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Michal Malý
Molstar
Commits
80506448
Commit
80506448
authored
5 years ago
by
Alexander Rose
Browse files
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mat3 symmetricEigenvalues and eigenvectors
parent
347c1986
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src/mol-math/linear-algebra/3d/mat3.ts
+190
-2
190 additions, 2 deletions
src/mol-math/linear-algebra/3d/mat3.ts
src/mol-math/linear-algebra/_spec/mat3.spec.ts
+35
-0
35 additions, 0 deletions
src/mol-math/linear-algebra/_spec/mat3.spec.ts
with
225 additions
and
2 deletions
src/mol-math/linear-algebra/3d/mat3.ts
+
190
−
2
View file @
80506448
/**
* Copyright (c) 2017-201
8
mol* contributors, licensed under MIT, See LICENSE file for more info.
* Copyright (c) 2017-201
9
mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author David Sehnal <david.sehnal@gmail.com>
* @author Alexander Rose <alexander.rose@weirdbyte.de>
...
...
@@ -17,10 +17,11 @@
* furnished to do so, subject to the following conditions:
*/
import
{
Mat4
}
from
'
../3d
'
import
{
Mat4
,
Vec3
}
from
'
../3d
'
import
{
NumberArray
}
from
'
../../../mol-util/type-helpers
'
;
interface
Mat3
extends
Array
<
number
>
{
[
d
:
number
]:
number
,
'
@type
'
:
'
mat3
'
,
length
:
9
}
interface
ReadonlyMat3
extends
Array
<
number
>
{
readonly
[
d
:
number
]:
number
,
'
@type
'
:
'
mat3
'
,
length
:
9
}
function
Mat3
()
{
return
Mat3
.
zero
();
...
...
@@ -102,6 +103,20 @@ namespace Mat3 {
return
out
;
}
export
function
create
(
a00
:
number
,
a01
:
number
,
a02
:
number
,
a10
:
number
,
a11
:
number
,
a12
:
number
,
a20
:
number
,
a21
:
number
,
a22
:
number
):
Mat3
{
const
out
=
zero
();
out
[
0
]
=
a00
out
[
1
]
=
a01
out
[
2
]
=
a02
out
[
3
]
=
a10
out
[
4
]
=
a11
out
[
5
]
=
a12
out
[
6
]
=
a20
out
[
7
]
=
a21
out
[
8
]
=
a22
return
out
;
}
export
function
hasNaN
(
m
:
Mat3
)
{
for
(
let
i
=
0
;
i
<
9
;
i
++
)
if
(
isNaN
(
m
[
i
]))
return
true
return
false
...
...
@@ -114,6 +129,13 @@ namespace Mat3 {
return
Mat3
.
copy
(
Mat3
.
zero
(),
a
);
}
export
function
areEqual
(
a
:
Mat3
,
b
:
Mat3
,
eps
:
number
)
{
for
(
let
i
=
0
;
i
<
9
;
i
++
)
{
if
(
Math
.
abs
(
a
[
i
]
-
b
[
i
])
>
eps
)
return
false
;
}
return
true
;
}
export
function
setValue
(
a
:
Mat3
,
i
:
number
,
j
:
number
,
value
:
number
)
{
a
[
3
*
j
+
i
]
=
value
;
}
...
...
