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Kirill Terekhov
INMOST
Commits
56dd2319
Commit
56dd2319
authored
Mar 30, 2018
by
Kirill Terekhov
Browse files
Some corrections to linear algebra
parent
6bc3a489
Changes
1
Hide whitespace changes
Inline
Side-by-side
Source/Headers/inmost_dense.h
View file @
56dd2319
...
...
@@ -198,6 +198,9 @@ namespace INMOST
/// @param Perm Array for reordering, size of columns of the matrix.
/// @param SL Diagonal for rescaling matrix from left, size of columns of the matrix.
/// @param SR Diagonal for rescaling matrix from right, size of rows of the matrix.
/// \todo
/// 1. Test rescaling.
/// 2. Test on non-square matrices.
void
MPT
(
INMOST_DATA_ENUM_TYPE
*
Perm
,
INMOST_DATA_REAL_TYPE
*
SL
=
NULL
,
INMOST_DATA_REAL_TYPE
*
SR
=
NULL
)
const
;
/// Singular value decomposition.
/// Reconstruct matrix: A = U*Sigma*V.Transpose().
...
...
@@ -238,18 +241,18 @@ namespace INMOST
V
.
Resize
(
m
,
m
);
std
::
swap
(
n
,
m
);
//this how original algorithm takes it
// Householder reduction to bidiagonal form
for
(
i
=
0
;
i
<
(
int
)
n
;
i
++
)
for
(
i
=
0
;
i
<
n
;
i
++
)
{
// left-hand reduction
l
=
i
+
1
;
rv1
[
i
]
=
scale
*
g
;
g
=
s
=
scale
=
0.0
;
if
(
i
<
(
int
)
m
)
if
(
i
<
m
)
{
for
(
k
=
i
;
k
<
(
int
)
m
;
k
++
)
scale
+=
fabs
(
U
(
k
,
i
));
for
(
k
=
i
;
k
<
m
;
k
++
)
scale
+=
fabs
(
U
(
k
,
i
));
if
(
get_value
(
scale
))
{
for
(
k
=
i
;
k
<
(
int
)
m
;
k
++
)
for
(
k
=
i
;
k
<
m
;
k
++
)
{
U
(
k
,
i
)
/=
scale
;
s
+=
U
(
k
,
i
)
*
U
(
k
,
i
);
...
...
@@ -260,25 +263,25 @@ namespace INMOST
U
(
i
,
i
)
=
f
-
g
;
if
(
i
!=
n
-
1
)
{
for
(
j
=
l
;
j
<
(
int
)
n
;
j
++
)
for
(
j
=
l
;
j
<
n
;
j
++
)
{
for
(
s
=
0.0
,
k
=
i
;
k
<
(
int
)
m
;
k
++
)
s
+=
U
(
k
,
i
)
*
U
(
k
,
j
);
for
(
s
=
0.0
,
k
=
i
;
k
<
m
;
k
++
)
s
+=
U
(
k
,
i
)
*
U
(
k
,
j
);
f
=
s
/
h
;
for
(
k
=
i
;
k
<
(
int
)
m
;
k
++
)
U
(
k
,
j
)
+=
f
*
U
(
k
,
i
);
for
(
k
=
i
;
k
<
m
;
k
++
)
U
(
k
,
j
)
+=
f
*
U
(
k
,
i
);
}
}
for
(
k
=
i
;
k
<
(
int
)
m
;
k
++
)
U
(
k
,
i
)
*=
scale
;
for
(
k
=
i
;
k
<
m
;
k
++
)
U
(
k
,
i
)
*=
scale
;
}
}
Sigma
(
i
,
i
)
=
scale
*
g
;
// right-hand reduction
g
=
s
=
scale
=
0.0
;
if
(
i
<
(
int
)
m
&&
i
!=
n
-
1
)
if
(
i
<
m
&&
i
!=
n
-
1
)
{
for
(
k
=
l
;
k
<
(
int
)
n
;
k
++
)
scale
+=
fabs
(
U
(
i
,
k
));
for
(
k
=
l
;
k
<
n
;
k
++
)
scale
+=
fabs
(
U
(
i
,
k
));
if
(
get_value
(
scale
))
{
for
(
k
=
l
;
k
<
(
int
)
n
;
k
++
)
for
(
k
=
l
;
k
<
n
;
k
++
)
{
U
(
i
,
k
)
=
U
(
i
,
k
)
/
scale
;
s
+=
U
(
i
,
k
)
*
U
(
i
,
k
);
...
...
