FunctionBaumWelchLibrary "FunctionBaumWelch"
Baum-Welch Algorithm, also known as Forward-Backward Algorithm, uses the well known EM algorithm
to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed
feature vectors.
---
### Function List:
> `forward (array pi, matrix a, matrix b, array obs)`
> `forward (array pi, matrix a, matrix b, array obs, bool scaling)`
> `backward (matrix a, matrix b, array obs)`
> `backward (matrix a, matrix b, array obs, array c)`
> `baumwelch (array observations, int nstates)`
> `baumwelch (array observations, array pi, matrix a, matrix b)`
---
### Reference:
> en.wikipedia.org
> github.com
> en.wikipedia.org
> www.rdocumentation.org
> www.rdocumentation.org
forward(pi, a, b, obs)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float ) : Initial probabilities.
a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int ) : List with actual state observation data.
Returns: - `matrix _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
forward(pi, a, b, obs, scaling)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float ) : Initial probabilities.
a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int ) : List with actual state observation data.
scaling (bool) : Normalize `alpha` scale.
Returns: - #### Tuple with:
> - `matrix _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
> - `array _c`: Array with normalization scale.
backward(a, b, obs)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int ) : Array with actual state observation data.
Returns: - `matrix _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
backward(a, b, obs, c)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int ) : Array with actual state observation data.
c (float ) : Array with Normalization scaling coefficients.
Returns: - `matrix _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
baumwelch(observations, nstates)
**(Random Initialization)** Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int ) : List of observed states.
nstates (int)
Returns: - #### Tuple with:
> - `array _pi`: Initial probability distribution.
> - `matrix _a`: Transition probability matrix.
> - `matrix _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
baumwelch(observations, pi, a, b)
Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int ) : List of observed states.
pi (float ) : Initial probaility distribution.
a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
Returns: - #### Tuple with:
> - `array _pi`: Initial probability distribution.
> - `matrix _a`: Transition probability matrix.
> - `matrix _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
Komut dosyalarını "欧易PI币开盘价格" için ara
pymath█ OVERVIEW
This library ➕ enhances Pine Script's built-in types (`float`, `int`, `array`, `array`) with mathematical methods, mirroring 🪞 many functions from Python's `math` module. Import this library to overload or add to built-in capabilities, enabling calls like `myFloat.sin()` or `myIntArray.gcd()`.
█ CONCEPTS
This library wraps Pine's built-in `math.*` functions and implements others where necessary, expanding the mathematical toolkit available within Pine Script. It provides a more object-oriented approach to mathematical operations on core data types.
█ HOW TO USE
• Import the library: i mport kaigouthro/pymath/1
• Call methods directly on variables: myFloat.sin() , myIntArray.gcd()
• For raw integer literals, you MUST use parentheses: `(1234).factorial()`.
█ FEATURES
• **Infinity Handling:** Includes `isinf()` and `isfinite()` for robust checks. Uses `POS_INF_PROXY` to represent infinity.
• **Comprehensive Math Functions:** Implements a wide range of methods, including trigonometric, logarithmic, hyperbolic, and array operations.
• **Object-Oriented Approach:** Allows direct method calls on `int`, `float`, and arrays for cleaner code.
• **Improved Accuracy:** Some functions (e.g., `remainder()`) offer improved accuracy compared to default Pine behavior.
• **Helper Functions:** Internal helper functions optimize calculations and handle edge cases.
█ NOTES
This library improves upon Pine Script's built-in `math` functions by adding new ones and refining existing implementations. It handles edge cases such as infinity, NaN, and zero values, enhancing the reliability of your Pine scripts. For Speed, it wraps and uses built-ins, as thy are fastest.
█ EXAMPLES
//@version=6
indicator("My Indicator")
// Import the library
import kaigouthro/pymath/1
// Create some Vars
float myFloat = 3.14159
int myInt = 10
array myIntArray = array.from(1, 2, 3, 4, 5)
// Now you can...
plot( myFloat.sin() ) // Use sin() method on a float, using built in wrapper
plot( (myInt).factorial() ) // Factorial of an integer (note parentheses)
plot( myIntArray.gcd() ) // GCD of an integer array
method isinf(self)
isinf: Checks if this float is positive or negative infinity using a proxy value.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) value to check.
Returns: (bool) `true` if the absolute value of `self` is greater than or equal to the infinity proxy, `false` otherwise.
method isfinite(self)
isfinite: Checks if this float is finite (not NaN and not infinity).
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The value to check.
Returns: (bool) `true` if `self` is not `na` and not infinity (as defined by `isinf()`), `false` otherwise.
method fmod(self, divisor)
fmod: Returns the C-library style floating-point remainder of `self / divisor` (result has the sign of `self`).
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) Dividend `x`.
divisor (float) : (float) Divisor `y`. Cannot be zero or `na`.
Returns: (float) The remainder `x - n*y` where n is `trunc(x/y)`, or `na` if divisor is 0, `na`, or inputs are infinite in a way that prevents calculation.
method factorial(self)
factorial: Calculates the factorial of this non-negative integer.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : (int) The integer `n`. Must be non-negative.
Returns: (float) `n!` as a float, or `na` if `n` is negative or overflow occurs (based on `isinf`).
method isqrt(self)
isqrt: Calculates the integer square root of this non-negative integer (floor of the exact square root).
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : (int) The non-negative integer `n`.
Returns: (int) The greatest integer `a` such that a² <= n, or `na` if `n` is negative.
method comb(self, k)
comb: Calculates the number of ways to choose `k` items from `self` items without repetition and without order (Binomial Coefficient).
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : (int) Total number of items `n`. Must be non-negative.
k (int) : (int) Number of items to choose. Must be non-negative.
Returns: (float) The binomial coefficient nCk, or `na` if inputs are invalid (n<0 or k<0), `k > n`, or overflow occurs.
method perm(self, k)
perm: Calculates the number of ways to choose `k` items from `self` items without repetition and with order (Permutations).
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : (int) Total number of items `n`. Must be non-negative.
k (simple int) : (simple int = na) Number of items to choose. Must be non-negative. Defaults to `n` if `na`.
Returns: (float) The number of permutations nPk, or `na` if inputs are invalid (n<0 or k<0), `k > n`, or overflow occurs.
method log2(self)
log2: Returns the base-2 logarithm of this float. Input must be positive. Wraps `math.log(self) / math.log(2.0)`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be positive.
Returns: (float) The base-2 logarithm, or `na` if input <= 0.
method trunc(self)
trunc: Returns this float with the fractional part removed (truncates towards zero).
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (int) The integer part, or `na` if input is `na` or infinite.
method abs(self)
abs: Returns the absolute value of this float. Wraps `math.abs()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (float) The absolute value, or `na` if input is `na`.
method acos(self)
acos: Returns the arccosine of this float, in radians. Wraps `math.acos()`. Input must be between -1 and 1.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be between -1 and 1.
Returns: (float) Angle in radians , or `na` if input is outside or `na`.
method asin(self)
asin: Returns the arcsine of this float, in radians. Wraps `math.asin()`. Input must be between -1 and 1.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be between -1 and 1.
Returns: (float) Angle in radians , or `na` if input is outside or `na`.
method atan(self)
atan: Returns the arctangent of this float, in radians. Wraps `math.atan()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (float) Angle in radians , or `na` if input is `na`.
method ceil(self)
ceil: Returns the ceiling of this float (smallest integer >= self). Wraps `math.ceil()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (int) The ceiling value, or `na` if input is `na` or infinite.
method cos(self)
cos: Returns the cosine of this float (angle in radians). Wraps `math.cos()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The angle in radians.
Returns: (float) The cosine, or `na` if input is `na`.
method degrees(self)
degrees: Converts this float from radians to degrees. Wraps `math.todegrees()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The angle in radians.
Returns: (float) The angle in degrees, or `na` if input is `na`.
method exp(self)
exp: Returns e raised to the power of this float. Wraps `math.exp()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The exponent.
Returns: (float) `e**self`, or `na` if input is `na`.
method floor(self)
floor: Returns the floor of this float (largest integer <= self). Wraps `math.floor()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (int) The floor value, or `na` if input is `na` or infinite.
method log(self)
log: Returns the natural logarithm (base e) of this float. Wraps `math.log()`. Input must be positive.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be positive.
Returns: (float) The natural logarithm, or `na` if input <= 0 or `na`.
method log10(self)
log10: Returns the base-10 logarithm of this float. Wraps `math.log10()`. Input must be positive.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be positive.
Returns: (float) The base-10 logarithm, or `na` if input <= 0 or `na`.
method pow(self, exponent)
pow: Returns this float raised to the power of `exponent`. Wraps `math.pow()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The base.
exponent (float) : (float) The exponent.
Returns: (float) `self**exponent`, or `na` if inputs are `na` or lead to undefined results.
method radians(self)
radians: Converts this float from degrees to radians. Wraps `math.toradians()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The angle in degrees.
Returns: (float) The angle in radians, or `na` if input is `na`.
method round(self)
round: Returns the nearest integer to this float. Wraps `math.round()`. Ties are rounded away from zero.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (int) The rounded integer, or `na` if input is `na` or infinite.
method sign(self)
sign: Returns the sign of this float (-1, 0, or 1). Wraps `math.sign()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (int) -1 if negative, 0 if zero, 1 if positive, `na` if input is `na`.
method sin(self)
sin: Returns the sine of this float (angle in radians). Wraps `math.sin()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The angle in radians.
Returns: (float) The sine, or `na` if input is `na`.
method sqrt(self)
sqrt: Returns the square root of this float. Wraps `math.sqrt()`. Input must be non-negative.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be non-negative.
Returns: (float) The square root, or `na` if input < 0 or `na`.
method tan(self)
tan: Returns the tangent of this float (angle in radians). Wraps `math.tan()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The angle in radians.
Returns: (float) The tangent, or `na` if input is `na`.
method acosh(self)
acosh: Returns the inverse hyperbolic cosine of this float. Input must be >= 1.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be >= 1.
Returns: (float) The inverse hyperbolic cosine, or `na` if input < 1 or `na`.
method asinh(self)
asinh: Returns the inverse hyperbolic sine of this float.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (float) The inverse hyperbolic sine, or `na` if input is `na`.
method atanh(self)
atanh: Returns the inverse hyperbolic tangent of this float. Input must be between -1 and 1 (exclusive).
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number. Must be between -1 and 1 (exclusive).
Returns: (float) The inverse hyperbolic tangent, or `na` if input is outside (-1, 1) or `na`.
method cosh(self)
cosh: Returns the hyperbolic cosine of this float.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (float) The hyperbolic cosine, or `na` if input is `na`.
method sinh(self)
sinh: Returns the hyperbolic sine of this float.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (float) The hyperbolic sine, or `na` if input is `na`.
method tanh(self)
tanh: Returns the hyperbolic tangent of this float.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The input number.
Returns: (float) The hyperbolic tangent, or `na` if input is `na`.
method atan2(self, dx)
atan2: Returns the angle in radians between the positive x-axis and the point (dx, self). Wraps `math.atan2()`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The y-coordinate `y`.
dx (float) : (float) The x-coordinate `x`.
Returns: (float) The angle in radians , result of `math.atan2(self, dx)`. Returns `na` if inputs are `na`. Note: `math.atan2(0, 0)` returns 0 in Pine.
Optimization: Use built-in math.atan2()
method cbrt(self)
cbrt: Returns the cube root of this float.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The value to find the cube root of.
Returns: (float) The real cube root. Handles negative inputs correctly, or `na` if input is `na`.
method exp2(self)
exp2: Returns 2 raised to the power of this float. Calculated as `2.0.pow(self)`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The exponent.
Returns: (float) `2**self`, or `na` if input is `na` or results in non-finite value.
method expm1(self)
expm1: Returns `e**self - 1`. Calculated as `self.exp() - 1.0`. May offer better precision for small `self` in some environments, but Pine provides no guarantee over `self.exp() - 1.0`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The exponent.
