AnabridREDAC

Documentation for AnabridREDAC.

Introduction

AnabridREDAC uses REDACProtocol to communicate with a network connected REDAC and is able to send a configuration for the analog components which when executed solve a differential equation and get a sampled solution back from the analog. AnabridREDAC also defines the compontents of the analog computer.

Usage

host = "lucidac-147476.ulm.anabrid.net"
port = 5732

using AnabridREDAC, Plots

RR = RemoteREDAC2(host,port)


RC = REDACConfig(
    AnabridREDAC.MIntBlock([AnabridREDAC.Integration(i*0.1,10000) for i in 1:8]),
    AnabridREDAC.MMulBlock(),
    AnabridREDAC.UBlock(nothing, [(i%8)+8 for i in 0:31]),
    AnabridREDAC.CBlock([ifelse(i<1,0.,-0.5) for i in 1:32]),
    AnabridREDAC.IBlock([ifelse(i<9, missing, [i]) for i in 0:15])
    )

data, time = run_remotely(RR,RC)

plot(time, data)

Analog calculation components

An analog computer is a network of calculating elements. Our network has a particular topology. Summed signals are processed by Integration or Multiplication. The results are then cloned, scaled and summed up again thus fed back into Integration or Multiplication.

Integration

The REDAC analog computer can integrate the summed signals 8 through 15. This enables us to solve to differential equations by feeding back the integrated signal into the input.

function integration(sum8,sum9,sum10,sum11,sum12,sum13,sum14,sum15)

return integrate(sum8/MINTBlock.outputs[1].k; ic=MINTBlock.outputs[1].ic), ... ,  integrate(sum15/MINTBlock.outputs[8].k; ic=MINTBlock.outputs[8].ic)
end

struct Integration

The REDAC has a MINTBlock which contains all 8 Integrators

struct IntegratorConfig

Lets assume we want to solve a Lotka-Volterra model where the second integrator is used for the prey population with an initial population of 0.1 and the seventh integrator is used for the preditor population with an initial population of 0.05. We choose 1/10000 to make the ODE run slower.

AnabridREDAC.MIntBlock(
    [
        AnabridREDAC.Integration(0.,10000),
        AnabridREDAC.Integration(0.2,10000),
        AnabridREDAC.Integration(0.,10000),
        AnabridREDAC.Integration(0.,10000),
        AnabridREDAC.Integration(0.,10000),
        AnabridREDAC.Integration(0.,10000),
        AnabridREDAC.Integration(0.05,10000),
        AnabridREDAC.Integration(0.,10000),
])

Multiplication

The Multiplication block has no configuration it operates on the the summed signals 0 through 7. Consider this pseudocode.

function multiplication(sum0,sum1,sum2,sum3,sum4,sum5,sum6,sum7)
    return sum0*sum1, sum2*sum3, sum4*sum5, sum6*sum7,1,1,1,1
end

It returns 4 products and a constant 4 times. The result of a network of self contained multipliers is undefined.

Linear operations

The output of the multiplication (0, ..., 7) and integration (8, ..., 15) can be copied into one of 32 signals for scalin, scaled and then summed up.

Duplicating signals

To clone or duplicate signals we use the UBlock.

In addition the cloned signals 8, ..., 15 can be recorded using and ADC returned to us as measurements. Only the cloned signals 8, ... , 15 can be recorded. The number of recorded channels must be a power of 2 and always starts at channel 8.

If we want to record the output of the first and last multiplier and the second and seventh integrator into the first 4 channels our configuration would look like:

AnabridREDAC.UBlock(nothing,
    [
    nothing,nothing,nothing,nothing,    nothing,nothing,nothing,nothing,
          0,      3,       9,    14,    nothing,nothing,nothing,nothing,
    nothing,nothing,nothing,nothing,    nothing,nothing,nothing,nothing,
    nothing,nothing,nothing,nothing,    nothing,nothing,nothing,nothing   
    ]
)

The integrators have 1 input each while the multiplier have two inputs each. Thus we need 6 summed signals for that we need more atleast 6 things to sum over. Thus this configuration is not sensible.

