[OpenSPARC-T2-DV] / tools / perl-5.8.0 / man / man3 / Math::Matrix.3

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.\" ========================================================================
.\"
.IX Title "Matrix 3"
.TH Matrix 3 "2001-09-24" "perl v5.8.0" "User Contributed Perl Documentation"
.SH "NAME"
Math::Matrix \- Multiply and invert Matrices
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
use Math::Matrix;
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
The following methods are available:
.Sh "new"
.IX Subsection "new"
Constructor arguments are a list of references to arrays of the same
length.  The arrays are copied. The method returns \fBundef\fR in case of
error.
.PP
.Vb 3
\&        $a = new Math::Matrix ([rand,rand,rand],
\&                               [rand,rand,rand],
\&                               [rand,rand,rand]);
.Ve
.PP
If you call  \f(CW\*(C`new\*(C'\fR as method, a zero filled matrix with identical deminsions is returned.
.Sh "clone"
.IX Subsection "clone"
You can clone a matrix by calling:
.PP
.Vb 1
\&        $b = $a->clone;
.Ve
.Sh "size"
.IX Subsection "size"
You can determine the dimensions of a matrix by calling:
.PP
.Vb 1
\&        ($m, $n) = $a->size;
.Ve
.Sh "concat"
.IX Subsection "concat"
Concatenates two matrices of same row count. The result is a new
matrix or \fBundef\fR in case of error.
.PP
.Vb 2
\&        $b = new Math::Matrix ([rand],[rand],[rand]);
\&        $c = $a->concat($b);
.Ve
.Sh "transpose"
.IX Subsection "transpose"
Returns the transposed matrix. This is the matrix where colums and
rows of the argument matrix are swaped.
.Sh "multiply"
.IX Subsection "multiply"
Multiplies two matrices where the length of the rows in the first
matrix is the same as the length of the columns in the second
matrix. Returns the product or \fBundef\fR in case of error.
.Sh "solve"
.IX Subsection "solve"
Solves a equation system given by the matrix. The number of colums
must be greater than the number of rows. If variables are dependent
from each other, the second and all further of the dependent
coefficients are 0. This means the method can handle such systems. The
method returns a matrix containing the solutions in its columns or
\&\fBundef\fR in case of error.
.Sh "multiply_scalar"
.IX Subsection "multiply_scalar"
Multiplies a matrix and a scalar resulting in a matrix of the same
dimensions with each element scaled with the scalar.
.PP
.Vb 1
\&  $a->multiply_scalar(2);  scale matrix by factor 2
.Ve
.Sh "add"
.IX Subsection "add"
Add two matrices of the same dimensions.
.Sh "substract"
.IX Subsection "substract"
Shorthand for \f(CW\*(C`add($other\->negative)\*(C'\fR
.Sh "equal"
.IX Subsection "equal"
Decide if two matrices are equal.  Beware of rounding errors!
.Sh "slice"
.IX Subsection "slice"
Extract columns:
.PP
.Vb 1
\&  a->slice(1,3,5);
.Ve
.Sh "determinant"
.IX Subsection "determinant"
Compute the determinant of a matrix.
.Sh "dot_product"
.IX Subsection "dot_product"
Compute the dot product of two vectors.
.Sh "absolute"
.IX Subsection "absolute"
Compute the absolute value of a vector.
.Sh "normalizing"
.IX Subsection "normalizing"
Normalize a vector.
.Sh "cross_product"
.IX Subsection "cross_product"
Compute the cross-product of vectors.
.Sh "print"
.IX Subsection "print"
Prints the matrix on \s-1STDOUT\s0. If the method has additional parameters,
these are printed before the matrix is printed.
.SH "EXAMPLE"
.IX Header "EXAMPLE"
.Vb 1
\&        use Math::Matrix;
.Ve
.PP
.Vb 11
\&        srand(time);
\&        $a = new Math::Matrix ([rand,rand,rand], 
\&                         [rand,rand,rand], 
\&                         [rand,rand,rand]);
\&        $x = new Math::Matrix ([rand,rand,rand]);
\&        $a->print("A\en");
\&        $E = $a->concat($x->transpose);
\&        $E->print("Equation system\en");
\&        $s = $E->solve;
\&        $s->print("Solutions s\en");
\&        $a->multiply($s)->print("A*s\en");
.Ve
.SH "AUTHOR"
.IX Header "AUTHOR"
Ulrich Pfeifer <\fIpfeifer@ls6.informatik.uni\-dortmund.de\fR>
.PP
Brian J. Watson <\fIbjbrew@power.net\fR>
.PP
Matthew Brett <matthew.brett@mrc\-cbu.cam.ac.uk>
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129	.\" ========================================================================
130	.\"
131	.IX Title "Matrix 3"
132	.TH Matrix 3 "2001-09-24" "perl v5.8.0" "User Contributed Perl Documentation"
133	.SH "NAME"
134	Math::Matrix \- Multiply and invert Matrices
135	.SH "SYNOPSIS"
136	.IX Header "SYNOPSIS"
137	use Math::Matrix;
138	.SH "DESCRIPTION"
139	.IX Header "DESCRIPTION"
140	The following methods are available:
141	.Sh "new"
142	.IX Subsection "new"
143	Constructor arguments are a list of references to arrays of the same
144	length. The arrays are copied. The method returns \fBundef\fR in case of
145	error.