Returns: (float) `e**self - 1`, or `na` if input is `na` or `self.exp()` is `na`.
method log1p(self)
log1p: Returns the natural logarithm of (1 + self). Calculated as `(1.0 + self).log()`. Pine provides no specific precision guarantee for self near zero.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) Value to add to 1. `1 + self` must be positive.
Returns: (float) Natural log of `1 + self`, or `na` if input is `na` or `1 + self <= 0`.
method modf(self)
modf: Returns the fractional and integer parts of this float as a tuple ` `. Both parts have the sign of `self`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The number `x` to split.
Returns: ( ) A tuple containing ` `, or ` ` if `x` is `na` or non-finite.
method remainder(self, divisor)
remainder: Returns the IEEE 754 style remainder of `self` with respect to `divisor`. Result `r` satisfies `abs(r) <= 0.5 * abs(divisor)`. Uses round-half-to-even.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) Dividend `x`.
divisor (float) : (float) Divisor `y`. Cannot be zero or `na`.
Returns: (float) The IEEE 754 remainder, or `na` if divisor is 0, `na`, or inputs are non-finite in a way that prevents calculation.
method copysign(self, signSource)
copysign: Returns a float with the magnitude (absolute value) of `self` but the sign of `signSource`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) Value providing the magnitude `x`.
signSource (float) : (float) Value providing the sign `y`.
Returns: (float) `abs(x)` with the sign of `y`, or `na` if either input is `na`.
method frexp(self)
frexp: Returns the mantissa (m) and exponent (e) of this float `x` as ` `, such that `x = m * 2^e` and `0.5 <= abs(m) < 1` (unless `x` is 0).
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) The number `x` to decompose.
Returns: ( ) A tuple ` `, or ` ` if `x` is 0, or ` ` if `x` is non-finite or `na`.
method isclose(self, other, rel_tol, abs_tol)
isclose: Checks if this float `a` and `other` float `b` are close within relative and absolute tolerances.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) First value `a`.
other (float) : (float) Second value `b`.
rel_tol (simple float) : (simple float = 1e-9) Relative tolerance. Must be non-negative and less than 1.0.
abs_tol (simple float) : (simple float = 0.0) Absolute tolerance. Must be non-negative.
Returns: (bool) `true` if `abs(a - b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)`. Handles `na`/`inf` appropriately. Returns `na` if tolerances are invalid.
method ldexp(self, exponent)
ldexp: Returns `self * (2**exponent)`. Inverse of `frexp`.
Namespace types: series float, simple float, input float, const float
Parameters:
self (float) : (float) Mantissa part `x`.
exponent (int) : (int) Exponent part `i`.
Returns: (float) The result of `x * pow(2, i)`, or `na` if inputs are `na` or result is non-finite.
method gcd(self)
gcd: Calculates the Greatest Common Divisor (GCD) of all integers in this array.
Namespace types: array
Parameters:
self (array) : (array) An array of integers.
Returns: (int) The largest positive integer that divides all non-zero elements, 0 if all elements are 0 or array is empty. Returns `na` if any element is `na`.
method lcm(self)
lcm: Calculates the Least Common Multiple (LCM) of all integers in this array.
Namespace types: array
Parameters:
self (array) : (array) An array of integers.
Returns: (int) The smallest positive integer that is a multiple of all non-zero elements, 0 if any element is 0, 1 if array is empty. Returns `na` on potential overflow or if any element is `na`.
method dist(self, other)
dist: Returns the Euclidean distance between this point `p` and another point `q` (given as arrays of coordinates).
Namespace types: array
Parameters:
self (array) : (array) Coordinates of the first point `p`.
other (array) : (array) Coordinates of the second point `q`. Must have the same size as `p`.
Returns: (float) The Euclidean distance, or `na` if arrays have different sizes, are empty, or contain `na`/non-finite values.
method fsum(self)
fsum: Returns an accurate floating-point sum of values in this array. Uses built-in `array.sum()`. Note: Pine Script does not guarantee the same level of precision tracking as Python's `math.fsum`.
Namespace types: array
Parameters:
self (array) : (array) The array of floats to sum.
Returns: (float) The sum of the array elements. Returns 0.0 for an empty array. Returns `na` if any element is `na`.
method hypot(self)
hypot: Returns the Euclidean norm (distance from origin) for this point given by coordinates in the array. `sqrt(sum(x*x for x in coordinates))`.
Namespace types: array
Parameters:
self (array) : (array) Array of coordinates defining the point.
Returns: (float) The Euclidean norm, or 0.0 if the array is empty. Returns `na` if any element is `na` or non-finite.
method prod(self, start)
prod: Calculates the product of all elements in this array.
Namespace types: array
Parameters:
self (array) : (array) The array of values to multiply.
start (simple float) : (simple float = 1.0) The starting value for the product (returned if the array is empty).
Returns: (float) The product of array elements * start. Returns `na` if any element is `na`.
method sumprod(self, other)
sumprod: Returns the sum of products of values from this array `p` and another array `q` (dot product).
Namespace types: array
Parameters:
self (array) : (array) First array of values `p`.
other (array) : (array) Second array of values `q`. Must have the same size as `p`.
Returns: (float) The sum of `p * q ` for all i, or `na` if arrays have different sizes or contain `na`/non-finite values. Returns 0.0 for empty arrays.
EMA Oracle and RSIEMA Oracle
- “See the market’s structure through the eyes of exponential wisdom.”
combines classic EMA stacks with Pi-based logic to reveal high-probability buy/sell zones and trend bias across timeframes
Multi-EMA Trend & Pi Signal Indicator
This advanced indicator combines classic trend analysis with Pi-based signal logic to help traders identify optimal entry and exit zones across multiple timeframes.
Core Features
EMA Trend Structure: Displays EMAs 9, 13, 20, 50, and 200 to visualize short-term and long-term trend orientation. Bullish momentum is indicated when shorter EMAs are stacked above longer ones.
Pi-Based Signal Logic: Inspired by the Pi Indicator, it includes EMA111 and EMA700 (350×2) on the daily chart:
Buy Zone: When price is trading below EMA111, it signals potential accumulation for spot or low-leverage position trades.
Sell Zone: When price is above EMA700, it suggests potential distribution or exit zones.
Trend Cross Alerts: Detects EMA crossovers and crossunders to highlight shifts in market structure and generate buy/sell signals.
Multi-Timeframe Analysis: Evaluates trend direction across selected timeframes (e.g., 15m, 30m, 1h, 4h, 1D), offering a broader market perspective.
RSI Integration: Combines Relative Strength Index (RSI) readings with EMA positioning to assess momentum and overbought/oversold conditions.
Trend Table Display: A dynamic table summarizes the asset’s trend status per timeframe, showing:
RSI values
EMA alignment
Overall trend bias (bullish, bearish, neutral)
Intellect_city - World Cycle - Ath - Timeframe 1D and 1WIndicator Overview
The Pi Cycle Top Indicator has historically been effective in picking out the timing of market cycle highs within 3 days.
It uses the 111 day moving average (111DMA) and a newly created multiple of the 350 day moving average, the 350DMA x 2.
Note: The multiple is of the price values of the 350DMA, not the number of days.
For the past three market cycles, when the 111DMA moves up and crosses the 350DMA x 2 we see that it coincides with the price of Bitcoin peaking.
It is also interesting to note that 350 / 111 is 3.153, which is very close to Pi = 3.142. In fact, it is the closest we can get to Pi when dividing 350 by another whole number.
It once again demonstrates the cyclical nature of Bitcoin price action over long time frames. However, in this instance, it does so with a high degree of accuracy over Bitcoin's adoption phase of growth.
Bitcoin Price Prediction Using This Tool
The Pi Cycle Top Indicator forecasts the cycle top of Bitcoin’s market cycles. It attempts to predict the point where Bitcoin price will peak before pulling back. It does this on major high time frames and has picked the absolute tops of Bitcoin’s major price moves throughout most of its history.
How It Can Be Used
Pi Cycle Top is useful to indicate when the market is very overheated. So overheated that the shorter-term moving average, which is the 111-day moving average, has reached an x2 multiple of the 350-day moving average. Historically, it has proved advantageous to sell Bitcoin around this time in Bitcoin's price cycles.
It is also worth noting that this indicator has worked during Bitcoin's adoption growth phase, the first 15 years or so of Bitcoin's life. With the launch of Bitcoin ETF's and Bitcoin's increased integration into the global financial system, this indicator may cease to be relevant at some point in this new market structure.
111D SMA / (350D SMA * 2)Indicator: Pi Cycle Ratio
This custom technical indicator calculates a ratio between two moving averages that are used for the PI Cycle Top indicator. The PI Cycle Top indicator triggers when the 111-day simple moving average (111D SMA) crosses up with the 350-day simple moving average (350D SMA *2).
The line value is ratio is calculated as:
Line Value = 111DSMA / (350D SMA × 2)
When the 111D SMA crosses with the 350D SMA triggering the PI Cycle Top, the value of the ratio between the two lines is 1.
This visualizes the ratio between the two moving averages into a single line. This indicator can be used for technical analysis for historical and future moves.
Bitcoin Cycle High/Low with functional Alert [heswaikcrypt]Introduction
Just as machines are fine-tuned for maximum efficiency, trading indicators must evolve to meet the demands of ever-changing markets.
Credit goes to the initial author, @NoCreditsLeft I only improved the existing Pi-cycle indicator with a functional alert and included a bull mode indicator in the script. The alert can help you get a live alert at candle close when the cycle tops, bottoms, and the potential bull phase switch occurs.
Philip Swift’s Pi Cycle Top Indicator is a brilliant example of leveraging mathematical relationships to signal critical turning points in Bitcoin’s price cycles. Historically, it has identified market and local tops with some relative accuracy, often within three days, as demonstrated in all the previous bull run cycles.
At its core, the Pi Cycle Indicator derives its name from the mathematical constant π (pi), achieved by using simple moving averages (MAs) in a specific ratio: 𝜋 = Long MA/short MA
The Bull mode switch is calculated using a crossover of the short exponentia moving average and the long moving average.
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.
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Knowing when Bitcoin reaches its top—and receiving timely alerts about it—is crucial for successful trading. The indicator is designed to signal;
Potential Bitcoin tops: Purple label
Potential Bitcoin bottoms : green Label, and
Parabolic swing : Yellow diamond shape (relating to the market switching to a potential bull mode)
"Please note: This indicator is tailored for Bitcoin using historical data analysis and should not be considered definitive. However accurate it might be."
Setting alerts
To set the alert conditions, select any alert function call to get alert whenever the conditions are met. The script is configured on dialy TF; you can set it on 1D or weekly TF.
Enjoy and Trade smartly
Bitcoin Macro Trend Map [Ox_kali]
## Introduction
__________________________________________________________________________________
The “Bitcoin Macro Trend Map” script is designed to provide a comprehensive analysis of Bitcoin’s macroeconomic trends. By leveraging a unique combination of Bitcoin-specific macroeconomic indicators, this script helps traders identify potential market peaks and troughs with greater accuracy. It synthesizes data from multiple sources to offer a probabilistic view of market excesses, whether overbought or oversold conditions.
This script offers significant value for the following reasons:
1. Holistic Market Analysis : It integrates a diverse set of indicators that cover various aspects of the Bitcoin market, from investor sentiment and market liquidity to mining profitability and network health. This multi-faceted approach provides a more complete picture of the market than relying on a single indicator.
2. Customization and Flexibility : Users can customize the script to suit their specific trading strategies and preferences. The script offers configurable parameters for each indicator, allowing traders to adjust settings based on their analysis needs.
3. Visual Clarity : The script plots all indicators on a single chart with clear visual cues. This includes color-coded indicators and background changes based on market conditions, making it easy for traders to quickly interpret complex data.
4. Proven Indicators : The script utilizes well-established indicators like the EMA, NUPL, PUELL Multiple, and Hash Ribbons, which are widely recognized in the trading community for their effectiveness in predicting market movements.
