKQUOTE>-<B>insertScalar</B>:<I>aScalar</I><B>at</B>:(int)<I>i</I></BLOCKQUOTE>
Inserts <I>aScalar</I> as i-th entry and returns <B>self</B>. The object <I>aScalar</I> belongs to the vector after insertion, and is not necessarily copied. If <I>i</I> is equal to zero, this method is identical to <B>-insertScalar:</B>. If <I>i</I> is equal to <B>numScalars</B>, this method inserts the scalar as last element. The reference count of the vector should be equal to one.<P>
<H3><A NAME="18">removeScalar</A></H3>
<BLOCKQUOTE>-<B>removeScalar</B></BLOCKQUOTE>
Removes (and returns) the first scalar in the vector (the scalar at index 0). Returns <B>nil</B> if there were no more elements left. This can be used in the following way :<P>
<BLOCKQUOTE><PRE>
while (c = [vector removeScalar]) { /* do something with c */ }
</PRE></BLOCKQUOTE>
To remove a scalar, the reference count of the vector should be equal to one.<P>
<H3><A NAME="19">removeScalarAt:</A></H3>
<BLOCKQUOTE>-<B>removeScalarAt</B>:(int)<I>i</I></BLOCKQUOTE>
Removes and returns the i-th scalar in the vector. If <I>i</I> is zero, this method is identical to <B>removeScalar</B>. The reference count of the vector should be equal to one. Unlike <B>removeScalar</B>, which returns <B>nil</B> if there are no more scalars in the vector, this method generates an error message if you attempt to remove a scalar at an illegal index.<P>
<H3><A NAME="20">freeScalarAt:</A></H3>
<BLOCKQUOTE>-<B>freeScalarAt</B>:(int)<I>i</I></BLOCKQUOTE>
Removes and frees the i-th scalar in the vector. The reference count of the vector should be equal to one. Returns <B>self</B>.<P>
<H3><A NAME="21">placeScalar:at:</A></H3>
<BLOCKQUOTE>-<B>placeScalar</B>:<I>aScalar</I><B>at</B>:(int)<I>i</I></BLOCKQUOTE>
Frees the scalar at position <I>i</I> and replaces it by the scalar object <I>aScalar</I>. Returns <B>self</B>. The scalar <I>aScalar</I> belongs to the receiving vector object; it is not necessarily copied. This is similar to List's -addObject: method. It is an error to use an illegal index <I>i</I> or to attempt to set a scalar in a vector whose reference count is not equal to one.<P>
<H3><A NAME="22">replaceScalarAt:with:</A></H3>
<BLOCKQUOTE>-<B>replaceScalarAt</B>:(int)<I>i</I><B>with</B>:<I>aScalar</I></BLOCKQUOTE>
Similar to <B>placeScalar:at:</B> but returns, rather than frees, the scalar at position <I>i</I> after replacing it by <I>aScalar</I>. It is an error to use an illegal index <I>i</I> or to attempt to replace a scalar in a vector whose reference count is not equal to one.<P>
<H3><A NAME="23">asCollection</A></H3>
<BLOCKQUOTE>-<B>asCollection</B></BLOCKQUOTE>
Returns a new collection containing new references to the scalars in the vector.<P>
<H3><A NAME="24">asNumerical</A></H3>
<BLOCKQUOTE>-<B>asNumerical</B></BLOCKQUOTE>
Returns a new vector, whose scalars are the numerical value of the scalars of the original vector.<P>
<H3><A NAME="25">asModp:</A></H3>
<BLOCKQUOTE>-<B>asModp</B>:(unsigned short)<I>p</I></BLOCKQUOTE>
Returns a new vector, whose scalars are the value of the scalars of the original vector mod <I>p</I>.<P>
<H3><A NAME="27">onCommonDenominator:</A></H3>
<BLOCKQUOTE>-<B>onCommonDenominator</B>:(id *)<I>denominator</I></BLOCKQUOTE>
Puts a vector with fractional scalars on a common denominator. Returns a new vector with integral scalars, and, by reference, the common denominator of the scalars in the vector.<P>
<H3><A NAME="30">eachScalar</A></H3>
<BLOCKQUOTE>-<B>eachScalar</B></BLOCKQUOTE>
Returns a new sequence object that gives access to the scalars of the vector.<P>
<H3><A NAME="31">floatValueAt:</A></H3>
<BLOCKQUOTE>- (float)<B>floatValueAt</B>:(int)<I>i</I></BLOCKQUOTE>
Returns the <B>floatValue</B> of the scalar at the <I>i</I>-th position.<P>
<H3><A NAME="32">intValueAt:</A></H3>
<BLOCKQUOTE>- (int)<B>intValueAt</B>:(int)<I>i</I></BLOCKQUOTE>
Returns the <B>intValue</B> of the scalar at the <I>i</I>-th position.<P>
<H3><A NAME="33">zero</A></H3>
<BLOCKQUOTE>-<B>zero</B></BLOCKQUOTE>
Returns a vector of the same dimension as the object that receives the message, but all filled with zero scalars.<P>
<H3><A NAME="34">addScalar:at:</A></H3>
<BLOCKQUOTE>-<B>addScalar</B>:<I>s</I><B>at</B>:(int)<I>i</I></BLOCKQUOTE>
Returns a <B>new</B> vector. Adds <I>s</I> to the scalar at position <I>i</I>, and replaces the scalar by the sum. <I>i</I> must be between 0 and the number of scalars in the vector. This method is <I>not</I> an insertion method.<P>
<B>See also:</B> insertScalar:at:, replaceScalar:at:<P>
<H3><A NAME="35">subtractScalar:at:</A></H3>
<BLOCKQUOTE>-<B>subtractScalar</B>:<I>s</I><B>at</B>:(int)<I>i</I></BLOCKQUOTE>
Returns a <B>new</B> vector. Subtracts <I>s</I> from the scalar at position <I>i</I>. <I>i</I> must be between 0 and the number of scalars in the vector. This method is <I>not</I> an insertion method.<P>
<H3><A NAME="36">dotSquare</A></H3>
<BLOCKQUOTE>-<B>dotSquare</B></BLOCKQUOTE>
Returns a new scalar product, the dot product of the vector by itself, defined as the sum of squares of the scalars in the vector.<P>
<H3><A NAME="37">dotMultiply:</A></H3>
<BLOCKQUOTE>-<B>dotMultiply</B>:<I>aVector</I></BLOCKQUOTE>
Returns a new scalar product, the dot product of the vector <I>self</I> by <I>aVector</I>, defined as the sum of the products of the scalars in the vectors.<P>
<H3><A NAME="38">multiplyLeftMatrix:</A></H3>
<BLOCKQUOTE>-<B>multiplyLeftMatrix</B>:<I>aMatrix</I></BLOCKQUOTE>
Returns a new vector, the product of <I>aMatrix</I> by the column vector <I>self</I>.<P>
<H3><A NAME="42">printOn:</A></H3>
<BLOCKQUOTE>-<B>printOn</B>:(IOD)<I>aFile</I></BLOCKQUOTE>
Prints, between braces, a comma separated list of the scalars (by sending <B>printOn:</B> messages to the scalars).<P>
|
