Systems and methods for design parameter selection

A method, comprising:

• for a model representing a behavior of a system, wherein the model has an input and an output and includes an operation representable by a matrix, obtaining a size of the matrix, an overflow probability for the operation, a numerical input range, a numerical output range of the model, and a regularization parameter;
• determining a singular value bound for the matrix based at least in part on the size, numerical input range, numerical output range, and the regularization parameter;
• determining a minimum value of a noise of the system, using the singular value bound, the size, and the overflow probability;
• providing an indication of the minimum noise value;
• simulating the behavior of the system using the minimum noise value;
• and
• generating software for the system from the model based on the simulation.

A method, comprising:

• obtaining, for a model representing a behavior of a device, the model having an input and an output and including a matrix representing characteristics or operations of the device, an input range, output range, noise value for a noise in the device, overflow probability for the device, and a regularization parameter;
• determining, using the input range and the output range, a scaled regularized singular value bound for the matrix;
• determining, using at least the scaled regularized singular value bound, the overflow probability, the regularization parameter, and the noise value:
• a size of the matrix, the size specifying a number of observations and a number of values for each observation;
• providing an indication of the determined size of the matrix;
• simulating the behavior of the device using the determined size for the matrix;
• and
• generating software for the device from the model based on the simulation.

A method for selecting a datatype for use by software running on a device, comprising:

• for a model representing a behavior of the device, wherein the model has an input and an output and includes an operation representable by a matrix,
• obtaining an overflow probability for the operation, statistics information concerning a noise of the device, and a desired number of accurate digits,
• determining a singular value bound for the matrix based on a size associated with the matrix, the overflow probability, and the statistics information,
• determining an upper bound on a condition number using the matrix and the singular value bound,
• determining a numerical range for the output using information about the input and the singular value bound,
• determining a required number of precision digits based on the desired number of accurate digits and the upper bound on the condition number, and
• selecting the datatype for the input or the output, based at least in part on the determined numerical range of the output and the required number of precision digits;
• providing an indication of the selected datatype;
• simulating the behavior of the device using the selected datatype;
• and
• generating the software for the device from the model using the selected datatype.