5. A New Comprehensive Indicator : By integrating background color changes based on the aggregate signals of various indicators, this script essentially creates a new, comprehensive indicator tailored specifically for Bitcoin. This visual representation provides an immediate overview of market conditions, enhancing the ability to spot potential market reversals.
Optimal for use on timeframes ranging from 1 day to 1 week , the “Bitcoin Macro Trend Map” provides traders with actionable insights, enhancing their ability to make informed decisions in the highly volatile Bitcoin market. By combining these indicators, the script delivers a robust tool for identifying market extremes and potential reversal points.
## Key Indicators
__________________________________________________________________________________
Macroeconomic Data: The script combines several relevant macroeconomic indicators for Bitcoin, such as the 10-month EMA, M2 money supply, CVDD, Pi Cycle, NUPL, PUELL, MRVR Z-Scores, and Hash Ribbons (Full description bellow).
Open Source Sources: Most of the scripts used are sourced from open-source projects that I have modified to meet the specific needs of this script.
Recommended Timeframes: For optimal performance, it is recommended to use this script on timeframes ranging from 1 day to 1 week.
Objective: The primary goal is to provide a probabilistic solution to identify market excesses, whether overbought or oversold points.
## Originality and Purpose
__________________________________________________________________________________
This script stands out by integrating multiple macroeconomic indicators into a single comprehensive tool. Each indicator is carefully selected and customized to provide insights into different aspects of the Bitcoin market. By combining these indicators, the script offers a holistic view of market conditions, helping traders identify potential tops and bottoms with greater accuracy. This is the first version of the script, and additional macroeconomic indicators will be added in the future based on user feedback and other inputs.
## How It Works
__________________________________________________________________________________
The script works by plotting each macroeconomic indicator on a single chart, allowing users to visualize and interpret the data easily. Here’s a detailed look at how each indicator contributes to the analysis:
EMA 10 Monthly: Uses an exponential moving average over 10 monthly periods to signal bullish and bearish trends. This indicator helps identify long-term trends in the Bitcoin market by smoothing out price fluctuations to reveal the underlying trend direction.Moving Averages w/ 18 day/week/month.
Credit to @ryanman0
M2 Money Supply: Analyzes the evolution of global money supply, indicating market liquidity conditions. This indicator tracks the changes in the total amount of money available in the economy, which can impact Bitcoin’s value as a hedge against inflation or economic instability.
Credit to @dylanleclair
CVDD (Cumulative Value Days Destroyed): An indicator based on the cumulative value of days destroyed, useful for identifying market turning points. This metric helps assess the Bitcoin market’s health by evaluating the age and value of coins that are moved, indicating potential shifts in market sentiment.
Credit to @Da_Prof
Pi Cycle: Uses simple and exponential moving averages to detect potential sell points. This indicator aims to identify cyclical peaks in Bitcoin’s price, providing signals for potential market tops.
Credit to @NoCreditsLeft
NUPL (Net Unrealized Profit/Loss): Measures investors’ unrealized profit or loss to signal extreme market levels. This indicator shows the net profit or loss of Bitcoin holders as a percentage of the market cap, helping to identify periods of significant market optimism or pessimism.
Credit to @Da_Prof
PUELL Multiple: Assesses mining profitability relative to historical averages to indicate buying or selling opportunities. This indicator compares the daily issuance value of Bitcoin to its yearly average, providing insights into when the market is overbought or oversold based on miner behavior.
Credit to @Da_Prof
MRVR Z-Scores: Compares market value to realized value to identify overbought or oversold conditions. This metric helps gauge the overall market sentiment by comparing Bitcoin’s market value to its realized value, identifying potential reversal points.
Credit to @Pinnacle_Investor
Hash Ribbons: Uses hash rate variations to signal buying opportunities based on miner capitulation and recovery. This indicator tracks the health of the Bitcoin network by analyzing hash rate trends, helping to identify periods of miner capitulation and subsequent recoveries as potential buying opportunities.
Credit to @ROBO_Trading
## Indicator Visualization and Interpretation
__________________________________________________________________________________
For each horizontal line representing an indicator, a legend is displayed on the right side of the chart. If the conditions are positive for an indicator, it will turn green, indicating the end of a bearish trend. Conversely, if the conditions are negative, the indicator will turn red, signaling the end of a bullish trend.
The background color of the chart changes based on the average of green or red indicators. This parameter is configurable, allowing adjustment of the threshold at which the background color changes, providing a clear visual indication of overall market conditions.
## Script Parameters
__________________________________________________________________________________
The script includes several configurable parameters to customize the display and behavior of the indicators:
Color Style:
Normal: Default colors.
Modern: Modern color style.
Monochrome: Monochrome style.
User: User-customized colors.
Custom color settings for up trends (Up Trend Color), down trends (Down Trend Color), and NaN (NaN Color)
Background Color Thresholds:
Thresholds: Settings to define the thresholds for background color change.
Low/High Red Threshold: Low and high thresholds for bearish trends.
Low/High Green Threshold: Low and high thresholds for bullish trends.
Indicator Display:
Options to show or hide specific indicators such as EMA 10 Monthly, CVDD, Pi Cycle, M2 Money, NUPL, PUELL, MRVR Z-Scores, and Hash Ribbons.
Specific Indicator Settings:
EMA 10 Monthly: Options to customize the period for the exponential moving average calculation.
M2 Money: Aggregation of global money supply data.
CVDD: Adjustments for value normalization.
Pi Cycle: Settings for simple and exponential moving averages.
NUPL: Thresholds for unrealized profit/loss values.
PUELL: Adjustments for mining profitability multiples.
MRVR Z-Scores: Settings for overbought/oversold values.
Hash Ribbons: Options for hash rate moving averages and capitulation/recovery signals.
## Conclusion
__________________________________________________________________________________
The “Bitcoin Macro Trend Map” by Ox_kali is a tool designed to analyze the Bitcoin market. By combining several macroeconomic indicators, this script helps identify market peaks and troughs. It is recommended to use it on timeframes from 1 day to 1 week for optimal trend analysis. The scripts used are sourced from open-source projects, modified to suit the specific needs of this analysis.
## Notes
__________________________________________________________________________________
This is the first version of the script and it is still in development. More indicators will likely be added in the future. Feedback and comments are welcome to improve this tool.
## Disclaimer:
__________________________________________________________________________________
Please note that the Open Interest liquidation map is not a guarantee of future market performance and should be used in conjunction with proper risk management. Always ensure that you have a thorough understanding of the indicator’s methodology and its limitations before making any investment decisions. Additionally, past performance is not indicative of future results.
Prometheus Polarized Fractal Efficiency (PFE)This indicator uses market data to calculate Polarized Fractal Efficiency (PFE) on an asset, so traders can have a better idea of which direction it may go.
Users can control the lookback length for the fractal calculation, the lookback length for the Exponential Moving Average (EMA), and whether or not to display lines at the -50 and 50 level, or -25 and 25 level.
Polarized Fractal Efficiency:
The Polarized Fractal Efficiency (PFE) indicator is a value between -100 and 100 with 0 as a midpoint.
A PFE above 0 indicates the asset may trend higher, a PFE below 0 indicates the asset may trend lower.
There are many ways to trade with PFE, the intuitive trend riding as described above, or reversals.
Even when the PFE is above 0, if it gets high enough, it may also be an indication of a reversal. A PFE of 90 - 100, or -100 - -90, may indicate price is ready to revert the other direction. Furthermore, traders already in a position may look to breaks of other levels to be their take profit or stop out spot.
Calculation:
Pi = 100 x (Price - Price )2 + N2 / Summation, j= 0, to N-2 (Price - Price )2 + 1
If Close < Close Pi = -Pi
PFEi = EMA(Pi, M)
Where:
N = period of indicator
M = smoothing period
Citation: www.investopedia.com
Scenarios:
Inputs are (9, 5) and every display option is on.
Trend example
Step 1: A short trade appears as PFE crosses below -25. We reach a safe take profit as PFE crosses below -50. Traders can use these levels to exit as well as enter.
Step 2: On the cross above 25 there is a safe long. As the PFE value breaks 0 a safe, early take profit could be appropriate for this trade. No guarantee we would see 50.
Step 3: Long scenario at break of 25, straight to 50. Simple, straightforward setup.
Step 4: This long results in a stop loss. Once again entry as PFE crosses 25, but as we cross the 0 line it is for a loss.
Step 5: The last trade in this example is reminiscent of step 3. This is a short trade entry at break of 25 and exit at break of 50.
Traders have liberty to use the PFE value to determine spots to enter and exit trades, long or short. 25 and 50 were chosen arbitrarily, values like 10 and 60 may work as well, we encourage traders to use their own discretion along with tools.
Reversal example
Step 1: PFE is around -100, crossing below it at one point! Strong zone for a potential reversal.
Step 2: PFE crosses above 25 adding conviction.
Step 3: Option to exit at 70.
Step 4: Option to exit at 90.
There is no “one size fits all method”, this approach may be more intuitive for some users and is just as feasible as the first.
Longer trend example
Step 1: Using -50 and 50 this time instead of -25 and 25 to be safer on our entries we see a short here. Was a good entry and as the value gets closer to -70 we can safely close.
Step 2: On this candle we see a long for the break of 50. On the next candle we break the 0 line, but because of our safe entry at 50, we could hold this and only stop out at a break of -25. We get close but stay in it and close at 70.
Step 3: Break of 50 for a long once again. This time the break of 0 line occurs as we are in profit, not letting a green trade go red is a golden rule of trading, so an early exit here.
Step 4: Same at step 2, break of 50 to long and stay in it, not stopping out at break of 0 line. The PFE value eventually reaches 70 and there is a good exit.
Quicker Reversal example
Step 1: Notice a close with PFE below -90, enter long for the reversal. Then close for profit when the PFE crosses above 70.
Step 2: When the PFE breaks above 90 we have a short entry. Like the long closing it when it crosses below -70.
Step 3: This step is the same setup as step 2. As PFE breaks above 90 we have a short entry. Closing it when it crosses below -70.
Recap:
Described above are 4 different examples with many different trades. Both trend and reversal trades. The PFE value is an indicator that can be used by traders in many different ways and Prometheus encourages traders to use their own discretion along with tools and not follow indicators blindly.
Options:
Users can control the input for the lookback of the indicator. The default is 9.
The smoothing factor for the EMA is also changeable, default is 5.
Users have options to display lines at -50, -25, 25, and 50.
Intelle_city - World Cycle - Ath & Atl - Logarithmic - Strategy.Overview
Indicators: Strategy !
INTELLECT_city - World Cycle - ATH & ATL - Timeframe 1D and 1W - Logarithmic - Strategy - The Pi Cycle Top and Bottom Oscillator is an adaptation of the original Pi Cycle Top chart. It compares the 111-Day Moving Average circle and the 2 * 350-Day Moving Average circle of Bitcoin’s Price. These two moving averages were selected as 350 / 111 = 3.153; An approximation of the important mathematical number Pi.
When the 111-Day Moving Average circle reaches the 2 * 350-Day Moving Average circle, it indicates that the market is becoming overheated. That is because the mid time frame momentum reference of the 111-Day Moving Average has caught up with the long timeframe momentum reference of the 2 * 350-Day Moving Average.
Historically this has occurred within 3 days of the very top of each market cycle.
When the 111 Day Moving Average circle falls back beneath the 2 * 350 Day Moving Average circle, it indicates that the market momentum of that cycle is significantly cooling down. The oscillator drops down into the lower green band shown where the 111 Day Moving Average is moving at a 75% discount relative to the 2 * 350 Day Moving Average.
Historically, this has highlighted broad areas of bear market lows.
IMPORTANT: You need to set a LOGARITHMIC graph. (The function is located at the bottom right of the screen)
IMPORTANT: The INTELLECT_city indicator is made for a buy-sell strategy; there is also a signal indicator from INTELLECT_city
IMPORTANT: The Chart shows all cycles, both buying and selling.