@@ -210,6 +232,172 @@ namespace Mat3 {
// Calculate the determinant
return
a00
*
b01
+
a01
*
b11
+
a02
*
b21
;
}
export
function
trace
(
a
:
Mat3
)
{
return
a
[
0
]
+
a
[
4
]
+
a
[
8
]
}
export
function
sub
(
out
:
Mat3
,
a
:
Mat3
,
b
:
Mat3
)
{
out
[
0
]
=
a
[
0
]
-
b
[
0
]
out
[
1
]
=
a
[
1
]
-
b
[
1
]
out
[
2
]
=
a
[
2
]
-
b
[
2
]
out
[
3
]
=
a
[
3
]
-
b
[
3
]
out
[
4
]
=
a
[
4
]
-
b
[
4
]
out
[
5
]
=
a
[
5
]
-
b
[
5
]
out
[
6
]
=
a
[
6
]
-
b
[
6
]
out
[
7
]
=
a
[
7
]
-
b
[
7
]
out
[
8
]
=
a
[
8
]
-
b
[
8
]
return
out
}
export
function
add
(
out
:
Mat3
,
a
:
Mat3
,
b
:
Mat3
)
{
out
[
0
]
=
a
[
0
]
+
b
[
0
]
out
[
1
]
=
a
[
1
]
+
b
[
1
]
out
[
2
]
=
a
[
2
]
+
b
[
2
]
out
[
3
]
=
a
[
3
]
+
b
[
3
]
out
[
4
]
=
a
[
4
]
+
b
[
4
]
out
[
5
]
=
a
[
5
]
+
b
[
5
]
out
[
6
]
=
a
[
6
]
+
b
[
6
]
out
[
7
]
=
a
[
7
]
+
b
[
7
]
out
[
8
]
=
a
[
8
]
+
b
[
8
]
return
out
}
export
function
mul
(
out
:
Mat3
,
a
:
Mat3
,
b
:
Mat3
)
{
const
a00
=
a
[
0
],
a01
=
a
[
1
],
a02
=
a
[
2
],
a10
=
a
[
3
],
a11
=
a
[
4
],
a12
=
a
[
5
],
a20
=
a
[
6
],
a21
=
a
[
7
],
a22
=
a
[
8
];
const
b00
=
b
[
0
],
b01
=
b
[
1
],
b02
=
b
[
2
],
b10
=
b
[
3
],
b11
=
b
[
4
],
b12
=
b
[
5
],
b20
=
b
[
6
],
b21
=
b
[
7
],
b22
=
b
[
8
];
out
[
0
]
=
b00
*
a00
+
b01
*
a10
+
b02
*
a20
;
out
[
1
]
=
b00
*
a01
+
b01
*
a11
+
b02
*
a21
;
out
[
2
]
=
b00
*
a02
+
b01
*
a12
+
b02
*
a22
;
out
[
3
]
=
b10
*
a00
+
b11
*
a10
+
b12
*
a20
;
out
[
4
]
=
b10
*
a01
+
b11
*
a11
+
b12
*
a21
;
out
[
5
]
=
b10
*
a02
+
b11
*
a12
+
b12
*
a22
;
out
[
6
]
=
b20
*
a00
+
b21
*
a10
+
b22
*
a20
;
out
[
7
]
=
b20
*
a01
+
b21
*
a11
+
b22
*
a21
;
out
[
8
]
=
b20
*
a02
+
b21
*
a12
+
b22
*
a22
;
return
out
;
}
export
function
subScalar
(
out
:
Mat3
,
a
:
Mat3
,
s
:
number
)
{
out
[
0
]
=
a
[
0
]
-
s
out
[
1
]
=
a
[
1
]
-
s
out
[
2
]
=
a
[
2
]
-
s
out
[
3
]
=
a
[
3
]
-
s
out
[
4
]
=
a
[
4
]
-
s
out
[
5
]
=
a
[
5
]
-
s
out
[
6
]
=
a
[
6
]
-
s
out
[
7
]
=
a
[
7
]
-
s
out
[
8
]
=
a
[
8
]
-
s
return
out
}
export
function
addScalar
(
out
:
Mat3
,
a
:
Mat3
,
s
:
number
)
{
out
[
0
]
=
a
[
0
]
+
s
out
[
1
]
=
a
[
1
]
+
s
out
[
2
]
=
a
[
2
]
+
s
out
[
3
]
=
a
[
3
]
+
s
out
[
4
]
=
a
[
4
]
+
s
out
[
5
]
=
a
[
5
]
+
s
out
[
6
]
=
a
[
6
]
+
s
out
[
7
]
=
a
[
7
]
+
s
out
[
8
]
=
a
[
8
]
+
s
return
out
}
export
function
mulScalar
(
out
:
Mat3
,
a
:
Mat3
,
s
:
number
)
{
out
[
0
]
=
a
[
0
]
*
s
out
[
1
]
=
a
[
1
]
*
s
out
[
2
]
=
a
[
2
]
*
s
out
[
3
]
=
a
[
3
]
*
s
out
[
4
]
=
a
[
4
]
*
s
out
[
5
]
=
a
[
5
]
*
s
out
[
6
]
=
a
[
6
]
*
s
out
[
7
]
=
a
[
7
]
*
s
out
[
8
]
=
a
[
8
]
*
s
return
out
}
const
piThird
=
Math
.
