Computer-Implemented Symbolic Differentiation Using Chain Rule

A computer accesses a first symbolic expression for an output value as a function of an input value. The computer computes a first symbolic Jacobian of the input value with respect to an input tangent space from a symbolic Lie group definition. The computer computes a second symbolic Jacobian of the...

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Bibliographische Detailangaben
Hauptverfasser:	Pattison, Dominic William, Solliday, Bradley Matthew, Kennedy, Ryan David, Zhu, Jack Louis, Bucki, Nathan Leo, Sun, Yixiao, Holtz, Kristen Marie, Miller, Aaron Christopher, Martirosyan, Hayk, VanderMey, Josiah Timothy, Wang, Samuel Shenghung, Cross, Gareth Benoit, Zheng, Harrison, Tomic, Teodor, Henry, Peter Benjamin
Format:	Patent
Sprache:	eng
Schlagworte:	CALCULATING COMPUTING CONTROLLING COUNTING ELECTRIC DIGITAL DATA PROCESSING PHYSICS REGULATING SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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Beschreibung
Zusammenfassung:	A computer accesses a first symbolic expression for an output value as a function of an input value. The computer computes a first symbolic Jacobian of the input value with respect to an input tangent space from a symbolic Lie group definition. The computer computes a second symbolic Jacobian of the output value with respect to the input value. The computer computes a third symbolic Jacobian of an output tangent space with respect to the input value from the symbolic Lie group definition. The computer applies symbolic matrix multiplication to the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space. The computer provides a representation of the second symbolic expression.