IMPORTANT: Suitable timeframes are 1 daily (recommended) and 1 weekly
-----------------------------
Описание на русском:
-----------------------------
Обзор индикатора
INTELLECT_city - World Cycle - ATH & ATL - Timeframe 1D and 1W - Logarithmic - Strategy - Логарифмический - Сигнал - Осциллятор вершины и основания цикла Пи представляет собой адаптацию оригинального графика вершины цикла Пи. Он сравнивает круг 111-дневной скользящей средней и круг 2 * 350-дневной скользящей средней цены Биткойна. Эти две скользящие средние были выбраны как 350/111 = 3,153; Приближение важного математического числа Пи.
Когда круг 111-дневной скользящей средней достигает круга 2 * 350-дневной скользящей средней, это указывает на то, что рынок перегревается. Это происходит потому, что опорный моментум среднего временного интервала 111-дневной скользящей средней догнал опорный момент импульса длинного таймфрейма 2 * 350-дневной скользящей средней.
Исторически это происходило в течение трех дней после вершины каждого рыночного цикла.
Когда круг 111-дневной скользящей средней опускается ниже круга 2 * 350-дневной скользящей средней, это указывает на то, что рыночный импульс этого цикла значительно снижается. Осциллятор опускается в нижнюю зеленую полосу, показанную там, где 111-дневная скользящая средняя движется со скидкой 75% относительно 2 * 350-дневной скользящей средней.
Исторически это высветило широкие области минимумов медвежьего рынка.
ВАЖНО: Выставлять нужно ЛОГАРИФМИЧЕСКИЙ график. (Находиться функция с правой нижней части экрана)
ВАЖНО: Индикатор INTELLECT_city сделан для стратегии покупок продаж, есть также и сигнальный от INTELLECT_сity
ВАЖНО: На Графике видны все циклы, как на покупку так и на продажу.
ВАЖНО: Подходящие таймфреймы 1 дневной (рекомендовано) и 1 недельный
-----------------------------
Beschreibung - Deutsch
-----------------------------
Indikatorübersicht
INTELLECT_city – Weltzyklus – ATH & ATL – Zeitrahmen 1T und 1W – Logarithmisch – Strategy – Der Pi-Zyklus-Top- und Bottom-Oszillator ist eine Anpassung des ursprünglichen Pi-Zyklus-Top-Diagramms. Er vergleicht den 111-Tage-Gleitenden-Durchschnittskreis und den 2 * 350-Tage-Gleitenden-Durchschnittskreis des Bitcoin-Preises. Diese beiden gleitenden Durchschnitte wurden als 350 / 111 = 3,153 ausgewählt; eine Annäherung an die wichtige mathematische Zahl Pi.
Wenn der 111-Tage-Gleitenden-Durchschnittskreis den 2 * 350-Tage-Gleitenden-Durchschnittskreis erreicht, deutet dies darauf hin, dass der Markt überhitzt. Das liegt daran, dass der Momentum-Referenzwert des 111-Tage-Gleitenden-Durchschnitts im mittleren Zeitrahmen den Momentum-Referenzwert des 2 * 350-Tage-Gleitenden-Durchschnitts im langen Zeitrahmen eingeholt hat.
Historisch gesehen geschah dies innerhalb von 3 Tagen nach dem Höhepunkt jedes Marktzyklus.
Wenn der Kreis des 111-Tage-Durchschnitts wieder unter den Kreis des 2 x 350-Tage-Durchschnitts fällt, deutet dies darauf hin, dass die Marktdynamik dieses Zyklus deutlich nachlässt. Der Oszillator fällt in das untere grüne Band, in dem der 111-Tage-Durchschnitt mit einem Abschlag von 75 % gegenüber dem 2 x 350-Tage-Durchschnitt verläuft.
Historisch hat dies breite Bereiche mit Tiefstständen in der Baisse hervorgehoben.
WICHTIG: Sie müssen ein logarithmisches Diagramm festlegen. (Die Funktion befindet sich unten rechts auf dem Bildschirm)
WICHTIG: Der INTELLECT_city-Indikator ist für eine Kauf-Verkaufs-Strategie konzipiert; es gibt auch einen Signalindikator von INTELLECT_city
WICHTIG: Das Diagramm zeigt alle Zyklen, sowohl Kauf- als auch Verkaufszyklen.
WICHTIG: Geeignete Zeitrahmen sind 1 täglich (empfohlen) und 1 wöchentlich
intellect_city - World Cycle - Ath & Atl - Logarithmic - Signal.Indicator Overview
INTELLECT_city - World Cycle - ATH & ATL - Timeframe 1D and 1W - Logarithmic - Signal - The Pi Cycle Top and Bottom Oscillator is an adaptation of the original Pi Cycle Top chart. It compares the 111-Day Moving Average circle and the 2 * 350-Day Moving Average circle of Bitcoin’s Price. These two moving averages were selected as 350 / 111 = 3.153; An approximation of the important mathematical number Pi.
When the 111-Day Moving Average circle reaches the 2 * 350-Day Moving Average circle, it indicates that the market is becoming overheated. That is because the mid time frame momentum reference of the 111-Day Moving Average has caught up with the long timeframe momentum reference of the 2 * 350-Day Moving Average.
Historically this has occurred within 3 days of the very top of each market cycle.
When the 111 Day Moving Average circle falls back beneath the 2 * 350 Day Moving Average circle, it indicates that the market momentum of that cycle is significantly cooling down. The oscillator drops down into the lower green band shown where the 111 Day Moving Average is moving at a 75% discount relative to the 2 * 350 Day Moving Average.
Historically, this has highlighted broad areas of bear market lows.
IMPORTANT: You need to set a LOGARITHMIC graph. (The function is located at the bottom right of the screen)
IMPORTANT: The INTELLECT_city indicator is made for signal purchases of sales, there is also a strategic one from INTELLECT_city
IMPORTANT: The Chart shows all cycles, both buying and selling.
IMPORTANT: Suitable timeframes are 1 daily (recommended) and 1 weekly
-----------------------------
Описание на русском:
-----------------------------
Обзор индикатора
INTELLECT_city - World Cycle - ATH & ATL - Timeframe 1D and 1W - Logarithmic - Signal - Логарифмический - Сигнал - Осциллятор вершины и основания цикла Пи представляет собой адаптацию оригинального графика вершины цикла Пи. Он сравнивает круг 111-дневной скользящей средней и круг 2 * 350-дневной скользящей средней цены Биткойна. Эти две скользящие средние были выбраны как 350/111 = 3,153; Приближение важного математического числа Пи.
Когда круг 111-дневной скользящей средней достигает круга 2 * 350-дневной скользящей средней, это указывает на то, что рынок перегревается. Это происходит потому, что опорный моментум среднего временного интервала 111-дневной скользящей средней догнал опорный момент импульса длинного таймфрейма 2 * 350-дневной скользящей средней.
Исторически это происходило в течение трех дней после вершины каждого рыночного цикла.
Когда круг 111-дневной скользящей средней опускается ниже круга 2 * 350-дневной скользящей средней, это указывает на то, что рыночный импульс этого цикла значительно снижается. Осциллятор опускается в нижнюю зеленую полосу, показанную там, где 111-дневная скользящая средняя движется со скидкой 75% относительно 2 * 350-дневной скользящей средней.
Исторически это высветило широкие области минимумов медвежьего рынка.
ВАЖНО: Выставлять нужно ЛОГАРИФМИЧЕСКИЙ график. (Находиться функция с правой нижней части экрана)
ВАЖНО: Индикатор INTELLECT_city сделан для сигнальных покупок продаж, есть также и стратегический от INTELLECT_сity
ВАЖНО: На Графике видны все циклы, как на покупку так и на продажу.
ВАЖНО: Подходящие таймфреймы 1 дневной (рекомендовано) и 1 недельный
-----------------------------
Beschreibung - Deutsch
-----------------------------
Indikatorübersicht
INTELLECT_city – Weltzyklus – ATH & ATL – Zeitrahmen 1T und 1W – Logarithmisch – Signal – Der Pi-Zyklus-Top- und Bottom-Oszillator ist eine Anpassung des ursprünglichen Pi-Zyklus-Top-Diagramms. Er vergleicht den 111-Tage-Gleitenden-Durchschnittskreis und den 2 * 350-Tage-Gleitenden-Durchschnittskreis des Bitcoin-Preises. Diese beiden gleitenden Durchschnitte wurden als 350 / 111 = 3,153 ausgewählt; eine Annäherung an die wichtige mathematische Zahl Pi.
Wenn der 111-Tage-Gleitenden-Durchschnittskreis den 2 * 350-Tage-Gleitenden-Durchschnittskreis erreicht, deutet dies darauf hin, dass der Markt überhitzt. Das liegt daran, dass der Momentum-Referenzwert des 111-Tage-Gleitenden-Durchschnitts im mittleren Zeitrahmen den Momentum-Referenzwert des 2 * 350-Tage-Gleitenden-Durchschnitts im langen Zeitrahmen eingeholt hat.
Historisch gesehen geschah dies innerhalb von 3 Tagen nach dem Höhepunkt jedes Marktzyklus.
Wenn der Kreis des 111-Tage-Durchschnitts wieder unter den Kreis des 2 x 350-Tage-Durchschnitts fällt, deutet dies darauf hin, dass die Marktdynamik dieses Zyklus deutlich nachlässt. Der Oszillator fällt in das untere grüne Band, in dem der 111-Tage-Durchschnitt mit einem Abschlag von 75 % gegenüber dem 2 x 350-Tage-Durchschnitt verläuft.
Historisch hat dies breite Bereiche mit Tiefstständen in der Baisse hervorgehoben.
WICHTIG: Sie müssen ein logarithmisches Diagramm festlegen. (Die Funktion befindet sich unten rechts auf dem Bildschirm)
WICHTIG: Der INTELLECT_city-Indikator dient zur Signalisierung von Käufen oder Verkäufen, es gibt auch einen strategischen Indikator von INTELLECT_city
WICHTIG: Das Diagramm zeigt alle Zyklen, sowohl Kauf- als auch Verkaufszyklen.
WICHTIG: Geeignete Zeitrahmen sind 1 täglich (empfohlen) und 1 wöchentlich
Vector2Library "Vector2"
Representation of two dimensional vectors or points.
This structure is used to represent positions in two dimensional space or vectors,
for example in spacial coordinates in 2D space.
~~~
references:
docs.unity3d.com
gist.github.com
github.com
gist.github.com
gist.github.com
gist.github.com
~~~
new(x, y)
Create a new Vector2 object.
Parameters:
x : float . The x value of the vector, default=0.
y : float . The y value of the vector, default=0.
Returns: Vector2. Vector2 object.
-> usage:
`unitx = Vector2.new(1.0) , plot(unitx.x)`
from(value)
Assigns value to a new vector `x,y` elements.
Parameters:
value : float, x and y value of the vector.
Returns: Vector2. Vector2 object.
-> usage:
`one = Vector2.from(1.0), plot(one.x)`
from(value, element_sep, open_par, close_par)
Assigns value to a new vector `x,y` elements.
Parameters:
value : string . The `x` and `y` value of the vector in a `x,y` or `(x,y)` format, spaces and parentesis will be removed automatically.
element_sep : string . Element separator character, default=`,`.
open_par : string . Open parentesis character, default=`(`.
close_par : string . Close parentesis character, default=`)`.
Returns: Vector2. Vector2 object.
-> usage:
`one = Vector2.from("1.0,2"), plot(one.x)`
copy(this)
Creates a deep copy of a vector.
Parameters:
this : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = Vector2.new(1.0) , b = a.copy() , plot(b.x)`
down()
Vector in the form `(0, -1)`.
Returns: Vector2. Vector2 object.
left()
Vector in the form `(-1, 0)`.
Returns: Vector2. Vector2 object.
right()
Vector in the form `(1, 0)`.
Returns: Vector2. Vector2 object.
up()
Vector in the form `(0, 1)`.