PI
/
3
const
tmpB
=
Mat3
()
/**
* Given a real symmetric 3x3 matrix A, compute the eigenvalues
*
* From https://en.wikipedia.org/wiki/Eigenvalue_algorithm#3.C3.973_matrices
*/
export
function
symmetricEigenvalues
(
out
:
Vec3
,
a
:
Mat3
)
{
const
p1
=
a
[
1
]
*
a
[
1
]
+
a
[
2
]
*
a
[
2
]
+
a
[
5
]
*
a
[
5
]
if
(
p1
===
0
)
{
out
[
0
]
=
a
[
0
]
out
[
1
]
=
a
[
4
]
out
[
2
]
=
a
[
8
]
}
else
{
const
q
=
trace
(
a
)
/
3
const
a1
=
a
[
0
]
-
q
const
a2
=
a
[
4
]
-
q
const
a3
=
a
[
8
]
-
q
const
p2
=
a1
*
a1
+
a2
*
a2
+
a3
*
a3
+
2
*
p1
const
p
=
Math
.
sqrt
(
p2
/
6
)
mulScalar
(
tmpB
,
Identity
,
q
)
sub
(
tmpB
,
a
,
tmpB
)
mulScalar
(
tmpB
,
tmpB
,
(
1
/
p
))
const
r
=
determinant
(
tmpB
)
/
2
// In exact arithmetic for a symmetric matrix -1 <= r <= 1
// but computation error can leave it slightly outside this range.
const
phi
=
r
<=
-
1
?
piThird
:
r
>=
1
?
0
:
Math
.
acos
(
r
)
/
3
// the eigenvalues satisfy eig3 <= eig2 <= eig1
out
[
0
]
=
q
+
2
*
p
*
Math
.
cos
(
phi
)
out
[
2
]
=
q
+
2
*
p
*
Math
.
cos
(
phi
+
(
2
*
piThird
))
out
[
1
]
=
3
*
q
-
out
[
0
]
-
out
[
2
]
// since trace(A) = eig1 + eig2 + eig3
}
return
out
}
const
tmpR0
=
[
0.1
,
0.0
,
0.0
]
as
Vec3
const
tmpR1
=
[
0.1
,
0.0
,
0.0
]
as
Vec3
const
tmpR2
=
[
0.1
,
0.0
,
0.0
]
as
Vec3
const
tmpR0xR1
=
[
0.1
,
0.0
,
0.0
]
as
Vec3
const
tmpR0xR2
=
[
0.1
,
0.0
,
0.0
]
as
Vec3
const
tmpR1xR2
=
[
0.1
,
0.0
,
0.0
]
as
Vec3
/**
* Calculates the eigenvector for the given eigenvalue `e` of matrix `a`
*/
export
function
eigenvector
(
out
:
Vec3
,
a
:
Mat3
,
e
:
number
)
{
Vec3
.
set
(
tmpR0
,
a
[
0
]
-
e
,
a
[
1
],
a
[
2
])
Vec3
.
set
(
tmpR1
,
a
[
1
],
a
[
4
]
-
e
,
a
[
5
])
Vec3
.
