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Functions

Dot Product

T(i,j) = A(i,k) B(k,j)

The Dot-Product performs a single contraction of Tensor components. Available combinations are:

  • Tensor1 and Tensor1
  • Tensor1 and Tensor2
  • Tensor2 and Tensor1
  • Tensor2 and Tensor2
  • Tensor2 and Tensor4
  • Tensor4 and Tensor4
  • Tensor2s and Tensor2s

Examples

T = A*B
T = A.dot.B

Multiplication of a Tensor and a Scalar

T(i,j) = A(i,j) * w

This special case is implemented within the Dot-Product where every Tensor component is multiplied by the scalar quantity w. As all Tensor data types are forced as double precision the scalar value is always converted to double precision.

Double-Dot Product

T(i,j) = A(i,j,k,l) : B(k,l)

The Double-Dot Product performs a double contraction of Tensor components. Available combinations are:

  • Tensor2 and Tensor2
  • Tensor2 and Tensor4
  • Tensor4 and Tensor4
  • Tensor2s and Tensor2s
  • Tensor2s and Tensor4s
  • Tensor4s and Tensor4s

Examples

T = A**B
T = A.ddot.B

Dyadic Product

T(i,j,k,l) = A(i,j) B(k,l)

The Dyadic Product performs a Tensor multiplication with no contraction. Available combinations are:

  • Tensor1 and Tensor1
  • Tensor2 and Tensor2
  • Tensor2s and Tensor2s

Examples

T = A.dya.B

Crossed Dyadic Product

T(i,j,k,l) = ( A(i,k) B(j,l) + A(i,l) B(j,k) ) / 2

The Crossed Dyadic Product performs a Tensor multiplication with no contraction but crossed indices as stated above. Due to compatibility with symmetric tensors this function refers to a symmetric crossed dyadic product. Available combinations are:

  • Tensor2 and Tensor2
  • Tensor2s and Tensor2s

Examples

T = A.cdya.B

Addition

T(i,j) = A(i,j) + B(i,j)

The Addition performs an elementwise addition of Tensor components. Available combinations are:

  • Tensor1 and Tensor1
  • Tensor2 and Tensor2
  • Tensor2s and Tensor2s
  • Tensor4 and Tensor4
  • Tensor4s and Tensor4s

Examples

T = A+B
T = A.add.B

Subtraction

T(i,j) = A(i,j) - B(i,j)

The Subraction performs an elementwise subtraction of Tensor components. Available combinations are:

  • Tensor1 and Tensor1
  • Tensor2 and Tensor2
  • Tensor2s and Tensor2s
  • Tensor4 and Tensor4
  • Tensor4s and Tensor4s

Examples

T = A-B
T = A.sub.B