Returns: Vector2. Vector2 object.
one()
Vector in the form `(1, 1)`.
Returns: Vector2. Vector2 object.
zero()
Vector in the form `(0, 0)`.
Returns: Vector2. Vector2 object.
minus_one()
Vector in the form `(-1, -1)`.
Returns: Vector2. Vector2 object.
unit_x()
Vector in the form `(1, 0)`.
Returns: Vector2. Vector2 object.
unit_y()
Vector in the form `(0, 1)`.
Returns: Vector2. Vector2 object.
nan()
Vector in the form `(float(na), float(na))`.
Returns: Vector2. Vector2 object.
xy(this)
Return the values of `x` and `y` as a tuple.
Parameters:
this : Vector2 . Vector2 object.
Returns: .
-> usage:
`a = Vector2.new(1.0, 1.0) , = a.xy() , plot(ax)`
length_squared(this)
Length of vector `a` in the form. `a.x^2 + a.y^2`, for comparing vectors this is computationaly lighter.
Parameters:
this : Vector2 . Vector2 object.
Returns: float. Squared length of vector.
-> usage:
`a = Vector2.new(1.0, 1.0) , plot(a.length_squared())`
length(this)
Magnitude of vector `a` in the form. `sqrt(a.x^2 + a.y^2)`
Parameters:
this : Vector2 . Vector2 object.
Returns: float. Length of vector.
-> usage:
`a = Vector2.new(1.0, 1.0) , plot(a.length())`
normalize(a)
Vector normalized with a magnitude of 1, in the form. `a / length(a)`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = normalize(Vector2.new(3.0, 2.0)) , plot(a.y)`
isNA(this)
Checks if any of the components is `na`.
Parameters:
this : Vector2 . Vector2 object.
Returns: bool.
usage:
p = Vector2.new(1.0, na) , plot(isNA(p)?1:0)
add(a, b)
Adds vector `b` to `a`, in the form `(a.x + b.x, a.y + b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = one() , c = add(a, b) , plot(c.x)`
add(a, b)
Adds vector `b` to `a`, in the form `(a.x + b, a.y + b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = 1.0 , c = add(a, b) , plot(c.x)`
add(a, b)
Adds vector `b` to `a`, in the form `(a + b.x, a + b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 1.0 , b = one() , c = add(a, b) , plot(c.x)`
subtract(a, b)
Subtract vector `b` from `a`, in the form `(a.x - b.x, a.y - b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = one() , c = subtract(a, b) , plot(c.x)`
subtract(a, b)
Subtract vector `b` from `a`, in the form `(a.x - b, a.y - b)`.
Parameters:
a : Vector2 . vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = 1.0 , c = subtract(a, b) , plot(c.x)`
subtract(a, b)
Subtract vector `b` from `a`, in the form `(a - b.x, a - b.y)`.
Parameters:
a : float . value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 1.0 , b = one() , c = subtract(a, b) , plot(c.x)`
multiply(a, b)
Multiply vector `a` with `b`, in the form `(a.x * b.x, a.y * b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = one() , c = multiply(a, b) , plot(c.x)`
multiply(a, b)
Multiply vector `a` with `b`, in the form `(a.x * b, a.y * b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = 1.0 , c = multiply(a, b) , plot(c.x)`
multiply(a, b)
Multiply vector `a` with `b`, in the form `(a * b.x, a * b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 1.0 , b = one() , c = multiply(a, b) , plot(c.x)`
divide(a, b)
Divide vector `a` with `b`, in the form `(a.x / b.x, a.y / b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = from(2.0) , c = divide(a, b) , plot(c.x)`
divide(a, b)
Divide vector `a` with value `b`, in the form `(a.x / b, a.y / b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = 2.0 , c = divide(a, b) , plot(c.x)`
divide(a, b)
Divide value `a` with vector `b`, in the form `(a / b.x, a / b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 3.0 , b = from(2.0) , c = divide(a, b) , plot(c.x)`
negate(a)
Negative of vector `a`, in the form `(-a.x, -a.y)`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = a.negate , plot(b.x)`
pow(a, b)
Raise vector `a` with exponent vector `b`, in the form `(a.x ^ b.x, a.y ^ b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = from(2.0) , c = pow(a, b) , plot(c.x)`
pow(a, b)
Raise vector `a` with value `b`, in the form `(a.x ^ b, a.y ^ b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = 2.0 , c = pow(a, b) , plot(c.x)`
pow(a, b)
Raise value `a` with vector `b`, in the form `(a ^ b.x, a ^ b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 3.0 , b = from(2.0) , c = pow(a, b) , plot(c.x)`
sqrt(a)
Square root of the elements in a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = sqrt(a) , plot(b.x)`
abs(a)
Absolute properties of the vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(-3.0) , b = abs(a) , plot(b.x)`
min(a)
Lowest element of a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = min(a) , plot(b)`
max(a)
Highest element of a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = max(a) , plot(b)`
vmax(a, b)
Highest elements of two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = vmax(a, b) , plot(c.x)`
vmax(a, b, c)
Highest elements of three vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = new(1.5, 4.5) , d = vmax(a, b, c) , plot(d.x)`
vmin(a, b)
Lowest elements of two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = vmin(a, b) , plot(c.x)`
vmin(a, b, c)
Lowest elements of three vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = new(1.5, 4.5) , d = vmin(a, b, c) , plot(d.x)`
perp(a)
Perpendicular Vector of `a`, in the form `(a.y, -a.x)`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = perp(a) , plot(b.x)`
floor(a)
Compute the floor of vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = floor(a) , plot(b.x)`
ceil(a)
Ceils vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = ceil(a) , plot(b.x)`
ceil(a, digits)
Ceils vector `a`.
Parameters:
a : Vector2 . Vector2 object.
digits : int . Digits to use as ceiling.
Returns: Vector2. Vector2 object.
round(a)
Round of vector elements.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = round(a) , plot(b.x)`
round(a, precision)
Round of vector elements.
Parameters:
a : Vector2 . Vector2 object.
precision : int . Number of digits to round vector "a" elements.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(0.123456, 1.234567) , b = round(a, 2) , plot(b.x)`
fractional(a)
Compute the fractional part of the elements from vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.123456, 1.23456) , b = fractional(a) , plot(b.x)`
dot_product(a, b)
dot_product product of 2 vectors, in the form `a.x * b.x + a.y * b.y.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = dot_product(a, b) , plot(c)`
cross_product(a, b)
cross product of 2 vectors, in the form `a.x * b.y - a.y * b.x`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = cross_product(a, b) , plot(c)`
equals(a, b)
Compares two vectors
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: bool. Representing the equality.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = equals(a, b) ? 1 : 0 , plot(c)`
sin(a)
Compute the sine of argument vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = sin(a) , plot(b.x)`
cos(a)
Compute the cosine of argument vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = cos(a) , plot(b.x)`
tan(a)
Compute the tangent of argument vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = tan(a) , plot(b.x)`
atan2(x, y)
Approximation to atan2 calculation, arc tangent of `y/x` in the range (-pi,pi) radians.
Parameters:
x : float . The x value of the vector.
y : float . The y value of the vector.
Returns: float. Value with angle in radians. (negative if quadrante 3 or 4)
-> usage:
`a = new(3.0, 1.5) , b = atan2(a.x, a.y) , plot(b)`
atan2(a)
Approximation to atan2 calculation, arc tangent of `y/x` in the range (-pi,pi) radians.
Parameters:
a : Vector2 . Vector2 object.
Returns: float, value with angle in radians. (negative if quadrante 3 or 4)
-> usage:
`a = new(3.0, 1.5) , b = atan2(a) , plot(b)`
distance(a, b)
Distance between vector `a` and `b`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = distance(a, b) , plot(c)`
rescale(a, length)
Rescale a vector to a new magnitude.
Parameters:
a : Vector2 . Vector2 object.
length : float . Magnitude.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = 2.0 , c = rescale(a, b) , plot(c.x)`
rotate(a, radians)
Rotates vector by a angle.
Parameters:
a : Vector2 . Vector2 object.
radians : float . Angle value in radians.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = 2.0 , c = rotate(a, b) , plot(c.x)`
rotate_degree(a, degree)
Rotates vector by a angle.
Parameters:
a : Vector2 . Vector2 object.
degree : float . Angle value in degrees.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = 45.0 , c = rotate_degree(a, b) , plot(c.x)`
rotate_around(this, center, angle)
Rotates vector `target` around `origin` by angle value.
Parameters:
this
center : Vector2 . Vector2 object.
angle : float . Angle value in degrees.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = rotate_around(a, b, 45.0) , plot(c.x)`
perpendicular_distance(a, b, c)
Distance from point `a` to line between `b` and `c`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(1.5, 2.6) , b = from(1.0) , c = from(3.0) , d = perpendicular_distance(a, b, c) , plot(d.x)`
project(a, axis)
Project a vector onto another.
Parameters:
a : Vector2 . Vector2 object.
axis : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = project(a, b) , plot(c.x)`
projectN(a, axis)
Project a vector onto a vector of unit length.
Parameters:
a : Vector2 . Vector2 object.
axis : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = projectN(a, b) , plot(c.x)`
reflect(a, axis)
Reflect a vector on another.
Parameters:
a : Vector2 . Vector2 object.
axis
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = reflect(a, b) , plot(c.x)`
reflectN(a, axis)
Reflect a vector to a arbitrary axis.
Parameters:
a : Vector2 . Vector2 object.
axis
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = reflectN(a, b) , plot(c.x)`
angle(a)
Angle in radians of a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = angle(a) , plot(b)`
angle_unsigned(a, b)
unsigned degree angle between 0 and +180 by given two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = angle_unsigned(a, b) , plot(c)`
angle_signed(a, b)
Signed degree angle between -180 and +180 by given two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = angle_signed(a, b) , plot(c)`
angle_360(a, b)
Degree angle between 0 and 360 by given two vectors
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = angle_360(a, b) , plot(c)`
clamp(a, min, max)
Restricts a vector between a min and max value.
Parameters:
a : Vector2 . Vector2 object.
min
max
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = from(2.5) , d = clamp(a, b, c) , plot(d.x)`
clamp(a, min, max)
Restricts a vector between a min and max value.
Parameters:
a : Vector2 . Vector2 object.
min : float . Lower boundary value.
max : float . Higher boundary value.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = clamp(a, 2.0, 2.5) , plot(b.x)`
lerp(a, b, rate)
Linearly interpolates between vectors a and b by rate.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
rate : float . Value between (a:-infinity -> b:1.0), negative values will move away from b.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = lerp(a, b, 0.5) , plot(c.x)`
herp(a, b, rate)
Hermite curve interpolation between vectors a and b by rate.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
rate : Vector2 . Vector2 object. Value between (a:0 > 1:b).
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = from(2.5) , d = herp(a, b, c) , plot(d.x)`
transform(position, mat)
Transform a vector by the given matrix.
Parameters:
position : Vector2 . Source vector.
mat : M32 . Transformation matrix
Returns: Vector2. Transformed vector.
transform(position, mat)
Transform a vector by the given matrix.
Parameters:
position : Vector2 . Source vector.
mat : M44 . Transformation matrix
Returns: Vector2. Transformed vector.
transform(position, mat)
Transform a vector by the given matrix.
Parameters:
position : Vector2 . Source vector.
mat : matrix . Transformation matrix, requires a 3x2 or a 4x4 matrix.
Returns: Vector2. Transformed vector.
transform(this, rotation)
Transform a vector by the given quaternion rotation value.
Parameters:
this : Vector2 . Source vector.
rotation : Quaternion . Rotation to apply.
Returns: Vector2. Transformed vector.
area_triangle(a, b, c)
Find the area in a triangle of vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(1.0, 2.0) , b = from(2.0) , c = from(1.0) , d = area_triangle(a, b, c) , plot(d.x)`
random(max)
2D random value.
