SymbolicDeltaProductArray
SymbolicDeltaProductArray[{n1,n2,…},{{j1,1,j1,2,…},{j2,1,j2,2,…},…}]
represents an n1×n2×… array with elements ai1,i2,… equal to 1 if all ijp,1ijp,2…, and 0 otherwise.
Details
- Valid dimension specifications nk in SymbolicDeltaProductArray[{n1,…,nr},{{j1,1,j1,2,…},{j2,1,j2,2,…},…}] are positive integers. Valid index specifications are integers 1≤jp,q≤r. It is also possible to work with symbolic dimension and index specifications.
- SymbolicDeltaProductArray[{n1,…,nr},{{j1,1,…,j1,k1},…,{jm,1,…,jm,km}}] is equal to Table[KroneckerDelta[ij1,1,…,ij1,k1]…KroneckerDelta[ijm,1,…,ijm,km],{i1,n1},…,{ir,nr}].
- SymbolicDeltaProductArray may be produced by differentiation involving ArraySymbol objects.
- For a SymbolicDeltaProductArray a array with positive integer specifications ni and jp,q, Normal[a] converts a to an explicit array. SparseArray[a] converts a to a SparseArray.
Examples
open allclose allBasic Examples (2)
The derivative of Total[a] with respect to a is a SymbolicDeltaProductArray:
The derivative of Tr[a] is a SymbolicDeltaProductArray as well:
Create a SymbolicDeltaProductArray with explicit numeric dimensions:
Convert a to an explicit array:
Convert a to a SparseArray:
Scope (2)
Array with explicit numeric dimensions:
Convert to a SparseArray:
Properties & Relations (7)
SymbolicDeltaProductArray gives a symbolic representation of the array:
Use Normal to convert a to an explicit array:
IdentityMatrix[n] gives an explicit version of SymbolicDeltaProductArray[{n,n},{{1,2}}]:
SymbolicIdentityArray is a special case of SymbolicDeltaProductArray:
SymbolicOnesArray is a special case of SymbolicDeltaProductArray:
The derivative of Total[a] with respect to a is a SymbolicDeltaProductArray:
The derivative of Tr[a] is a SymbolicDeltaProductArray:
The derivative of Total[a] with respect to a can be computed in the indexed format:
Compare with the results computed in the symbolic array format:
Text
Wolfram Research (2024), SymbolicDeltaProductArray, Wolfram Language function, https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html.
CMS
Wolfram Language. 2024. "SymbolicDeltaProductArray." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html.
APA
Wolfram Language. (2024). SymbolicDeltaProductArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymbolicDeltaProductArray.html