added dy/dx for all functions

source/carbon/carbon_model_to_core_fun_kit.f90

@@ -38,15 +38,19 @@ contains
                 fun_kit%dfun => dfun_lin
             case('exp')
                 fun_kit%fun => fun_exp
+                fun_kit%dfun => dfun_exp
             case('hyp')
                 fun_kit%fun => fun_hyp
+                fun_kit%dfun => dfun_hyp
             case('mm')
                 fun_kit%fun => fun_mm
+                fun_kit%dfun => dfun_mm
             case('step')
                 fun_kit%fun => fun_step
                 fun_kit%dfun => dfun_step
             case('PieWise1')
                 fun_kit%fun => fun_PieWise1
+                fun_kit%dfun => dfun_PieWise1
             case('PieWise2')
                 fun_kit%fun => fun_PieWise2
                 fun_kit%dfun => dfun_PieWise2
@@ -136,6 +140,15 @@ contains
         y = pars(3) / (args(1) - pars(2)) + pars(1)
     end function fun_hyp
 
+    !> Deriv of hyperbolic function: y' = -k/(x-x0)**2
+    function dfun_hyp(args, pars) result(dy)
+        implicit none
+        real, intent(in) :: args(narg_default)
+        real, intent(in) :: pars(npar_default)
+        real :: dy
+        dy = - pars(3) / ((args(1) - pars(2)) * (args(1) - pars(2)))
+    end function dfun_hyp
+
     !> Michaelis-Menthen function: y = k*x/(x-x0) + y0
     function fun_mm(args, pars) result(y)
         implicit none
@@ -145,6 +158,15 @@ contains
         y = pars(3) * args(1) / (args(1) - pars(2)) + pars(1)
     end function fun_mm
 
+    !> Deriv of Michaelis-Menthen function: y' = -k*x0/(x-x0)**2
+    function dfun_mm(args, pars) result(dy)
+        implicit none
+        real, intent(in) :: args(narg_default)
+        real, intent(in) :: pars(npar_default)
+        real :: dy
+        dy = - (pars(3) * pars(2)) / ((args(1) - pars(2)) * (args(1) - pars(2)))
+    end function dfun_mm
+
     !> Step function: y = k*θ(x-x0) + y0
     function fun_step(args, pars) result(y)
         implicit none
@@ -155,6 +177,7 @@ contains
         y = pars(1) + pars(3) * theta
     end function fun_step
 
+    !> Deriv of step function: y' = 0
     function dfun_step(args, pars) result(dy)
         implicit none
         real, intent(in) :: args(narg_default)
@@ -172,6 +195,15 @@ contains
         y = pars(5) * pars(4)**( pars(3) * (args(1) - pars(2)) ) + pars(1)
     end function fun_exp
 
+    !> Deriv of exponent function: y' = amp*a**[k*(x-x0)]*k*ln(a)
+    function dfun_exp(args, pars) result(dy)
+        implicit none
+        real, intent(in) :: args(narg_default)
+        real, intent(in) :: pars(npar_default)
+        real :: dy
+        dy = pars(5) * pars(4) ** (pars(3) * (args(1) - pars(2))) * pars(3) * log(pars(4))
+    end function dfun_exp
+    
     !> Piecewise1 function: y = θ1(x1-x)*(k1*x + b1) + θ2(x-x1)*(k2*x + b2)
     function fun_PieWise1(args, pars) result(y)
         implicit none
@@ -183,6 +215,17 @@ contains
         y = theta1*(pars(3)*args(1) + pars(7)) + theta2*(pars(4)*args(1) + pars(8))
     end function fun_PieWise1
 
+    !> Deriv of piecewise1 function: y' = θ1(x1-x)*k1 + θ2(x-x1)*k2
+    function dfun_PieWise1(args, pars) result(dy)
+        implicit none
+        real, intent(in) :: args(narg_default)
+        real, intent(in) :: pars(npar_default)
+        real :: dy, theta1, theta2
+        theta1 = 0.5*(1. + sign(1.,pars(2) - args(1)))
+        theta2 = 0.5*(1. + sign(1.,(args(1) - pars(2))))
+        dy = theta1*pars(3) + theta2*pars(4)
+    end function dfun_PieWise1
+
     !> Piecewise2 function: y = θ1(x1-x)*(k1*x + b1) + θ2(x-x1)(x2-x)*(k2*x + b2) + θ3(x-x2)*(k3*x + b3)
     function fun_PieWise2(args, pars) result(y)
         implicit none
@@ -196,6 +239,7 @@ contains
         &   theta3*(pars(5)*args(1) + pars(6))
     end function fun_PieWise2
 
+    !> Deriv of piecewise2 function: y' = θ1(x1-x)*k1 + θ2(x-x1)(x2-x)*k2 + θ3(x-x2)*k3
     function dfun_PieWise2(args, pars) result(dy)
         implicit none
         real, intent(in) :: args(narg_default)