Parameters:
max : Vector2 . Vector2 object. Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(2.0) , b = random(a) , plot(b.x)`
random(max)
2D random value.
Parameters:
max : float, Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = random(2.0) , plot(a.x)`
random(min, max)
2D random value.
Parameters:
min : Vector2 . Vector2 object. Vector lower boundary.
max : Vector2 . Vector2 object. Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(1.0) , b = from(2.0) , c = random(a, b) , plot(c.x)`
random(min, max)
2D random value.
Parameters:
min : Vector2 . Vector2 object. Vector lower boundary.
max : Vector2 . Vector2 object. Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = random(1.0, 2.0) , plot(a.x)`
noise(a)
2D Noise based on Morgan McGuire @morgan3d.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(2.0) , b = noise(a) , plot(b.x)`
to_string(a)
Converts vector `a` to a string format, in the form `"(x, y)"`.
Parameters:
a : Vector2 . Vector2 object.
Returns: string. In `"(x, y)"` format.
-> usage:
`a = from(2.0) , l = barstate.islast ? label.new(bar_index, 0.0, to_string(a)) : label(na)`
to_string(a, format)
Converts vector `a` to a string format, in the form `"(x, y)"`.
Parameters:
a : Vector2 . Vector2 object.
format : string . Format to apply transformation.
Returns: string. In `"(x, y)"` format.
-> usage:
`a = from(2.123456) , l = barstate.islast ? label.new(bar_index, 0.0, to_string(a, "#.##")) : label(na)`
to_array(a)
Converts vector to a array format.
Parameters:
a : Vector2 . Vector2 object.
Returns: array.
-> usage:
`a = from(2.0) , b = to_array(a) , plot(array.get(b, 0))`
to_barycentric(this, a, b, c)
Captures the barycentric coordinate of a cartesian position in the triangle plane.
Parameters:
this : Vector2 . Source cartesian coordinate position.
a : Vector2 . Triangle corner `a` vertice.
b : Vector2 . Triangle corner `b` vertice.
c : Vector2 . Triangle corner `c` vertice.
Returns: bool.
from_barycentric(this, a, b, c)
Captures the cartesian coordinate of a barycentric position in the triangle plane.
Parameters:
this : Vector2 . Source barycentric coordinate position.
a : Vector2 . Triangle corner `a` vertice.
b : Vector2 . Triangle corner `b` vertice.
c : Vector2 . Triangle corner `c` vertice.
Returns: bool.
to_complex(this)
Translate a Vector2 structure to complex.
Parameters:
this : Vector2 . Source vector.
Returns: Complex.
to_polar(this)
Translate a Vector2 cartesian coordinate into polar coordinates.
Parameters:
this : Vector2 . Source vector.
Returns: Pole. The returned angle is in radians.
ALL TIME HIGHHH BTC!
Ola Amigos,
Weekly indicator.
This indicator, more commonly called "the Pi indicator", is based on the use of two moving averages: mm50 and mm16.
By dividing a mm50 in order to try to get as close as possible to PI, we fall back on mm16.
50/16 = 3.13
When the white curve passes above the blue curve, we are on historic highs.
It is very easy to test on the BLX, being the graph with the most history.
We can say thank you to JDC for this nice discovery which remains very useful for the rest of the BTC run.
Love!
Ola Amigos,
Weekly indicator.
Cet indicateur, plus communément appelé "the Pi indicator" est basé sur l'utilisation de deux moyennes mobiles : mm50 et mm16.
En divisant une mm50 afin de chercher a essayer de se rapprocher le plus pres de PI, on retombe sur la mm16.
50/16= 3.13
Lorsque la courbe blanche passe au dessus de la courbe bleue, on se trouve sur des plus hauts historiques.
Il est très facile a tester sur le BLX , étant le graph avec le plus d'historique.
On peut dire merci a JDC pour cette jolie découverte qui reste tres utile pour la suite du run BTC .
Love!
Blackman Filter - The Smoother The BetterIntroduction
Who doesn't like smooth things? I'd like a smooth market price for christmas! But i can't get it, instead its so noisy...so you apply a filter to smooth it, such filters are called low-pass filters, they smooth and its great but they have lag, so nobody really use them, but they are pretty to look at.
Its on a childish note that i will introduce this indicator, so what it is all about? I propose a new FIR filter using a blackman function as filter kernel for financial time-series smoothing, do you prefer the childish tone ? Fear not its surprisingly easy!
The Blackman Function
The blackman function look like a bell shaped curve, look:
The blackman function will produce such curve. This function is called a cosine sum function because she is based on the sum of cosine functions, here only 2.
0.42 - 0.5 * cos(2 * pi * k) + 0.08 * cos(4 * pi * k)
Originally you use this function for windowing , what does it means? In signal processing you have a function called sync function , if you use this function as filter kernel you would get the ideal frequency domain response filter, sometime called brickwall filter, it would be extremely smooth.
Above the optimal low pass filter frequency response.
However the sync function has no ending values and goes on forever, therefore we can't use it for convolution, expect if we apply windowing. Filters using windowing are called windowed-sinc filters, i will describe the procedure below :
1 - Create a sync function = sin(pi*n)/(pi*n)
2 - Truncate it = I only keep the first length points of the sync function.
This create a abrupt end, the frequency of a filter using step 1 as kernel would contain ripples in the pass band and stop band, this is bad! The frequency response would look like this :
3 - I multiply my values of step 2 by a window function, it can the blackman window, i no longer have an abrupt end, its smooth!
The frequency response of the filter using this kernel would no longer have ripples! This is the power of windowing functions.
Here we are not using such thing, but we could in the future. Here instead we use the blackman function as filter kernel, because this function is bell shaped this mean that the filter will certainly be smooth (symmetrical weighting is a rule of thumb for kernels when we want really smooth filters).
The Filter
This filter is quite smooth, unlike the gaussian filter this filter give less weights to recent and past values, this is because the blackman function has fatter tails than the gaussian one. I could make a comparison of both, however they are quite alike, if you often use a gaussian filter its up to you to decide which one you prefer.
The filter can do a better job than the moving average when it comes to preserve the frequency components that constitute the cycles/trend.
We can see that the filter has a greater performance when it comes to keep the shape of the market price, thus it has a slightly better fit.
Conclusion
Ok so in this post you learned a bit about the sync function and windowing, those are basic subjects in signal processing, they allow us to approximate the filter with the ideal frequency response, i also showed you that those windowing function could be used as kernel and that they where pretty smooth on their own, there are many others, but the one i prefer is the blackman windowing function.
I know what you are thinking, "we want trailing stops, alerts, colors, arrows!", and i understand you pal, but sometimes its cool to take a break from all this stuff. However i can tell that i'am working on a side project that aim to estimate rolling maximum/minimum as fast as possible, any experiments will be published here, and i can ensure you that those indicators will make your day quite brighter, we will see that soon.
I hope you learned something from this post! I'am a bit tired (look i'am disappearing !)
Thanks for reading !
BTC Arcturus IndicatorBTC Arcturus Indicator: This indicator is designed to create buy and sell signals based on the market value of Bitcoin. It also predicts potential market tops with the Pi Cycle Top indicator.
How Does It Work?
1. MVRVZ (Market Value to Realized Value-Z Score) Calculation:
MC: Bitcoin's market cap (Market Cap) is pulled daily from Glassnode data.
MCR: Realized Market Cap of Bitcoin is taken daily from Coinmetrics data.
MVRVZ: It is calculated by dividing the difference between Bitcoin's market value and realized market value by one standard deviation. This value indicates whether the market is overvalued or undervalued.
2. Reception and Warning Signals:
Buy Signal: When MVRVZ falls below the -0.255 threshold value, the indicator gives a "Buy" signal. This indicates that Bitcoin is undervalued and may be a buying opportunity.
Warning Signal: A warning signal turns on when MVRVZ exceeds the threshold value of 2.765. This indicates that the market is approaching saturation and caution is warranted.
3. Tracking the Highest MVRVZ Value:
The indicator records the highest MVRVZ value in the last 10 candlesticks. This value is used to determine whether the market has reached its highest risk levels.
4. Warning Display:
If the MVRVZ value matches the highest value in the last 10 bars and this warning has not been displayed before, a "Warning" signal is displayed.
Once the warning signal is shown, no further warnings are shown for 10 candles.
5. Pi Cycle Top Indicator:
Pi Cycle Top: This indicator predicts Bitcoin tops by comparing two moving averages (350-day and 111-day). If the short-term moving average falls below the long-term moving average, this is considered a sell signal.
The indicator displays this signal with the label "Sell", indicating a potential market top.
User Guide:
Green Buy Signal: It means Bitcoin is cheap and offers a buying opportunity.
Yellow Warning Signal: Indicates that Bitcoin has reached possible profit taking points and caution should be exercised.
Red Sell Signal: Indicates that Bitcoin has reached market saturation and it may be appropriate to sell.
SATAN Cycle BitcoinWith this indicator I want to dismantle the Pi Cycle Bitcoin indicator since the community thinks that it has a mathematical basis based on the Pi number, nothing is further from reality, the indicator uses averages which, divided, result in the Pi number but in the code uses some multipliers to adjust the crossing of averages and I demonstrate it with this indicator in which if you add the averages you get the number 666, is the demon behind the Bitcoin cycles? NO, it is only an adjustment of averages and multipliers. With this I only intend to alert the community that the indicator is 0% reliable.
[blackcat] L2 Sine-Weighted Moving Average (SWMA)Level: 2
Background
Invented by Patrick Lafferty in 1999, a Sine Weighted Moving Average (SWMA) takes its weighting from the first half of a Sine wave cycle and accordingly, the most weighting is given to the data in the middle of the data set. It is therefore very similar to the Triangular Moving Average.
Function
A sine weighted moving average (Sine-MA) applies weights to each bar in the shape of the bulge in a sine curve from 0 to pi. For an N-bar average the weightings are
/ 1 \ / 2 \ / N \
sin | --- * pi |, sin | --- * pi |, ..., sin | --- * pi |
\ N+1 / \ N+1 / \ N+1 /
The effect is that middle prices have the greatest weight (much like the TMA, Triangular Moving Average). A Sine Weighted Moving Average ( Sine WMA ) takes its weighting from the first half of a Sine wave cycle and accordingly, the most weighting is given to the data in the middle of the data set.
Key Signal
SWMA(FastLength) --> SWMA Fast Line.
SWMA(SlowLength) --> SWMA Slow Line.
Remarks
This is a Level 2 free and open source indicator.
Feedbacks are appreciated.
Filter Information Box - PineCoders FAQWhen designing filters it can be interesting to have information about their characteristics, which can be obtained from the set of filter coefficients (weights). The following script analyzes the impulse response of a filter in order to return the following information:
Lag
Smoothness via the Herfindahl index
Percentage Overshoot
Percentage Of Positive Weights
The script also attempts to determine the type of the analyzed filter, and will issue warnings when the filter shows signs of unwanted behavior.
DISPLAYED INFORMATION AND METHODS
The script displays one box on the chart containing two sections. The filter metrics section displays the following information:
- Lag : Measured in bars and calculated from the convolution between the filter's impulse response and a linearly increasing sequence of value 0,1,2,3... . This sequence resets when the impulse response crosses under/over 0.
- Herfindahl index : A measure of the filter's smoothness described by Valeriy Zakamulin. The Herfindahl index measures the concentration of the filter weights by summing the squared filter weights, with lower values suggesting a smoother filter. With normalized weights the minimum value of the Herfindahl index for low-pass filters is 1/N where N is the filter length.
- Percentage Overshoot : Defined as the maximum value of the filter step response, minus 1 multiplied by 100. Larger values suggest higher overshoots.
- Percentage Positive Weights : Percentage of filter weights greater than 0.
Each of these calculations is based on the filter's impulse response, with the impulse position controlled by the Impulse Position setting (its default is 1000). Make sure the number of inputs the filter uses is smaller than Impulse Position and that the number of bars on the chart is also greater than Impulse Position . In order for these metrics to be as accurate as possible, make sure the filter weights add up to 1 for low-pass and band-stop filters, and 0 for high-pass and band-pass filters.
