From 8841dbae32cffe436de20eff9d6b709da2b59c67 Mon Sep 17 00:00:00 2001
From: FloDev <43553244+Ultiminer@users.noreply.github.com>
Date: Wed, 10 Apr 2024 23:10:17 +0200
Subject: [PATCH] Did some stuff with quads and watched Simpson

---
 qm_analysis.h => qm_derivative.h | 52 ++++++++++++++++++++++++++++++--
 qm_quadrature.h                  | 22 ++++++++++++++
 quick_math.h                     |  2 +-
 3 files changed, 73 insertions(+), 3 deletions(-)
 rename qm_analysis.h => qm_derivative.h (73%)
 create mode 100644 qm_quadrature.h

diff --git a/qm_analysis.h b/qm_derivative.h
similarity index 73%
rename from qm_analysis.h
rename to qm_derivative.h
index 3e1deb9..06472c3 100644
--- a/qm_analysis.h
+++ b/qm_derivative.h
@@ -1,5 +1,5 @@
-#ifndef QM_ANALYSIS_H_
-#define QM_ANALYSIS_H_
+#ifndef QM_DERIVATIVE_H_
+#define QM_DERIVATIVE_H_
 #include "quick_math.h"
 #include <array>
 #include <functional>
@@ -45,6 +45,10 @@ constexpr FRetVal operator+(const FRetVal& A, FCONST c)
 {
     return {A.val+c,A.slope}; 
 }
+constexpr FRetVal operator+(FCONST c, const FRetVal& A)
+{
+    return {A.val+c,A.slope}; 
+}
 constexpr FRetVal operator-(const FRetVal& A, FCONST c)
 {
     return {A.val-c,A.slope}; 
@@ -53,6 +57,10 @@ constexpr FRetVal operator*(const FRetVal& A, FCONST c)
 {
     return {A.val*c,A.slope*c}; 
 }
+constexpr FRetVal operator*(FCONST c,const FRetVal& A)
+{
+    return {A.val*c,A.slope*c}; 
+}
 constexpr FRetVal operator/(const FRetVal& A, FCONST c)
 {
     return {A.val/c,A.slope/c}; 
@@ -122,6 +130,46 @@ constexpr float finite_difference(const std::function<float(float)>& fun, float
     return N*fun(param+eps)-N*fun(param-eps); 
 }
 
+template <size_t N>
+constexpr float newton_iteration(const std::function<FRetVal(FRetVal)>& fun, float guess)
+{
+    for(size_t i=0; i<N; ++i)
+    {
+        const FRetVal y=fun(guess);
+        guess-=y.val/y.slope;
+    } 
+
+    return guess; 
+}
+template <size_t N>
+constexpr FRetVal fixpoint_iteration(const std::function<FRetVal(FRetVal)>& fun, FRetVal guess)
+{
+    for(size_t i=0; i<N; ++i)guess=fun(guess);
+
+    return guess; 
+}
+template <size_t N>
+constexpr float fixpoint_iteration(const std::function<float(float)>& fun, float guess)
+{
+    for(size_t i=0; i<N; ++i)guess=fun(guess);
+
+    return guess; 
+}
+template <size_t N>
+constexpr float newton_iteration(const std::function<float(float)>& fun, float guess)
+{
+    for(size_t i=0; i<N; ++i)guess-=fun(guess)/finite_difference<1000>(fun,guess);
+    
+
+    return guess; 
+}
+
+
+
+
+
+
+
 
 }
 
diff --git a/qm_quadrature.h b/qm_quadrature.h
new file mode 100644
index 0000000..3ac0b8c
--- /dev/null
+++ b/qm_quadrature.h
@@ -0,0 +1,22 @@
+#ifndef QM_QUADRATURE_H_
+#define QM_QUADRATURE_H_
+#include <functional>
+
+namespace QM{
+
+template <size_t N>
+constexpr float quadrature(const std::function<float(float)>& f, float a, float b)
+{
+    const float alpha{(b-a)/N};
+    float sum=0.5f*(f(a)+f(b));
+    for(size_t i=1; i< N-1;++i)sum+=f(a+i*alpha);
+
+    return alpha*sum; 
+}
+
+
+
+}
+
+
+#endif
\ No newline at end of file
diff --git a/quick_math.h b/quick_math.h
index ed9a9d3..b99f879 100644
--- a/quick_math.h
+++ b/quick_math.h
@@ -1,6 +1,6 @@
 #ifndef QUICK_MATH_H_
 #define QUICK_MATH_H_
-
+#include <cstdint>
 
 
 namespace QM{