geophys (version 1.4-1)

PolarDecomp: Polar Decomposition

Description

Polar Decomposition for Strain

Usage

PolarDecomp(A)

Arguments

A

Strain Matrix

Value

P

matrix, stretch tensor

U

matrix, orthogonal rotation matrix

Details

Polar decomposition uses the svd to extract 2 matrices that represent the stretch and rotation of a strain: A = UP. U is orthogonal rotation matrix and P is the stretch tensor. These are extracted from the singular value decomposition.

References

<http://en.wikipedia.org/wiki/Finite_strain_theory>

See Also

svd

Examples

# NOT RUN {

A = matrix(runif(4, -1, 1), ncol=2)
PD = PolarDecomp(A)

E = svd(A)

###  W         S           V
 E$u 
# }
# NOT RUN {
<!-- %*% diag(E$d)%*%  t(E$v) -->
# }
# NOT RUN {
 ###t(E$v) %*% diag(E$d)%*%  (E$u)

P = E$v
# }
# NOT RUN {
<!-- %*% diag(E$d)%*%  t(E$v) -->
# }
# NOT RUN {
U =  E$u 
# }
# NOT RUN {
<!-- %*% t(E$v) -->
# }
# NOT RUN {

U 
# }
# NOT RUN {
<!-- %*% P  -->
# }
# NOT RUN {

# }