The comments section displays information related to the type of filter analyzed. The detection algorithm is based on the metrics described above. The script can detect the following type of filters:
All-Pass
Low-Pass
High-Pass
Band-Pass
Band-Stop
It is assumed that the user is analyzing one of these types of filters. The comments box also displays various warnings. For example, a warning will be displayed when a low-pass/band-stop filter has a non-unity pass-band, and another is displayed if the filter overshoot is considered too important.
HOW TO SET THE SCRIPT UP
In order to use this script, the user must first enter the filter settings in the section provided for this purpose in the top section of the script. The filter to be analyzed must then be entered into the:
f(input)
function, where `input` is the filter's input source. By default, this function is a simple moving average of period length . Be sure to remove it.
If, for example, we wanted to analyze a Blackman filter, we would enter the following:
f(input)=>
pi = 3.14159,sum = 0.,sumw = 0.
for i = 0 to length-1
k = i/length
w = 0.42 - 0.5 * cos(2 * pi * k) + 0.08 * cos(4 * pi * k)
sumw := sumw + w
sum := sum + w*input
sum/sumw
EXAMPLES
In this section we will look at the information given by the script using various filters. The first filter we will showcase is the linearly weighted moving average (WMA) of period 9.
As we can see, its lag is 2.6667, which is indeed correct as the closed form of the lag of the WMA is equal to (period-1)/3 , which for period 9 gives (9-1)/3 which is approximately equal to 2.6667. The WMA does not have overshoots, this is shown by the the percentage overshoot value being equal to 0%. Finally, the percentage of positive weights is 100%, as the WMA does not possess negative weights.
Lets now analyze the Hull moving average of period 9. This moving average aims to provide a low-lag response.
Here we can see how the lag is way lower than that of the WMA. We can also see that the Herfindahl index is higher which indicates the WMA is smoother than the HMA. In order to reduce lag the HMA use negative weights, here 55% (as there are 45% of positive ones). The use of negative weights creates overshoots, we can see with the percentage overshoot being 26.6667%.
The WMA and HMA are both low-pass filters. In both cases the script correctly detected this information. Let's now analyze a simple high-pass filter, calculated as follows:
input - sma(input,length)
Most weights of a high-pass filters are negative, which is why the lag value is negative. This would suggest the indicator is able to predict future input values, which of course is not possible. In the case of high-pass filters, the Herfindahl index is greater than 0.5 and converges toward 1, with higher values of length . The comment box correctly detected the type of filter we were using.
Let's now test the script using the simple center of gravity bandpass filter calculated as follows:
wma(input,length) - sma(input,length)
The script correctly detected the type of filter we are using. Another type of filter that the script can detect is band-stop filters. A simple band-stop filter can be made as follows:
input - (wma(input,length) - sma(input,length))
The script correctly detect the type of filter. Like high-pass filters the Herfindahl index is greater than 0.5 and converges toward 1, with greater values of length . Finally the script can detect all-pass filters, which are filters that do not change the frequency content of the input.
WARNING COMMENTS
The script can give warning when certain filter characteristics are detected. One of them is non-unity pass-band for low-pass filters. This warning comment is displayed when the weights of the filter do not add up to 1. As an example, let's use the following function as a filter:
sum(input,length)
Here the filter pass-band has non unity, and the sum of the weights is equal to length . Therefore the script would display the following comments:
We can also see how the metrics go wild (note that no filter type is detected, as the detected filter could be of the wrong type). The comment mentioning the detection of high overshoot appears when the percentage overshoot is greater than 50%. For example if we use the following filter:
5*wma(input,length) - 4*sma(input,length)
The script would display the following comment:
We can indeed see high overshoots from the filter:
@alexgrover for PineCoders
Look first. Then leap.
Signal To Noise RatioDetermines a S:N ratio and plots a level as a threshold for noise. From ProRealCode www.prorealcode.com
This technical indicator is an attempt to find the good momentum of trend : is it actually trending or in a range market?
Interestingly, it follows that pi is not only the ratio between the length of a circle to its diameter, it is also a constant rather appears in statistics and, oddly enough, in the relationship between the distance between a price oscillation and a straight line.
If the signal / noise ratio is less than or equal to 1/2 pi, we will be in a trading range or range.
If the signal / noise ratio is greater than 1/2 pi, we are in a trending market.
Kent Directional Filter🧭 Kent Directional Filter
Author: GabrielAmadeusLau
Type: Filter
📖 What It Is
The Kent Directional Filter is a directionality-sensitive smoothing tool inspired by the Kent distribution, a probability model used to describe directional and elliptical shapes on a sphere. In this context, it's repurposed for analyzing the angular trajectory of price movements and smoothing them for actionable insights.
It’s ideal for:
Detecting directional bias with probabilistic weighting
Enhancing momentum or trend-following systems
Filtering non-linear price action
🔬 How It Works
Price Angle Estimation:
Computes a rough angular shift in price using atan(src - src ) to estimate direction.
Kent Distribution Weighting:
κ (kappa) controls concentration strength (how sharply it prefers a direction).
β (beta) controls ellipticity (bias toward curved vs. linear moves).
These parameters influence how strongly the indicator favors movements at ~45° angles, simulating a directional “lens.”
Smoothing:
A Simple Moving Average (SMA) is applied over the raw directional probabilities to reduce noise and highlight the underlying trend signal.
⚙️ Inputs
Source: Price series used for angle calculation (default: close)
Smoothing Length: Window size for the moving average
Pi Divisor: Pi / 4 would be 45 degrees, you can change the 4 to 3, 2, etc.
Kappa (κ): Controls how focused the directionality is (higher = sharper filter)
Beta (β): Adds curvature sensitivity; higher values accentuate asymmetrical moves
🧠 Tips for Best Results
Use κ = 1–2 for moderate directional filtering, and β = 0.3–0.7 for smooth elliptical bias.
Combine with volume-based indicators to confirm breakout strength.
Works best in higher timeframes (1h–1D) to capture macro directional structure.
I might revisit this.
Bitcoin Reversal PredictorOverview
This indicator displays two lines that, when they cross, signal a potential reversal in Bitcoin's price trend. Historically, the high or low of a bull market cycle often occurs near the moment these lines intersect. The lines consist of an Exponential Moving Average (EMA) and a logarithmic regression line fitted to all of Bitcoin's historical data.
Inspiration
The inspiration for this indicator came from the PI Cycle Top indicator, which has accurately predicted past bull market peaks. However, I believe the PI Cycle Top indicator may not be as effective in the future. In that indicator, two lines cross to mark the top, but the extent of the cross has been diminishing over time. This was especially noticeable in the 2021 cycle, where the lines barely crossed. Because of this, I created a new indicator that I think will continue to provide reliable reversal signals in the future.
How It Works
The logarithmic regression line is fitted to the Bitcoin (BTCUSD) chart using two key factors: the 'a' factor (slope) and the 'b' factor (intercept). This results in a steadily decreasing line. The EMA oscillates above and below this regression line. Each time the two lines cross, a vertical colored bar appears, indicating that Bitcoin's price momentum is likely to reverse.
Use Cases
- Price Bottoming:
Bitcoin often bottoms out when the EMA crosses below the logarithmic regression line.
- Price Topping:
In contrast, Bitcoin often peaks when the EMA crosses above the logarithmic regression line.
- Profitable Strategy:
Trading at the crossovers of these lines can be a profitable strategy, as these moments often signal significant price reversals.
Autotable█ OVERVIEW
The library allows to automatically draw a table based on a string or float matrix (or both) controlling all of the parameters of the table (including merging cells) with parameter matrices (like, e.g. matrix of cell colors).
All things you would normally do with table.new() and table.cell() are now possible using respective parameters of library's main function, autotable() (as explained further below).
Headers can be supplied as arrays.
Merging of the cells is controlled with a special matrix of "L" and "U" values which instruct a cell to merged with the cell to the left or upwards (please see examples in the script and in this description).
█ USAGE EXAMPLES
The simplest and most straightforward:
mxF = matrix.new(3,3, 3.14)
mxF.autotable(bgcolor = color.rgb(249, 209, 29)) // displays float matrix as a table in the top right corner with defalult settings
mxS = matrix.new(3,3,"PI")
// displays string matrix as a table in the top right corner with defalult settings
mxS.autotable(Ypos = "bottom", Xpos = "right", bgcolor = #b4d400)
// displays matrix displaying a string value over a float value in each cell
mxS.autotable(mxF, Ypos = "middle", Xpos = "center", bgcolor = color.gray, text_color = #86f62a)
Draws this:
Tables with headers:
if barstate.islast
mxF = matrix.new(3,3, 3.14)
mxS = matrix.new(3,3,"PI")
arColHeaders = array.from("Col1", "Col2", "Col3")
arRowHeaders = array.from("Row1", "Row2", "Row3")
// float matrix with col headers
mxF.autotable(
bgcolor = #fdfd6b
, arColHeaders = arColHeaders
)
// string matrix with row headers
mxS.autotable(arRowHeaders = arRowHeaders, Ypos = "bottom", Xpos = "right", bgcolor = #b4d400)
// string/float matrix with both row and column headers
mxS.autotable(mxF
, Ypos = "middle", Xpos = "center"
, arRowHeaders = arRowHeaders
, arColHeaders = arColHeaders
, cornerBgClr = #707070, cornerTitle = "Corner\ncell", cornerTxtClr = #ffdc13
, bgcolor = color.gray, text_color = #86f62a
)
Draws this:
█ FUNCTIONS
One main function is autotable() which has only one required argument mxValS, a string matrix.
Please see below the description of all of the function parameters:
The table:
tbl (table) (Optional) If supplied, this table will be deleted.
The data:
mxValS (matrix ) (Required) Cell text values
mxValF (matrix) (Optional) Numerical part of cell text values. Is concatenated to the mxValS values via `string_float_separator` string (default "\n")
Table properties, have same effect as in table.new() :
defaultBgColor (color) (Optional) bgcolor to be used if mxBgColor is not supplied
Ypos (string) (Optional) "top", "bottom" or "center"
Xpos (string) (Optional) "left", "right", or "center"
frame_color (color) (Optional) frame_color like in table.new()
frame_width (int) (Optional) frame_width like in table.new()
border_color (color) (Optional) border_color like in table.new()
border_width (int) (Optional) border_width like in table.new()
force_overlay (simple bool) (Optional) If true draws table on main pane.