@@ -287,16 +290,16 @@ namespace INMOST
g
=
-
sign_func
(
sqrt
(
s
),
f
);
h
=
f
*
g
-
s
;
U
(
i
,
l
)
=
f
-
g
;
for
(
k
=
l
;
k
<
(
int
)
n
;
k
++
)
rv1
[
k
]
=
U
(
i
,
k
)
/
h
;
for
(
k
=
l
;
k
<
n
;
k
++
)
rv1
[
k
]
=
U
(
i
,
k
)
/
h
;
if
(
i
!=
m
-
1
)
{
for
(
j
=
l
;
j
<
(
int
)
m
;
j
++
)
for
(
j
=
l
;
j
<
m
;
j
++
)
{
for
(
s
=
0.0
,
k
=
l
;
k
<
(
int
)
n
;
k
++
)
s
+=
U
(
j
,
k
)
*
U
(
i
,
k
);
for
(
k
=
l
;
k
<
(
int
)
n
;
k
++
)
U
(
j
,
k
)
+=
s
*
rv1
[
k
];
for
(
s
=
0.0
,
k
=
l
;
k
<
n
;
k
++
)
s
+=
U
(
j
,
k
)
*
U
(
i
,
k
);
for
(
k
=
l
;
k
<
n
;
k
++
)
U
(
j
,
k
)
+=
s
*
rv1
[
k
];
}
}
for
(
k
=
l
;
k
<
(
int
)
n
;
k
++
)
U
(
i
,
k
)
*=
scale
;
for
(
k
=
l
;
k
<
n
;
k
++
)
U
(
i
,
k
)
*=
scale
;
}
}
anorm
=
max_func
(
anorm
,
fabs
(
get_value
(
Sigma
(
i
,
i
)))
+
fabs
(
get_value
(
rv1
[
i
])));
...
...
@@ -305,19 +308,19 @@ namespace INMOST
// accumulate the right-hand transformation
for
(
i
=
n
-
1
;
i
>=
0
;
i
--
)
{
if
(
i
<
(
int
)
(
n
-
1
))
if
(
i
<
(
n
-
1
))
{
if
(
get_value
(
g
))
{
for
(
j
=
l
;
j
<
(
int
)
n
;
j
++
)
V
(
j
,
i
)
=
((
U
(
i
,
j
)
/
U
(
i
,
l
))
/
g
);
for
(
j
=
l
;
j
<
n
;
j
++
)
V
(
j
,
i
)
=
((
U
(
i
,
j
)
/
U
(
i
,
l
))
/
g
);
// double division to avoid underflow
for
(
j
=
l
;
j
<
(
int
)
n
;
j
++
)
for
(
j
=
l
;
j
<
n
;
j
++
)
{
for
(
s
=
0.0
,
k
=
l
;
k
<
(
int
)
n
;
k
++
)
s
+=
U
(
i
,
k
)
*
V
(
k
,
j
);
for
(
k
=
l
;
k
<
(
int
)
n
;
k
++
)
V
(
k
,
j
)
+=
s
*
V
(
k
,
i
);
for
(
s
=
0.0
,
k
=
l
;
k
<
n
;
k
++
)
s
+=
U
(
i
,
k
)
*
V
(
k
,
j
);
for
(
k
=
l
;
k
<
n
;
k
++
)
V
(
k
,
j
)
+=
s
*
V
(
k
,
i
);
}
}
for
(
j
=
l
;
j
<
(
int
)
n
;
j
++
)
V
(
i
,
j
)
=
V
(
j
,
i
)
=
0.0
;
for
(
j
=
l
;
j
<
n
;
j
++
)
V
(
i
,
j
)
=
V
(
j
,
i
)
=
0.0
;
}
V
(
i
,
i
)
=
1.0
;
g
=
rv1
[
i
];
...
...
