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javascript-algorithms/src/algorithms/math/matrix/Matrix.js at master · frogkind/javascript-algorithms · GitHub
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algorithms
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math
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matrix
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Matrix.js
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javascript-algorithms
/
src
/
algorithms
/
math
/
matrix
/
Matrix.js
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309 lines (276 loc) · 7.28 KB
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/**
*
@typedef
{
number
} Cell
*
@typedef
{
Cell[][]|Cell[][][]
} Matrix
*
@typedef
{
number[]
} Shape
*
@typedef
{
number[]
} CellIndices
*/
/**
* Gets the matrix's shape.
*
*
@param
{
Matrix
} m
*
@returns
{
Shape
}
*/
export
const
shape
=
(
m
)
=>
{
const
shapes
=
[
]
;
let
dimension
=
m
;
while
(
dimension
&&
Array
.
isArray
(
dimension
)
)
{
shapes
.
push
(
dimension
.
length
)
;
dimension
=
(
dimension
.
length
&&
[
...
dimension
]
[
0
]
)
||
null
;
}
return
shapes
;
}
;
/**
* Checks if matrix has a correct type.
*
*
@param
{
Matrix
} m
*
@throws
{
Error
}
*/
const
validateType
=
(
m
)
=>
{
if
(
!
m
||
!
Array
.
isArray
(
m
)
||
!
Array
.
isArray
(
m
[
0
]
)
)
{
throw
new
Error
(
'Invalid matrix format'
)
;
}
}
;
/**
* Checks if matrix is two dimensional.
*
*
@param
{
Matrix
} m
*
@throws
{
Error
}
*/
const
validate2D
=
(
m
)
=>
{
validateType
(
m
)
;
const
aShape
=
shape
(
m
)
;
if
(
aShape
.
length
!==
2
)
{
throw
new
Error
(
'Matrix is not of 2D shape'
)
;
}
}
;
/**
* Validates that matrices are of the same shape.
*
*
@param
{
Matrix
} a
*
@param
{
Matrix
} b
*
@trows
{Error}
*/
export
const
validateSameShape
=
(
a
,
b
)
=>
{
validateType
(
a
)
;
validateType
(
b
)
;
const
aShape
=
shape
(
a
)
;
const
bShape
=
shape
(
b
)
;
if
(
aShape
.
length
!==
bShape
.
length
)
{
throw
new
Error
(
'Matrices have different dimensions'
)
;
}
while
(
aShape
.
length
&&
bShape
.
length
)
{
if
(
aShape
.
pop
(
)
!==
bShape
.
pop
(
)
)
{
throw
new
Error
(
'Matrices have different shapes'
)
;
}
}
}
;
/**
* Generates the matrix of specific shape with specific values.
*
*
@param
{
Shape
} mShape - the shape of the matrix to generate
*
@param
{
function({CellIndex}): Cell
} fill - cell values of a generated matrix.
*
@returns
{
Matrix
}
*/
export
const
generate
=
(
mShape
,
fill
)
=>
{
/**
* Generates the matrix recursively.
*
*
@param
{
Shape
} recShape - the shape of the matrix to generate
*
@param
{
CellIndices
} recIndices
*
@returns
{
Matrix
}
*/
const
generateRecursively
=
(
recShape
,
recIndices
)
=>
{
if
(
recShape
.
length
===
1
)
{
return
Array
(
recShape
[
0
]
)
.
fill
(
null
)
.
map
(
(
cellValue
,
cellIndex
)
=>
fill
(
[
...
recIndices
,
cellIndex
]
)
)
;
}
const
m
=
[
]
;
for
(
let
i
=
0
;
i
<
recShape
[
0
]
;
i
+=
1
)
{
m
.
push
(
generateRecursively
(
recShape
.
slice
(
1
)
,
[
...
recIndices
,
i
]
)
)
;
}
return
m
;
}
;
return
generateRecursively
(
mShape
,
[
]
)
;
}
;
/**
* Generates the matrix of zeros of specified shape.