Cell parameters, have same effect as in table.cell() ):
mxBgColor (matrix) (Optional) like bgcolor argument in table.cell()
mxTextColor (matrix) (Optional) like text_color argument in table.cell()
mxTt (matrix) (Optional) like tooltip argument in table.cell()
mxWidth (matrix) (Optional) like width argument in table.cell()
mxHeight (matrix) (Optional) like height argument in table.cell()
mxHalign (matrix) (Optional) like text_halign argument in table.cell()
mxValign (matrix) (Optional) like text_valign argument in table.cell()
mxTextSize (matrix) (Optional) like text_size argument in table.cell()
mxFontFamily (matrix) (Optional) like text_font_family argument in table.cell()
Other table properties:
tableWidth (float) (Optional) Overrides table width if cell widths are non zero. E.g. if there are four columns and cell widths are 20 (either as set via cellW or via mxWidth) then if tableWidth is set to e.g. 50 then cell widths will be 50 * (20 / 80), where 80 is 20*4 = total width of all cells. Works simialar for widths set via mxWidth - determines max sum of widths across all cloumns of mxWidth and adjusts cell widths proportionally to it. If cell widths are 0 (i.e. auto-adjust) tableWidth has no effect.
tableHeight (float) (Optional) Overrides table height if cell heights are non zero. E.g. if there are four rows and cell heights are 20 (either as set via cellH or via mxHeight) then if tableHeigh is set to e.g. 50 then cell heights will be 50 * (20 / 80), where 80 is 20*4 = total height of all cells. Works simialar for heights set via mxHeight - determines max sum of heights across all cloumns of mxHeight and adjusts cell heights proportionally to it. If cell heights are 0 (i.e. auto-adjust) tableHeight has no effect.
defaultTxtColor (color) (Optional) text_color to be used if mxTextColor is not supplied
text_size (string) (Optional) text_size to be used if mxTextSize is not supplied
font_family (string) (Optional) cell text_font_family value to be used if a value in mxFontFamily is no supplied
cellW (float) (Optional) cell width to be used if a value in mxWidth is no supplied
cellH (float) (Optional) cell height to be used if a value in mxHeight is no supplied
halign (string) (Optional) cell text_halign value to be used if a value in mxHalign is no supplied
valign (string) (Optional) cell text_valign value to be used if a value in mxValign is no supplied
Headers parameters:
arColTitles (array) (Optional) Array of column titles. If not na a header row is added.
arRowTitles (array) (Optional) Array of row titles. If not na a header column is added.
cornerTitle (string) (Optional) If both row and column titles are supplied allows to set the value of the corner cell.
colTitlesBgColor (color) (Optional) bgcolor for header row
colTitlesTxtColor (color) (Optional) text_color for header row
rowTitlesBgColor (color) (Optional) bgcolor for header column
rowTitlesTxtColor (color) (Optional) text_color for header column
cornerBgClr (color) (Optional) bgcolor for the corner cell
cornerTxtClr (color) (Optional) text_color for the corner cell
Cell merge parameters:
mxMerge (matrix) (Optional) A matrix determining how cells will be merged. "L" - cell merges to the left, "U" - upwards.
mergeAllColTitles (bool) (Optional) Allows to print a table title instead of column headers, merging all header row cells and leaving just the value of the first cell. For more flexible options use matrix arguments leaving header/row arguments na.
mergeAllRowTitles (bool) (Optional) Allows to print one text value merging all header row cells and leaving just the value of the first cell. For more flexible options use matrix arguments leaving header/row arguments na.
Format:
string_float_separator (string) (Optional) A string used to separate string and float parts of cell values (mxValS and mxValF). Default is "\n"
format (string) (Optional) format string like in str.format() used to format numerical values
nz (string) (Optional) Determines how na numerical values are displayed.
The only other available function is autotable(string,... ) with a string parameter instead of string and float matrices which draws a one cell table.
█ SAMPLE USE
E.g., CSVParser library demo uses Autotable's for generating complex tables with merged cells.
█ CREDITS
The library was inspired by @kaigouthro's matrixautotable . A true master. Many thanks to him for his creative, beautiful and very helpful libraries.
Gaussian Filter [BigBeluga]The Gaussian Filter - BigBeluga indicator is a trend-following tool that uses a Gaussian filter to smooth price data and identify directional shifts in the market. It provides dynamic signals for entering and exiting trades based on trend changes, helping traders stay aligned with the market's momentum. What sets this indicator apart is its ability to display precise entry and exit points with real-time tracking of percentage price changes, making it ideal for trend-based strategies.
SP500:
NIFTY50:
🔵 KEY FEATURES & USAGE
◉ Gaussian Filter Trend Line:
//@function GaussianFilter is used for smoothing, reducing noise, and computing derivatives of data.
//@param src (float) The source data (e.g., close price) to be smoothed.
//@param params (GaussianFilterParams) Gaussian filter parameters that include length and sigma.
//@returns (float) The smoothed value from the Gaussian filter.
gaussian_filter(float src, params) =>
var float weights = array.new_float(params.length) // Array to store Gaussian weights
total = 0.0
pi = math.pi
for i = 0 to params.length - 1
weight = math.exp(-0.5 * math.pow((i - params.length / 2) / params.sigma, 2.0))
/ math.sqrt(params.sigma * 2.0 * pi)
weights.set(i, weight)
total := total + weight
for i = 0 to params.length - 1
weights.set(i, weights.get(i) / total)
sum = 0.0
for i = 0 to params.length - 1
sum := sum + src * weights.get(i)
sum
The core functionality of the Gaussian Filter line is to show trend direction. When the trend line increases four times consecutively, it indicates an uptrend signal. Similarly, if it decreases four times in a row, it signals a downtrend. The smoothness of the filter helps traders stay on the right side of the market by filtering out noise and emphasizing the dominant trend direction.
◉ Entry and Exit Levels with Real-Time Price and Performance Data:
Each time the indicator detects a trend change, it plots an entry or exit level on the chart. For an uptrend, an entry level is marked, and for a downtrend, an exit level is plotted. These levels display the price at the time of the signal.
While the trend is ongoing, the indicator tracks the percentage change in price from the initial entry or exit signal to the current bar, updating in real-time. When a trend concludes, it displays the total percentage change from the entry or exit point to the trend's end. This feature provides valuable insights into how much the price has moved during each trend phase and allows traders to monitor the performance of each trade.
◉ Color-Coded Candlestick Representation with Trend Shift Alerts:
In addition to coloring the candlesticks based on the trend direction, the indicator also uses gray candles to highlight potential early trend shifts. For example, if the Gaussian Filter detects a downtrend but the price moves above the filter line, the candles turn gray, signaling a possible reversal or shift in momentum. Similarly, in an uptrend, if the price moves below the Gaussian Filter line, the candles turn gray as an early indication of potential bearish momentum. This visual cue helps traders stay alert to possible faster shifts in market direction, allowing for quicker decision-making.
🔵 CUSTOMIZATION
Length and Sigma for Gaussian Filter:
Adjust the length and sigma parameters to control how the Gaussian Filter smooths the price data. A longer length provides smoother trend lines, while adjusting sigma can fine-tune the level of smoothing applied.
Levels Display and Candle Coloring:
You can toggle the visibility of entry and exit levels as well as enable or disable the dynamic coloring of candlesticks based on the trend direction. The additional gray color setting provides an extra layer of information, allowing you to spot potential trend reversals early.
🔵 CONCLUSION
The Gaussian Filter indicator is a powerful tool for identifying and following market trends. By providing clear entry and exit signals, along with real-time tracking of price changes, it gives traders a structured way to manage trades and monitor performance. The color-coded candles, including gray to highlight possible trend shifts, add another dimension to visualizing market dynamics. The added flexibility of customizing colors and trend levels makes it a versatile indicator suitable for both trend-following and reversal strategies.
Adaptive Trend Lines [MAMA and FAMA]Updated my previous algo on the Adaptive Trend lines, however I have added new functionalities and sorted out the settings.
You can now switch between normalized and non-normalized settings, the colors have also been updated and look much better.
The MAMA and FAMA
These indicators was originally developed by John F. Ehlers (Stocks & Commodities V. 19:10: MESA Adaptive Moving Averages). Everget wrote the initial functions for these in pine script. I have simply normalized the indicators and chosen to use the Laplace transformation instead of the hilbert transformation
How the Indicator Works:
The indicator employs a series of complex calculations, but we'll break it down into key steps to understand its functionality:
LaplaceTransform: Calculates the Laplace distribution for the given src input. The Laplace distribution is a continuous probability distribution, also known as the double exponential distribution. I use this because of the assymetrical return profile
MESA Period: The indicator calculates a MESA period, which represents the dominant cycle length in the price data. This period is continuously adjusted to adapt to market changes.
InPhase and Quadrature Components: The InPhase and Quadrature components are derived from the Hilbert Transform output. These components represent different aspects of the price's cyclical behavior.
Homodyne Discriminator: The Homodyne Discriminator is a phase-sensitive technique used to determine the phase and amplitude of a signal. It helps in detecting trend changes.
Alpha Calculation: Alpha represents the adaptive factor that adjusts the sensitivity of the indicator. It is based on the MESA period and the phase of the InPhase component. Alpha helps in dynamically adjusting the indicator's responsiveness to changes in market conditions.
MAMA and FAMA Calculation: The MAMA and FAMA values are calculated using the adaptive factor (alpha) and the input price data. These values are essentially adaptive moving averages that aim to capture the current trend more effectively than traditional moving averages.
But Omar, why would anyone want to use this?
The MAMA and FAMA lines offer benefits:
The indicator offers a distinct advantage over conventional moving averages due to its adaptive nature, which allows it to adjust to changing market conditions. This adaptability ensures that investors can stay on the right side of the trend, as the indicator becomes more responsive during trending periods and less sensitive in choppy or sideways markets.
One of the key strengths of this indicator lies in its ability to identify trends effectively by combining the MESA and MAMA techniques. By doing so, it efficiently filters out market noise, making it highly valuable for trend-following strategies. Investors can rely on this feature to gain clearer insights into the prevailing trends and make well-informed trading decisions.
This indicator is primarily suppoest to be used on the big timeframes to see which trend is prevailing, however I am not against someone using it on a timeframe below the 1D, just be careful if you are using this for modern portfolio theory, this is not suppoest to be a mid-term component, but rather a long term component that works well with proper use of detrended fluctuation analysis.
Dont hesitate to ask me if you have any questions
Again, I want to give credit to Everget and ChartPrime!
Code explanation as required by House Rules:
fastLimit = input.float(title='Fast Limit', step=0.01, defval=0.01, group = "Indicator Settings")
slowLimit = input.float(title='Slow Limit', step=0.01, defval=0.08, group = "Indicator Settings")
src = input(title='Source', defval=close, group = "Indicator Settings")
input.float: Used to create input fields for the user to set the fastLimit and slowLimit values.
input: General function to get user inputs, like the data source (close price) used for calculations.
norm_period = input.int(3, 'Normalization Period', 1, group = "Normalized Settings")
norm = input.bool(defval = true, title = "Use normalization", group = "Normalized Settings")
input.int: Creates an input field for the normalization period.
input.bool: Allows the user to toggle normalization on or off.
Color settings in the code:
col_up = input.color(#22ab94, group = "Color Settings")
col_dn = input.color(#f7525f, group = "Color Settings")
Constants and functions
var float PI = math.pi
laplace(src) =>
(0.5) * math.exp(-math.abs(src))
_computeComponent(src, mesaPeriodMult) =>
out = laplace(src) * mesaPeriodMult
out
_smoothComponent(src) =>
out = 0.2 * src + 0.8 * nz(src )
out
math.pi: Represents the mathematical constant π (pi).
laplace: A function that applies the Laplace transform to the source data.
_computeComponent: Computes a component of the data using the Laplace transform.
_smoothComponent: Smooths data by averaging the current value with the previous one (nz function is used to handle null values).
Alpha function:
_computeAlpha(src, fastLimit, slowLimit) =>
mesaPeriod = 0.0
mesaPeriodMult = 0.075 * nz(mesaPeriod ) + 0.54
...
alpha = math.max(fastLimit / deltaPhase, slowLimit)
out = alpha
out
_computeAlpha: Calculates the adaptive alpha value based on the fastLimit and slowLimit. This value is crucial for determining the MAMA and FAMA lines.
Calculating MAMA and FAMA:
mama = 0.0
mama := alpha * src + (1 - alpha) * nz(mama )
fama = 0.0
fama := alpha2 * mama + (1 - alpha2) * nz(fama )
Normalization:
lowest = ta.lowest(mama_fama_diff, norm_period)
highest = ta.highest(mama_fama_diff, norm_period)
normalized = (mama_fama_diff - lowest) / (highest - lowest) - 0.5
ta.lowest and ta.highest: Find the lowest and highest values of mama_fama_diff over the normalization period.
The oscillator is normalized to a range, making it easier to compare over different periods.
And finally, the plotting:
plot(norm == true ? normalized : na, style=plot.style_columns, color=col_wn, title = "mama_fama_diff Oscillator Normalized")
plot(norm == false ? mama_fama_diff : na, style=plot.style_columns, color=col_wnS, title = "mama_fama_diff Oscillator")
Example of Normalized settings:
Example for setup:
Try to make sure the lower timeframe follows the higher timeframe if you take a trade based on this indicator!
