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// Helpers for Array and complex maths
function
complex_mul
(
C1
,
C2
)
{
const
len
=
C1
[
0
]
.
length
let
ret
=
[
new
Array
(
len
)
,
new
Array
(
len
)
]
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
const
ac
=
C1
[
0
]
[
i
]
*
C2
[
0
]
[
i
]
const
bd
=
C1
[
1
]
[
i
]
*
C2
[
1
]
[
i
]
const
ad
=
C1
[
0
]
[
i
]
*
C2
[
1
]
[
i
]
const
bc
=
C1
[
1
]
[
i
]
*
C2
[
0
]
[
i
]
ret
[
0
]
[
i
]
=
ac
-
bd
ret
[
1
]
[
i
]
=
ad
+
bc
}
return
ret
}
function
complex_div
(
C1
,
C2
)
{
const
len
=
C1
[
0
]
.
length
let
ret
=
[
new
Array
(
len
)
,
new
Array
(
len
)
]
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
const
ac
=
C1
[
0
]
[
i
]
*
C2
[
0
]
[
i
]
const
bd
=
C1
[
1
]
[
i
]
*
C2
[
1
]
[
i
]
const
ad
=
C1
[
0
]
[
i
]
*
C2
[
1
]
[
i
]
const
bc
=
C1
[
1
]
[
i
]
*
C2
[
0
]
[
i
]
const
denominator
=
1
/
(
C2
[
0
]
[
i
]
**
2
+
C2
[
1
]
[
i
]
**
2
)
ret
[
0
]
[
i
]
=
(
ac
+
bd
)
*
denominator
ret
[
1
]
[
i
]
=
(
bc
-
ad
)
*
denominator
}
return
ret
}
function
complex_abs
(
C
)
{
const
len
=
C
[
0
]
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
(
(
C
[
0
]
[
i
]
**
2
)
+
(
C
[
1
]
[
i
]
**
2
)
)
**
0.5
}
return
ret
}
function
complex_inverse
(
C
)
{
const
len
=
C
[
0
]
.
length
let
ret
=
[
new
Array
(
len
)
,
new
Array
(
len
)
]
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
const
denominator
=
1
/
(
(
C
[
0
]
[
i
]
**
2
)
+
(
C
[
1
]
[
i
]
**
2
)
)
ret
[
0
]
[
i
]
=
C
[
0
]
[
i
]
*
denominator
ret
[
1
]
[
i
]
=
C
[
1
]
[
i
]
*
-
denominator
}
return
ret
}
function
complex_square
(
C
)
{
const
len
=
C
[
0
]
.
length
let
ret
=
[
new
Array
(
len
)
,
new
Array
(
len
)
]
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
0
]
[
i
]
=
(
C
[
0
]
[
i
]
**
2
)
-
(
C
[
1
]
[
i
]
**
2
)
ret
[
1
]
[
i
]
=
C
[
0
]
[
i
]
*
C
[
1
]
[
i
]
*
2
}
return
ret
}
function
complex_phase
(
C
)
{
const
len
=
C
[
0
]
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
Math
.
atan2
(
C
[
1
]
[
i
]
,
C
[
0
]
[
i
]
)
}
return
ret
}
function
complex_conj
(
C
)
{
return
[
C
[
0
]
.
slice
(
)
,
array_scale
(
C
[
1
]
,
-
1
)
]
}
function
exp_jw
(
freq
,
rate
)
{
const
scale
=
(
2
*
Math
.
PI
)
/
rate
const
len
=
freq
.
length
let
ret
=
[
new
Array
(
len
)
,
new
Array
(
len
)
]
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
// e^(ic) = (cos c) + i(sin c)
// no real component in jw
const
jw
=
freq
[
i
]
*
scale
ret
[
0
]
[
i
]
=
Math
.
cos
(
jw
)
ret
[
1
]
[
i
]
=
Math
.
sin
(
jw
)
}
return
ret
}
function
array_max
(
A
,
B
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
Math
.
max
(
A
[
i
]
,
B
[
i
]
)
}
return
ret
}
function
array_min
(
A
,
B
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
Math
.
min
(
A
[
i
]
,
B
[
i
]
)
}
return
ret
}
function
array_scale
(
A
,
scale
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
A
[
i
]
*
scale
}
return
ret
}
function
array_inverse
(
A
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
1
/
A
[
i
]
}
return
ret
}
function
array_mul
(
A
,
B
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
A
[
i
]
*
B
[
i
]
}
return
ret
}
function
array_div
(
A
,
B
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
A
[
i
]
/
B
[
i
]
}
return
ret
}
function
array_offset
(
A
,
offset
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
A
[
i
]
+
offset
}
return
ret
}
function
array_add
(
A
,
B
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
A
[
i
]
+
B
[
i
]
}
return
ret
}
function
array_sub
(
A
,
B
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
A
[
i
]
-
B
[
i
]
}
return
ret
}
function
array_log10
(
A
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
Math
.
log10
(
A
[
i
]
)
}
return
ret
}
function
array_all_equal
(
A
,
val
)
{
const
len
=
A
.
length
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
if
(
A
[
i
]
!=
val
)
{
return
false
}
}
return
true
}
function
array_all_NaN
(
A
)
{
const
len
=
A
.
length
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
if
(
!
isNaN
(
A
[
i
]
)
)
{
return
false
}
}
return
true
}
function
array_abs
(
A
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
Math
.
abs
(
A
[
i
]
)
}
return
ret
}
function
array_sqrt
(
A
)
{
const
len
=
A
.
length
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
Math
.
sqrt
(
A
[
i
]
)
}
return
ret
}
function
array_sum
(
A
)
{
const
len
=
A
.
length
let
ret
=
0
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
+=
A
[
i
]
}
return
ret
}
function
array_mean
(
A
)
{
return
array_sum
(
A
)
/
A
.
length
}
// Return a range, including start and end points
function
array_from_range
(
start
,
end
,
step
)
{
const
len
=
Math
.
floor
(
(
end
-
start
)
/
step
)
+
1
let
val
=
start
let
ret
=
new
Array
(
len
)
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
ret
[
i
]
=
val
val
+=
step
}
return
ret
}
// Linear interpolation between arrays
function
linear_interp
(
values
,
index
,
query_index
)
{
const
len
=
query_index
.
length
let
ret
=
new
Array
(
len
)
const
last_value_index
=
index
.
length
-
1
let
interpolate_index
=
0
for
(
let
i
=
0
;
i
<
len
;
i
++
)
{
if
(
query_index
[
i
]
<=
index
[
0
]
)
{
// Before start
ret
[
i
]
=
values
[
0
]
continue
}
if
(
query_index
[
i
]
>=
index
[
last_value_index
]
)
{
// After end
ret
[
i
]
=
values
[
last_value_index
]
continue
}
// increment index until there is a point after the target
for
(
interpolate_index
;
interpolate_index
<
last_value_index
;
interpolate_index
++
)
{
if
(
query_index
[
i
]
<
index
[
interpolate_index
+
1
]
)
{
const
ratio
=
(
query_index
[
i
]
-
index
[
interpolate_index
]
)
/
(
index
[
interpolate_index
+
1
]
-
index
[
interpolate_index
]
)
ret
[
i
]
=
values
[
interpolate_index
]
+
(
values
[
interpolate_index
+
1
]
-
values
[
interpolate_index
]
)
*
ratio
break
}
}
}
return
ret
}
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