AnabridREDAC.UBlock(nothing,
    [
    nothing,nothing,nothing,nothing,          6,      6,nothing,nothing,
          0,      3,       9,    14,    nothing,nothing,nothing,nothing,
          0,nothing,       9,    14,    nothing,nothing,nothing,nothing,
    nothing,nothing,       9,    14,    nothing,nothing,nothing,nothing   
    ]
)

The 5th output of a multiplier is a constant, thus cloned signals 4 and 5 can be set to be any constant even while they are fed by the same constant (6). We also created a second copy of a multiplier and 2 additional copies of the integrators.

Scaling signals

Only cloned signals can be scaled.

struct CBlock

struct ScalarMultiplicationElement

Let's scale our example like this.

AnabridREDAC.CBlock(
    [
         0. , 0. , 0. , 0. ,    0.5,-1. , 0. , 0. ,
         0.3, 0. , 0.4,-0.2,    0. , 0. , 0. , 0. ,
        -0.3, 0. , 1. , 1. ,    0. , 0. , 0. , 0. ,
         0. , 0. , 1. , 1. ,    0. , 0. , 0. , 0. ,
    ]
)

We masked of one multiplier and the second multiplier is scaled with -0.3 and 0.3. We have the constants 0.3 and -1 available. The integrators are available unchanged 2 times each and the cloned signal of the output of the second integrator is scaled by 0.4 while the seventh integrator is scaled by -0.2.

Summing signals

Only scaled signals can be summed. Scaled signal can only appear in one sum.

struct IBlock

To see how to configure the IBlock for a Lotka-Volterra equation lets study the equation structure. Let y be the prey population and r the preditor population.

\[\dot y(t) = +\alpha y(t) -\beta y(t) r(t) \\ \dot r(t) = -\delta r(t) +\varepsilon y(t) r(t)\]

We will use the other mulitplier to calculate this non-sense

\[(y(t)+0.5) (r(t)-1.)\]

Since we have two copies of the first multiplier with different sign this is our product $y(t) r(t)$. Thus we need to feed our states $y(t), r(t)$ in to the multiplier block by making them the 0th and 1st summed signal respectively. The two middle multipliers go unused.

AnabridREDAC.IBlock(
    [
        [18],[19],
        missing,missing,
        missing,missing,
        ....
    ]
)

The other multiplier should calculate the non-sense term. We only use the second multiplier for prey and the seventh multiplier for the preditor population.

AnabridREDAC.IBlock(
    [   #Multipliers
        [18],[19], ## y(t), r(t)
        missing,missing,
        missing,missing,
        [4,18+8], [5,19+8], ## (0.5 +y(t)), (-1+r(t))
        # Integrators
        missing,
        [10,16], ## 0.4*y(t) + -0.3*y(t)*r(t)
        missing,
        missing,
        nothing,
        nothing,
        [11,8],  ## -0.2*r(t) + 0.3*y(t)*r(t)
        nothing       
    ]
)

Scaling differential equations

We should measure the outputs: [y(t)*r(t), (y(t)+0.5)*(r(t)-1.), y(t), r(t)] however we did not consider scaling our differential equations so that it remains between -1 and 1. The output will look very different.

All docs

• AnabridREDAC.AbstractResources
• AnabridREDAC.CBlock
• AnabridREDAC.CBlockElements
• AnabridREDAC.IBlock
• AnabridREDAC.IBlockElements
• AnabridREDAC.Integration
• AnabridREDAC.IntegratorConfig
• AnabridREDAC.MIntBlock
• AnabridREDAC.MMulBlock
• AnabridREDAC.MatchTypeClientREDAC
• AnabridREDAC.MatchTypeHcREDAC
• AnabridREDAC.REDACConfig
• AnabridREDAC.ScalarMultiplicationElement
• AnabridREDAC.UBlock
• AnabridREDAC.process
• AnabridREDAC.process

AbstractResources

struct CBlockElements

struct IBlockElements

process(RR::RemoteREDAC2, env::MatchType)

process(RR::RemoteREDAC2, c::Channel, msg)