*
*
@param
{
Shape
} mShape - shape of the matrix
*
@returns
{
Matrix
}
*/
export
const
zeros
=
(
mShape
)
=>
{
return
generate
(
mShape
,
(
)
=>
0
)
;
}
;
/**
*
@param
{
Matrix
} a
*
@param
{
Matrix
} b
*
@return
Matrix
*
@throws
{
Error
}
*/
export
const
dot
=
(
a
,
b
)
=>
{
// Validate inputs.
validate2D
(
a
)
;
validate2D
(
b
)
;
// Check dimensions.
const
aShape
=
shape
(
a
)
;
const
bShape
=
shape
(
b
)
;
if
(
aShape
[
1
]
!==
bShape
[
0
]
)
{
throw
new
Error
(
'Matrices have incompatible shape for multiplication'
)
;
}
// Perform matrix multiplication.
const
outputShape
=
[
aShape
[
0
]
,
bShape
[
1
]
]
;
const
c
=
zeros
(
outputShape
)
;
for
(
let
bCol
=
0
;
bCol
<
b
[
0
]
.
length
;
bCol
+=
1
)
{
for
(
let
aRow
=
0
;
aRow
<
a
.
length
;
aRow
+=
1
)
{
let
cellSum
=
0
;
for
(
let
aCol
=
0
;
aCol
<
a
[
aRow
]
.
length
;
aCol
+=
1
)
{
cellSum
+=
a
[
aRow
]
[
aCol
]
*
b
[
aCol
]
[
bCol
]
;
}
c
[
aRow
]
[
bCol
]
=
cellSum
;
}
}
return
c
;
}
;
/**
* Transposes the matrix.
*
*
@param
{
Matrix
} m
*
@returns
Matrix
*
@throws
{
Error
}
*/
export
const
t
=
(
m
)
=>
{
validate2D
(
m
)
;
const
mShape
=
shape
(
m
)
;
const
transposed
=
zeros
(
[
mShape
[
1
]
,
mShape
[
0
]
]
)
;
for
(
let
row
=
0
;
row
<
m
.
length
;
row
+=
1
)
{
for
(
let
col
=
0
;
col
<
m
[
0
]
.
length
;
col
+=
1
)
{
transposed
[
col
]
[
row
]
=
m
[
row
]
[
col
]
;
}
}
return
transposed
;
}
;
/**
* Traverses the matrix.
*
*
@param
{
Matrix
} m
*
@param
{
function(indices: CellIndices, c: Cell)
} visit
*/
export
const
walk
=
(
m
,
visit
)
=>
{
/**
* Traverses the matrix recursively.
*
*
@param
{
Matrix
} recM
*
@param
{
CellIndices
} cellIndices
*
@return
{
Matrix
}
*/
const
recWalk
=
(
recM
,
cellIndices
)
=>
{
const
recMShape
=
shape
(
recM
)
;
if
(
recMShape
.
length
===
1
)
{
for
(
let
i
=
0
;
i
<
recM
.
length
;
i
+=
1
)
{
visit
(
[
...
cellIndices
,
i
]
,
recM
[
i
]
)
;
}
}
for
(
let
i
=
0
;
i
<
recM
.
length
;
i
+=
1
)
{
recWalk
(
recM
[
i
]
,
[
...
cellIndices
,
i
]
)
;
}
}
;
recWalk
(
m
,
[
]
)
;
}
;
/**
* Gets the matrix cell value at specific index.
