Merge pull request #214 from haampie/mohamedmaster

LOBPCG docs take 2

docs/make.jl

@@ -23,6 +23,7 @@ makedocs(
 		],
 		"Eigenproblems" => [
 			"Power method" => "eigenproblems/power_method.md",
+			"LOBPCG" => "eigenproblems/lobpcg.md"
 		],
 		"SVDL" => "svd/svdl.md",
 		"The iterator approach" => "iterators.md",
@@ -37,7 +38,7 @@ deploydocs(
 	repo = "github.com/JuliaMath/IterativeSolvers.jl.git",
 	target = "build",
 	osname = "linux",
-	julia  = "0.6",
+	julia  = "0.7",
 	deps = nothing,
 	make = nothing,
 )

docs/src/eigenproblems/lobpcg.md

@@ -0,0 +1,22 @@
+# [Locally optimal block preconditioned conjugate gradient (LOBPCG)](@id LOBPCG)
+
+Solves the generalized eigenproblem $Ax = λBx$ approximately where $A$ and $B$ are Hermitian linear maps, and $B$ is positive definite. $B$ is taken to be the identity by default. It can find the smallest (or largest) `k` eigenvalues and their corresponding eigenvectors which are B-orthonormal. It also admits a preconditioner and a "constraints" matrix `C`, such that the algorithm returns the smallest (or largest) eigenvalues associated with the eigenvectors in the nullspace of `C'B`.
+
+## Usage
+
+```@docs
+lobpcg
+lobpcg!
+```
+
+## Implementation Details
+
+A `LOBPCGIterator` is created to pre-allocate all the memory required by the method using the constructor `LOBPCGIterator(A, B, largest, X, P, C)` where `A` and `B` are the matrices from the generalized eigenvalue problem, `largest` indicates if the problem is a maximum or minimum eigenvalue problem, `X` is the initial eigenbasis, randomly sampled if not input, where `size(X, 2)` is the block size `bs`. `P` is the preconditioner, `nothing` by default, and `C` is the constraints matrix. The desired `k` eigenvalues are found `bs` at a time.
+
+
+## References
+Implementation is based on [^Knyazev1993] and [^Scipy].
+
+[^Knyazev1993]: Andrew V. Knyazev. "Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method" SIAM Journal on Scientific Computing, 23(2):517–541 2001.
+
+[^Scipy]: See [Scipy LOBPCG implementation](https://github.com/scipy/scipy/blob/v1.1.0/scipy/sparse/linalg/eigen/lobpcg/lobpcg.py#L109-L568)