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"""
Linear algebra routines
=======================
Linear Algebra Basics::
inv --- Find the inverse of a square matrix
solve --- Solve a linear system of equations
solve_banded --- Solve a linear system of equations with a banded matrix
solveh_banded --- Solve a linear system of equations with a Hermitian or symmetric banded matrix, returning the Cholesky decomposition as well
det --- Find the determinant of a square matrix
norm --- matrix and vector norm
lstsq --- Solve linear least-squares problem
pinv --- Pseudo-inverse (Moore-Penrose) using lstsq
pinv2 --- Pseudo-inverse using svd
Eigenvalues and Decompositions::
eig --- Find the eigenvalues and vectors of a square matrix
eigvals --- Find the eigenvalues of a square matrix
eig_banded --- Find the eigenvalues and vectors of a band matrix
eigvals_banded --- Find the eigenvalues of a band matrix
lu --- LU decomposition of a matrix
lu_factor --- LU decomposition returning unordered matrix and pivots
lu_solve --- solve Ax=b using back substitution with output of lu_factor
svd --- Singular value decomposition of a matrix
svdvals --- Singular values of a matrix
diagsvd --- construct matrix of singular values from output of svd
orth --- construct orthonormal basis for range of A using svd
cholesky --- Cholesky decomposition of a matrix
cholesky_banded --- Cholesky decomposition of a banded symmetric or Hermitian matrix
cho_factor --- Cholesky decomposition for use in solving linear system
cho_solve --- Solve previously factored linear system
qr --- QR decomposition of a matrix
schur --- Schur decomposition of a matrix
rsf2csf --- Real to complex schur form
hessenberg --- Hessenberg form of a matrix
matrix Functions::
expm --- matrix exponential using Pade approx.
expm2 --- matrix exponential using Eigenvalue decomp.
expm3 --- matrix exponential using Taylor-series expansion
logm --- matrix logarithm
cosm --- matrix cosine
sinm --- matrix sine
tanm --- matrix tangent
coshm --- matrix hyperbolic cosine
sinhm --- matrix hyperbolic sine
tanhm --- matrix hyperbolic tangent
signm --- matrix sign
sqrtm --- matrix square root
funm --- Evaluating an arbitrary matrix function.
Iterative linear systems solutions::
cg --- Conjugate gradient (symmetric systems only)
cgs --- Conjugate gradient squared
qmr --- Quasi-minimal residual
gmres --- Generalized minimal residual
bicg --- Bi-conjugate gradient
bicgstab --- Bi-conjugate gradient stabilized
"""
postpone_import = 1
depends = ['misc','lib.lapack']
|
