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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def calc_targetedrelease_v1(self):
 """Calculate the targeted water release for reducing drought events, taking into account both the required water release and the actual inflow into the dam. Some dams are supposed to maintain a certain degree of low flow variability downstream. In case parameter |RestrictTargetedRelease| is set to `True`, method |calc_targetedrelease_v1| simulates this by (approximately) passing inflow as outflow whenever inflow is below the value of the threshold parameter |NearDischargeMinimumThreshold|. If parameter |RestrictTargetedRelease| is set to `False`, does nothing except assigning the value of sequence |RequiredRelease| to sequence |TargetedRelease|. Required control parameter: |RestrictTargetedRelease| |NearDischargeMinimumThreshold| Required derived parameters: |NearDischargeMinimumSmoothPar1| |dam_derived.TOY| Required flux sequence: |RequiredRelease| Calculated flux sequence: |TargetedRelease| Used auxiliary method: |smooth_logistic1| Basic equation: :math:`TargetedRelease = w \\cdot RequiredRelease + (1-w) \\cdot Inflow` :math:`w = smooth_{logistic1}( Inflow-NearDischargeMinimumThreshold, NearDischargeMinimumSmoothPar1)` Examples: As in the examples above, define a short simulation time period first: Prepare the dam model: We start with enabling |RestrictTargetedRelease|: Define a minimum discharge value for a cross section immediately downstream of 6 m³/s for the summer months and of 4 m³/s for the winter months: Also define related tolerance values that are 1 m³/s in summer and 0 m³/s in winter: Prepare a test function that calculates the targeted water release based on the parameter values defined above and for inflows into the dam ranging from 0 m³/s to 10 m³/s: Firstly, assume the required release of water for reducing droughts has already been determined to be 10 m³/s: On May 31, the tolerance value is 0 m³/s. Hence the targeted release jumps from the inflow value to the required release when exceeding the threshold value of 6 m³/s: | ex. | inflow | targetedrelease | | 1 | 0.0 | 0.0 | | 2 | 0.5 | 0.5 | | 3 | 1.0 | 1.0 | | 4 | 1.5 | 1.5 | | 5 | 2.0 | 2.0 | | 6 | 2.5 | 2.5 | | 7 | 3.0 | 3.0 | | 8 | 3.5 | 3.5 | | 9 | 4.0 | 4.0 | | 10 | 4.5 | 4.5 | | 11 | 5.0 | 5.0 | | 12 | 5.5 | 5.5 | | 13 | 6.0 | 8.0 | | 14 | 6.5 | 10.0 | | 15 | 7.0 | 10.0 | | 16 | 7.5 | 10.0 | | 17 | 8.0 | 10.0 | | 18 | 8.5 | 10.0 | | 19 | 9.0 | 10.0 | | 20 | 9.5 | 10.0 | | 21 | 10.0 | 10.0 | On April 1, the threshold value is 4 m³/s and the tolerance value is 2 m³/s. Hence there is a smooth transition for inflows ranging between 2 m³/s and 6 m³/s: | ex. | inflow | targetedrelease | | 1 | 0.0 | 0.00102 | | 2 | 0.5 | 0.503056 | | 3 | 1.0 | 1.009127 | | 4 | 1.5 | 1.527132 | | 5 | 2.0 | 2.08 | | 6 | 2.5 | 2.731586 | | 7 | 3.0 | 3.639277 | | 8 | 3.5 | 5.064628 | | 9 | 4.0 | 7.0 | | 10 | 4.5 | 8.676084 | | 11 | 5.0 | 9.543374 | | 12 | 5.5 | 9.861048 | | 13 | 6.0 | 9.96 | | 14 | 6.5 | 9.988828 | | 15 | 7.0 | 9.996958 | | 16 | 7.5 | 9.999196 | | 17 | 8.0 | 9.999796 | | 18 | 8.5 | 9.999951 | | 19 | 9.0 | 9.99999 | | 20 | 9.5 | 9.999998 | | 21 | 10.0 | 10.0 | An required release substantially below the threshold value is a rather unlikely scenario, but is at least instructive regarding the functioning of the method (when plotting the results On May 31, the relationship between targeted