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Java/DataStructures/Matrix/MatrixFastPower.java at master · android9527/Java · GitHub
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Matrix
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MatrixFastPower.java
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DataStructures
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Matrix
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MatrixFastPower.java
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/**
*
* Java implementation of Matrix fast power
* It can calculate the high power of constant Matrix with O( log(K) )
* where K is the power of the Matrix
*
* In order to do that, Matrix must be square Matrix ( columns equals rows)
*
* Notice : large power of Matrix may cause overflow
*
*
* other Matrix basic operator is based on @author Kyler Smith, 2017
*
* @author DDullahan, 2018
*
*/
class
MatrixFastPower
{
/**
* Matrix Fast Power
*
* @param matrix : square Matrix
* @param k : power of Matrix
* @return product
*/
public
static
Matrix
FastPower
(
Matrix
matrix
,
int
k
)
throws
RuntimeException
{
if
(
matrix
.
getColumns
() !=
matrix
.
getRows
())
throw
new
RuntimeException
(
"Matrix is not square Matrix."
);
int
[][]
newData
=
new
int
[
matrix
.
getColumns
()][
matrix
.
getRows
()];
for
(
int
i
=
0
;
i
<
matrix
.
getColumns
();
i
++)
newData
[
i
][
i
] =
1
;
Matrix
newMatrix
=
new
Matrix
(
newData
),
coMatrix
=
new
Matrix
(
matrix
.
data
);
while
(
k
!=
0
) {
if
((
k
&
1
) !=
0
)
newMatrix
=
newMatrix
.
multiply
(
coMatrix
);
k
>>=
1
;
coMatrix
=
coMatrix
.
multiply
(
coMatrix
);
}
return
newMatrix
;
}
public
static
void
main
(
String
[]
argv
) {
int
[][]
data
= {{
1
,
2
,
3
}, {
4
,
5
,
6
}, {
7
,
8
,
9
}};
Matrix
matrix
=
new
Matrix
(
data
);
System
.
out
.
println
(
"original matrix : "
);
System
.
out
.
println
(
matrix
.
toString
());
matrix
=
MatrixFastPower
.
FastPower
(
matrix
,
5
);
System
.
out
.
println
(
"after power : "
);
System
.
out
.
println
(
matrix
.
toString
());
matrix
=
MatrixFastPower
.
FastPower
(
matrix
,
1000000
);
System
.
out
.
println
(
"notice, large power may cause overflow : "
);
System
.
out
.
print
(
matrix
.
toString
());
System
.
out
.
println
(
"you can use mod to fix that :-) "
);
}
}
class
Matrix
{
public
int
[][]
data
;
/**
* Constructor for the matrix takes in a 2D array
*
* @param pData
*/
public
Matrix
(
int
[][]
pData
) {
/** Make a deep copy of the data */
if
(
pData
.
length
!=
0
) {
int
[][]
newData
=
new
int
[
pData
.
length
][
pData
[
0
].
length
];
for
(
int
i
=
0
;
i
<
pData
.
length
;
i
++)
for
(
int
j
=
0
;
j
<
pData
[
0
].
length
;
j
++)
newData
[
i
][
j
] =
pData
[
i
][
j
];
this
.
data
=
newData
;
}
else
{
this
.
data
=
null
;
}
}
/**
* Returns the element specified by the given location
*
* @param x : x cooridinate
* @param y : y cooridinate
* @return int : value at location
*/
public
int
getElement
(
int
x
,
int
y
) {
return
data
[
x
][
y
];
}
/**
* Returns the number of rows in the Matrix
*
* @return rows
*/
public
int
getRows
() {
if
(
this
.
data
==
null
)
return
0
;
return
data
.
length
;
}
/**
* Returns the number of rows in the Matrix
*
* @return columns
*/
public
int
getColumns
() {
if
(
this
.
data
==
null
)
return
0
;
return
data
[
0
].
length
;
}
/**
* Multiplies this matrix with another matrix.
*
* @param other : Matrix to be multiplied with
* @return product
*/
public
Matrix
multiply
(
Matrix
other
)
throws
RuntimeException
{
int
[][]
newData
=
new
int
[
this
.
data
.
length
][
other
.
getColumns
()];
if
(
this
.
getColumns
() !=
other
.
getRows
())
throw
new
RuntimeException
(
"The two matrices cannot be multiplied."
);
int
sum
;
for
(
int
i
=
0
;
i
<
this
.
getRows
(); ++
i
)
for
(
int
j
=
0
;
j
<
other
.
getColumns
(); ++
j
) {
sum
=
0
;
for
(
int
k
=
0
;
k
<
this
.
getColumns
(); ++
k
) {
sum
+=
this
.
data
[
i
][
k
] *
other
.
getElement
(
k
,
j
);
}
newData
[
i
][
j
] =
sum
;
}
return
new
Matrix
(
newData
);
}
/**
* Returns the Matrix as a String in the following format
*
* [ a b c ] ...
* [ x y z ] ...
* [ i j k ] ...
* ...
*
* @return Matrix as String
* TODO: Work formatting for different digit sizes
*/
public
String
toString
() {
String
str
=
""
;
for
(
int
i
=
0
;
i
<
this
.
data
.
length
;
i
++) {
str
+=
"[ "
;
for
(
int
j
=
0
;
j
<
this
.
data
[
0
].
length
;
j
++) {
str
+=
data
[
i
][
j
];
str
+=
" "
;
}
str
+=
"]"
;
str
+=
"
\n
"
;
}
return
str
;
}
}
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