set
(
tmpR2
,
a
[
2
],
a
[
5
],
a
[
8
]
-
e
)
Vec3
.
cross
(
tmpR0xR1
,
tmpR0
,
tmpR1
)
Vec3
.
cross
(
tmpR0xR2
,
tmpR0
,
tmpR2
)
Vec3
.
cross
(
tmpR1xR2
,
tmpR1
,
tmpR2
)
const
d0
=
Vec3
.
dot
(
tmpR0xR1
,
tmpR0xR1
)
const
d1
=
Vec3
.
dot
(
tmpR0xR2
,
tmpR0xR2
)
const
d2
=
Vec3
.
dot
(
tmpR1xR2
,
tmpR1xR2
)
let
dmax
=
d0
let
imax
=
0
if
(
d1
>
dmax
)
{
dmax
=
d1
imax
=
1
}
if
(
d2
>
dmax
)
imax
=
2
if
(
imax
===
0
)
{
Vec3
.
scale
(
out
,
tmpR0xR1
,
1
/
Math
.
sqrt
(
d0
))
}
else
if
(
imax
===
1
)
{
Vec3
.
scale
(
out
,
tmpR0xR2
,
1
/
Math
.
sqrt
(
d1
))
}
else
{
Vec3
.
scale
(
out
,
tmpR1xR2
,
1
/
Math
.
sqrt
(
d2
))
}
return
out
}
export
const
Identity
:
ReadonlyMat3
=
identity
()
}
export
default
Mat3
\ No newline at end of file
This diff is collapsed.
Click to expand it.
src/mol-math/linear-algebra/_spec/mat3.spec.ts
0 → 100644
+
35
−
0
View file @
80506448
/**
* Copyright (c) 2019 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author Alexander Rose <alexander.rose@weirdbyte.de>
*/
import
{
Mat3
,
Vec3
}
from
'
../3d
'
describe
(
'
Mat3
'
,
()
=>
{
it
(
'
symmetricEigenvalues
'
,
()
=>
{
const
m
=
Mat3
.
create
(
0.1945
,
-
0.0219
,
-
0.0416
,
-
0.0219
,
0.1995
,
-
0.0119
,
-
0.0416
,
-
0.0119
,
0.3673
)
const
e
=
Vec3
.
create
(
0.377052701425898
,
0.21713981522725134
,
0.1671074833468507
)
expect
(
Vec3
.
equals
(
e
,
Mat3
.
symmetricEigenvalues
(
Vec3
(),
m
))).
toBe
(
true
);
});
it
(
'
eigenvectors
'
,
()
=>
{
const
m
=
Mat3
.
create
(
0.1945
,
-
0.0219
,
-
0.0416
,
-
0.0219
,
0.1995
,
-
0.0119
,
-
0.0416
,
-
0.0119
,
0.3673
)
const
e
=
Vec3
.
create
(
0.377052701425898
,
0.21713981522725134
,
0.1671074833468507
)
const
v0
=
Vec3
.
create
(
-
0.2176231019882068
,
-
0.038522620041966125
,
0.9752723687391808
)
const
v1
=
Vec3
.
create
(
-
0.5905636938047126
,
0.8007524989198634
,
-
0.10014968314142503
)
const
v2
=
Vec3
.
create
(
0.7770937582036648
,
0.5977553372576602
,
0.19701230352667118
)
expect
(
Vec3
.
equals
(
v0
,
Mat3
.
eigenvector
(
Vec3
(),
m
,
e
[
0
]))).
toBe
(
true
);
expect
(
Vec3
.
equals
(
v1
,
Mat3
.
eigenvector
(
Vec3
(),
m
,
e
[
1
]))).
toBe
(
true
);
expect
(
Vec3
.
equals
(
v2
,
Mat3
.
eigenvector
(
Vec3
(),
m
,
e
[
2
]))).
toBe
(
true
);
});
});
\ No newline at end of file
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