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 all close allBasic Examples (2)
The derivative of Total[a] with respect to a is a SymbolicDeltaProductArray:
a = ArraySymbol["a", {m, n, p}];D[Total[a], a]The derivative of Tr[a] is a SymbolicDeltaProductArray as well:
D[Tr[a], a]Create a SymbolicDeltaProductArray with explicit numeric dimensions:
a = SymbolicDeltaProductArray[{2, 2, 2, 2}, {{1, 4}, {2, 3}}]Convert a to an explicit array:
Normal[a]Convert a to a SparseArray:
SparseArray[a]Scope (2)
Array with explicit numeric dimensions:
a = SymbolicDeltaProductArray[{2, 3, 4}, {{1, 2, 3}}]Convert to a SparseArray:
SparseArray[a]Normal[a]Array with symbolic dimensions:
a = SymbolicDeltaProductArray[{m, n, p, q}, {{1, 2}, {3, 4}}]TensorDimensions[a]a - aProperties & Relations (7)
SymbolicDeltaProductArray gives a symbolic representation of the array:
a = SymbolicDeltaProductArray[{2, 2, 2}, {{1, 3}}]Use Normal to convert a to an explicit array:
Normal[a]IdentityMatrix[n] gives an explicit version of SymbolicDeltaProductArray[{n,n},{{1,2}}]:
a = IdentityMatrix[3]b = SymbolicDeltaProductArray[{3, 3}, {{1, 2}}]a === Normal[b]SymbolicIdentityArray is a special case of SymbolicDeltaProductArray:
a = SymbolicDeltaProductArray[{2, 3, 4, 2, 3, 4}, {{1, 4}, {2, 5}, {3, 6}}]b = SymbolicIdentityArray[{2, 3, 4}]Normal[a] === Normal[b]SymbolicOnesArray is a special case of SymbolicDeltaProductArray:
SymbolicDeltaProductArray[{2, 3, 4}, {}]The derivative of Total[a] with respect to a is a SymbolicDeltaProductArray:
a = ArraySymbol["a", {2, 3, 4, 5}];D[Total[a], a]D[Total[a, 3], a]D[Total[a, {2, 3}], a]The derivative of Tr[a] is a SymbolicDeltaProductArray:
a = ArraySymbol["a", {3, 4, 5, 6, 7}];D[Tr[a], a]The derivative of Total[a] with respect to a can be computed in the indexed format:
iA = Inactive[Table][Indexed[A, {i, j, k}], {i, m}, {j, n}, {k, p}]iTotalA = Inactive[Table][Inactive[Sum][Indexed[A, {i, j, k}], {i, m}], {j, n}, {k, p}]iDTotalA = D[iTotalA, {iA}]Compare with the results computed in the symbolic array format:
sA = ArraySymbol["A", {m, n, p}]sDTotalA = D[Total[sA], sA]Block[{m = 2, n = 3, p = 4}, Activate[iDTotalA] === Normal[sDTotalA]]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