146	.PP
147	.Vb 3
148	\& $a = new Math::Matrix ([rand,rand,rand],
149	\& [rand,rand,rand],
150	\& [rand,rand,rand]);
151	.Ve
152	.PP
153	If you call \f(CW\(C`new\(C'\fR as method, a zero filled matrix with identical deminsions is returned.
154	.Sh "clone"
155	.IX Subsection "clone"
156	You can clone a matrix by calling:
157	.PP
158	.Vb 1
159	\& $b = $a->clone;
160	.Ve
161	.Sh "size"
162	.IX Subsection "size"
163	You can determine the dimensions of a matrix by calling:
164	.PP
165	.Vb 1
166	\& ($m, $n) = $a->size;
167	.Ve
168	.Sh "concat"
169	.IX Subsection "concat"
170	Concatenates two matrices of same row count. The result is a new
171	matrix or \fBundef\fR in case of error.
172	.PP
173	.Vb 2
174	\& $b = new Math::Matrix ([rand],[rand],[rand]);
175	\& $c = $a->concat($b);
176	.Ve
177	.Sh "transpose"
178	.IX Subsection "transpose"
179	Returns the transposed matrix. This is the matrix where colums and
180	rows of the argument matrix are swaped.
181	.Sh "multiply"
182	.IX Subsection "multiply"
183	Multiplies two matrices where the length of the rows in the first
184	matrix is the same as the length of the columns in the second
185	matrix. Returns the product or \fBundef\fR in case of error.
186	.Sh "solve"
187	.IX Subsection "solve"
188	Solves a equation system given by the matrix. The number of colums
189	must be greater than the number of rows. If variables are dependent
190	from each other, the second and all further of the dependent
191	coefficients are 0. This means the method can handle such systems. The
192	method returns a matrix containing the solutions in its columns or
193	\&\fBundef\fR in case of error.
194	.Sh "multiply_scalar"
195	.IX Subsection "multiply_scalar"
196	Multiplies a matrix and a scalar resulting in a matrix of the same
197	dimensions with each element scaled with the scalar.
198	.PP
199	.Vb 1
200	\& $a->multiply_scalar(2); scale matrix by factor 2
201	.Ve
202	.Sh "add"
203	.IX Subsection "add"
204	Add two matrices of the same dimensions.
205	.Sh "substract"
206	.IX Subsection "substract"
207	Shorthand for \f(CW\(C`add($other\->negative)\(C'\fR
208	.Sh "equal"
209	.IX Subsection "equal"
210	Decide if two matrices are equal. Beware of rounding errors!
211	.Sh "slice"
212	.IX Subsection "slice"
213	Extract columns:
214	.PP
215	.Vb 1
216	\& a->slice(1,3,5);
217	.Ve
218	.Sh "determinant"
219	.IX Subsection "determinant"
220	Compute the determinant of a matrix.
221	.Sh "dot_product"
222	.IX Subsection "dot_product"
223	Compute the dot product of two vectors.
224	.Sh "absolute"
225	.IX Subsection "absolute"
226	Compute the absolute value of a vector.
227	.Sh "normalizing"
228	.IX Subsection "normalizing"
229	Normalize a vector.
230	.Sh "cross_product"
231	.IX Subsection "cross_product"
232	Compute the cross-product of vectors.
233	.Sh "print"
234	.IX Subsection "print"
235	Prints the matrix on \s-1STDOUT\s0. If the method has additional parameters,
236	these are printed before the matrix is printed.
237	.SH "EXAMPLE"
238	.IX Header "EXAMPLE"
239	.Vb 1
240	\& use Math::Matrix;
241	.Ve
242	.PP
243	.Vb 11
244	\& srand(time);
245	\& $a = new Math::Matrix ([rand,rand,rand],
246	\& [rand,rand,rand],
247	\& [rand,rand,rand]);
248	\& $x = new Math::Matrix ([rand,rand,rand]);
249	\& $a->print("A\en");
250	\& $E = $a->concat($x->transpose);
251	\& $E->print("Equation system\en");
252	\& $s = $E->solve;
253	\& $s->print("Solutions s\en");
254	\& $a->multiply($s)->print("A*s\en");
255	.Ve
256	.SH "AUTHOR"
257	.IX Header "AUTHOR"
258	Ulrich Pfeifer <\fIpfeifer@ls6.informatik.uni\-dortmund.de\fR>
259	.PP
260	Brian J. Watson <\fIbjbrew@power.net\fR>
261	.PP
262	Matthew Brett <matthew.brett@mrc\-cbu.cam.ac.uk>