@@ -329,24 +332,24 @@ namespace INMOST
{
l
=
i
+
1
;
g
=
Sigma
(
i
,
i
);
if
(
i
<
(
int
)
(
n
-
1
))
for
(
j
=
l
;
j
<
(
int
)
n
;
j
++
)
if
(
i
<
(
n
-
1
))
for
(
j
=
l
;
j
<
n
;
j
++
)
U
(
i
,
j
)
=
0.0
;
if
(
get_value
(
g
))
{
g
=
1.0
/
g
;
if
(
i
!=
n
-
1
)
{
for
(
j
=
l
;
j
<
(
int
)
n
;
j
++
)
for
(
j
=
l
;
j
<
n
;
j
++
)
{
for
(
s
=
0.0
,
k
=
l
;
k
<
(
int
)
m
;
k
++
)
s
+=
(
U
(
k
,
i
)
*
U
(
k
,
j
));
for
(
s
=
0.0
,
k
=
l
;
k
<
m
;
k
++
)
s
+=
(
U
(
k
,
i
)
*
U
(
k
,
j
));
f
=
(
s
/
U
(
i
,
i
))
*
g
;
for
(
k
=
i
;
k
<
(
int
)
m
;
k
++
)
U
(
k
,
j
)
+=
f
*
U
(
k
,
i
);
for
(
k
=
i
;
k
<
m
;
k
++
)
U
(
k
,
j
)
+=
f
*
U
(
k
,
i
);
}
}
for
(
j
=
i
;
j
<
(
int
)
m
;
j
++
)
U
(
j
,
i
)
=
U
(
j
,
i
)
*
g
;
for
(
j
=
i
;
j
<
m
;
j
++
)
U
(
j
,
i
)
=
U
(
j
,
i
)
*
g
;
}
else
for
(
j
=
i
;
j
<
(
int
)
m
;
j
++
)
U
(
j
,
i
)
=
0.0
;
else
for
(
j
=
i
;
j
<
m
;
j
++
)
U
(
j
,
i
)
=
0.0
;
U
(
i
,
i
)
+=
1
;
}
...
...
@@ -383,7 +386,7 @@ namespace INMOST
h
=
1.0
/
h
;
c
=
g
*
h
;
s
=
(
-
f
*
h
);
for
(
j
=
0
;
j
<
(
int
)
m
;
j
++
)
for
(
j
=
0
;
j
<
m
;
j
++
)
{
y
=
U
(
j
,
nm
);
z
=
U
(
j
,
i
);
...
...
@@ -399,7 +402,7 @@ namespace INMOST
if
(
z
<
0.0
&&
nonnegative
)
{
// make singular value nonnegative
Sigma
(
k
,
k
)
=
-
z
;
for
(
j
=
0
;
j
<
(
int
)
n
;
j
++
)
V
(
j
,
k
)
=
-
V
(
j
,
k
);
for
(
j
=
0
;
j
<
n
;
j
++
)
V
(
j
,
k
)
=
-
V
(
j
,
k
);
}
break
;
}
...
...
@@ -435,7 +438,7 @@ namespace INMOST
g
=
g
*
c
-
x
*
s
;
h
=
y
*
s
;
y
=
y
*
c
;
for
(
jj
=
0
;
jj
<
(
int
)
n
;
jj
++
)
for
(
jj
=
0
;
jj
<
n
;
jj
++
)
{
x
=
V
(
jj
,
j
);
z
=
V
(
jj
,
i
);
...
...
@@ -452,7 +455,7 @@ namespace INMOST
}
f
=
(
c
*
g
)
+
(
s
*
y
);
x
=
(
c
*
y
)
-
(
s
*
g
);
for
(
jj
=
0
;
jj
<
(
int
)
m
;
jj
++
)
for
(
jj
=
0
;
jj
<
m
;
jj
++
)
{
y
=
U
(
jj
,
j
);
z
=
U
(
jj
,
i
);
...
...
@@ -469,10 +472,10 @@ namespace INMOST
if
(
order_singular_values
)
{
Var
temp
;
for
(
i
=
0
;
i
<
(
int
)
n
;
i
++
)
for
(
i
=
0
;
i
<
n
;
i
++
)
{
k
=
i
;
for
(
j
=
i
+
1
;
j
<
(
int
)
n
;
++
j
)
for
(
j
=
i
+
1
;
j
<
n
;
++
j
)
if
(
Sigma
(
k
,
k
)
<
Sigma
(
j
,
j
)
)
k
=
j
;
if
(
Sigma
(
k
,
k
)
>
Sigma
(
i
,
i
)
)
{
...
...
@@ -480,14 +483,14 @@ namespace INMOST
Sigma
(
k
,
k
)
=
Sigma
(
i
,
i
);
Sigma
(
i
,
i
)
=
temp
;
// U is m by n
for
(
int
j
=
0
;
j
<
(
int
)
m
;
++
j
)
for
(
int
j
=
0
;
j
<
m
;
++
j
)
{
temp
=
U
(
j
,
k
);
U
(
j
,
k
)
=
U
(
j
,
i
);
U
(
j
,
i
)
=
temp
;
}
// V is n by n
for
(
int
j
=
0
;
j
<
(
int
)
n
;
++
j
)
for
(
int
j
=
0
;
j
<
n
;
++
j
)
{
temp
=
V
(
j
,
k
);
V
(
j
,
k
)
=
V
(
j
,
i
);
...
...
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