*
*
@param
{
Matrix
} m - Matrix that contains the cell that needs to be updated
*
@param
{
CellIndices
} cellIndices - Array of cell indices
*
@return
{
Cell
}
*/
export
const
getCellAtIndex
=
(
m
,
cellIndices
)
=>
{
// We start from the row at specific index.
let
cell
=
m
[
cellIndices
[
0
]
]
;
// Going deeper into the next dimensions but not to the last one to preserve
// the pointer to the last dimension array.
for
(
let
dimIdx
=
1
;
dimIdx
<
cellIndices
.
length
-
1
;
dimIdx
+=
1
)
{
cell
=
cell
[
cellIndices
[
dimIdx
]
]
;
}
// At this moment the cell variable points to the array at the last needed dimension.
return
cell
[
cellIndices
[
cellIndices
.
length
-
1
]
]
;
}
;
/**
* Update the matrix cell at specific index.
*
*
@param
{
Matrix
} m - Matrix that contains the cell that needs to be updated
*
@param
{
CellIndices
} cellIndices - Array of cell indices
*
@param
{
Cell
} cellValue - New cell value
*/
export
const
updateCellAtIndex
=
(
m
,
cellIndices
,
cellValue
)
=>
{
// We start from the row at specific index.
let
cell
=
m
[
cellIndices
[
0
]
]
;
// Going deeper into the next dimensions but not to the last one to preserve
// the pointer to the last dimension array.
for
(
let
dimIdx
=
1
;
dimIdx
<
cellIndices
.
length
-
1
;
dimIdx
+=
1
)
{
cell
=
cell
[
cellIndices
[
dimIdx
]
]
;
}
// At this moment the cell variable points to the array at the last needed dimension.
cell
[
cellIndices
[
cellIndices
.
length
-
1
]
]
=
cellValue
;
}
;
/**
* Adds two matrices element-wise.
*
*
@param
{
Matrix
} a
*
@param
{
Matrix
} b
*
@return
{
Matrix
}
*/
export
const
add
=
(
a
,
b
)
=>
{
validateSameShape
(
a
,
b
)
;
const
result
=
zeros
(
shape
(
a
)
)
;
walk
(
a
,
(
cellIndices
,
cellValue
)
=>
{
updateCellAtIndex
(
result
,
cellIndices
,
cellValue
)
;
}
)
;
walk
(
b
,
(
cellIndices
,
cellValue
)
=>
{
const
currentCellValue
=
getCellAtIndex
(
result
,
cellIndices
)
;
updateCellAtIndex
(
result
,
cellIndices
,
currentCellValue
+
cellValue
)
;
}
)
;
return
result
;
}
;
/**
* Multiplies two matrices element-wise.
*
*
@param
{
Matrix
} a
*
@param
{
Matrix
} b
*
@return
{
Matrix
}
*/
export
const
mul
=
(
a
,
b
)
=>
{
validateSameShape
(
a
,
b
)
;
const
result
=
zeros
(
shape
(
a
)
)
;
walk
(
a
,
(
cellIndices
,
cellValue
)
=>
{
updateCellAtIndex
(
result
,
cellIndices
,
cellValue
)
;
}
)
;
walk
(
b
,
(
cellIndices
,
cellValue
)
=>
{
const
currentCellValue
=
getCellAtIndex
(
result
,
cellIndices
)
;
updateCellAtIndex
(
result
,
cellIndices
,
currentCellValue
*
cellValue
)
;
}
)
;
return
result
;
}
;
/**
* Subtract two matrices element-wise.
*
*
@param
{
Matrix
} a
*
@param
{
Matrix
} b
*
@return
{
Matrix
}
*/
export
const
sub
=
(
a
,
b
)
=>
{
validateSameShape
(
a
,
b
)
;
const
result
=
zeros
(
shape
(
a
)
)
;
walk
(
a
,
(
cellIndices
,
cellValue
)
=>
{
updateCellAtIndex
(
result
,
cellIndices
,
cellValue
)
;
}
)
;
walk
(
b
,
(
cellIndices
,
cellValue
)
=>
{
const
currentCellValue
=
getCellAtIndex
(
result
,
cellIndices
)
;
updateCellAtIndex
(
result
,
cellIndices
,
currentCellValue
-
cellValue
)
;
}
)
;
return
result
;
}
;
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