release and inflow is again highly discontinous: | ex. | inflow | targetedrelease | | 1 | 0.0 | 0.0 | | 2 | 0.5 | 0.5 | | 3 | 1.0 | 1.0 | | 4 | 1.5 | 1.5 | | 5 | 2.0 | 2.0 | | 6 | 2.5 | 2.5 | | 7 | 3.0 | 3.0 | | 8 | 3.5 | 3.5 | | 9 | 4.0 | 4.0 | | 10 | 4.5 | 4.5 | | 11 | 5.0 | 5.0 | | 12 | 5.5 | 5.5 | | 13 | 6.0 | 4.0 | | 14 | 6.5 | 2.0 | | 15 | 7.0 | 2.0 | | 16 | 7.5 | 2.0 | | 17 | 8.0 | 2.0 | | 18 | 8.5 | 2.0 | | 19 | 9.0 | 2.0 | | 20 | 9.5 | 2.0 | | 21 | 10.0 | 2.0 | And on April 1, it is again absolutely smooth: | ex. | inflow | targetedrelease | | 1 | 0.0 | 0.000204 | | 2 | 0.5 | 0.500483 | | 3 | 1.0 | 1.001014 | | 4 | 1.5 | 1.501596 | | 5 | 2.0 | 2.0 | | 6 | 2.5 | 2.484561 | | 7 | 3.0 | 2.908675 | | 8 | 3.5 | 3.138932 | | 9 | 4.0 | 3.0 | | 10 | 4.5 | 2.60178 | | 11 | 5.0 | 2.273976 | | 12 | 5.5 | 2.108074 | | 13 | 6.0 | 2.04 | | 14 | 6.5 | 2.014364 | | 15 | 7.0 | 2.005071 | | 16 | 7.5 | 2.00177 | | 17 | 8.0 | 2.000612 | | 18 | 8.5 | 2.00021 | | 19 | 9.0 | 2.000072 | | 20 | 9.5 | 2.000024 | | 21 | 10.0 | 2.000008 | For required releases equal with the threshold value, there is generally no jump in the relationship. But on May 31, there remains a discontinuity in the first derivative: | ex. | inflow | targetedrelease | | 1 | 0.0 | 0.0 | | 2 | 0.5 | 0.5 | | 3 | 1.0 | 1.0 | | 4 | 1.5 | 1.5 | | 5 | 2.0 | 2.0 | | 6 | 2.5 | 2.5 | | 7 | 3.0 | 3.0 | | 8 | 3.5 | 3.5 | | 9 | 4.0 | 4.0 | | 10 | 4.5 | 4.5 | | 11 | 5.0 | 5.0 | | 12 | 5.5 | 5.5 | | 13 | 6.0 | 6.0 | | 14 | 6.5 | 6.0 | | 15 | 7.0 | 6.0 | | 16 | 7.5 | 6.0 | | 17 | 8.0 | 6.0 | | 18 | 8.5 | 6.0 | | 19 | 9.0 | 6.0 | | 20 | 9.5 | 6.0 | | 21 | 10.0 | 6.0 | On April 1, this second order discontinuity is smoothed with the help of a little hump around the threshold: | ex. | inflow | targetedrelease | | 1 | 0.0 | 0.000408 | | 2 | 0.5 | 0.501126 | | 3 | 1.0 | 1.003042 | | 4 | 1.5 | 1.50798 | | 5 | 2.0 | 2.02 | | 6 | 2.5 | 2.546317 | | 7 | 3.0 | 3.091325 | | 8 | 3.5 | 3.620356 | | 9 | 4.0 | 4.0 | | 10 | 4.5 | 4.120356 | | 11 | 5.0 | 4.091325 | | 12 | 5.5 | 4.046317 | | 13 | 6.0 | 4.02 | | 14 | 6.5 | 4.00798 | | 15 | 7.0 | 4.003042 | | 16 | 7.5 | 4.001126 | | 17 | 8.0 | 4.000408 | | 18 | 8.5 | 4.000146 | | 19 | 9.0 | 4.000051 | | 20 | 9.5 | 4.000018 | | 21 | 10.0 | 4.000006 | Repeating the above example with the |RestrictTargetedRelease| flag disabled results in identical values for sequences |RequiredRelease| and |TargetedRelease|: | ex. | inflow | targetedrelease | | 1 | 0.0 | 4.0 | | 2 | 0.5 | 4.0 | | 3 | 1.0 | 4.0 | | 4 | 1.5 | 4.0 | | 5 | 2.0 | 4.0 | | 6 | 2.5 | 4.0 | | 7 | 3.0 | 4.0 | | 8 | 3.5 | 4.0 | | 9 | 4.0 | 4.0 | | 10 | 4.5 | 4.0 | | 11 | 5.0 | 4.0 | | 12 | 5.5 | 4.0 | | 13 | 6.0 | 4.0 | | 14 | 6.5 | 4.0 | | 15 | 7.0 | 4.0 | | 16 | 7.5 | 4.0 | | 17 | 8.0 | 4.0 | | 18 | 8.5 | 4.0 | | 19 | 9.0 | 4.0 | | 20 | 9.5 | 4.0 | | 21 | 10.0 | 4.0 | """

    con = self.parameters.control.fastaccess
    der = self.parameters.derived.fastaccess
    flu = self.sequences.fluxes.fastaccess
    if con.restricttargetedrelease:
        flu.targetedrelease = smoothutils.smooth_logistic1(
            flu.inflow-con.neardischargeminimumthreshold[
                der.toy[self.idx_sim]],
            der.neardischargeminimumsmoothpar1[der.toy[self.idx_sim]])
        flu.targetedrelease = (flu.targetedrelease * flu.requiredrelease +
                               (1.-flu.targetedrelease) * flu.inflow)
    else:
        flu.targetedrelease = flu.requiredrelease