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Move implementation details to docs, add FillArrays REQUIRE
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‎README.md

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@@ -3,8 +3,8 @@ A Julia package for representing block-block-banded matrices and banded-block-ba
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[![Build Status](https://travis-ci.org/JuliaMatrices/BlockBandedMatrices.jl.svg?branch=master)](https://travis-ci.org/JuliaMatrices/BlockBandedMatrices.jl)
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<!-- [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMatrices.github.io/BlockBandedMatrices.jl/stable)
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[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaMatrices.github.io/BlockBandedMatrices.jl/latest) -->
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<!-- [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMatrices.github.io/BlockBandedMatrices.jl/stable)-->
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[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaMatrices.github.io/BlockBandedMatrices.jl/latest)
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@@ -36,57 +36,3 @@ BandedBlockBandedMatrix(Zeros(sum(rows),sum(cols)), (rows,cols), (l,u), (λ,μ))
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BandedBlockBandedMatrix(Ones(sum(rows),sum(cols)), (rows,cols), (l,u), (λ,μ)) # creates a banded-block-banded matrix with ones in the non-zero entries
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BandedBlockBandedMatrix(I, (rows,cols), (l,u), (λ,μ))) # creates a banded-block-banded identity matrix
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```
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## Implementation
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A `BlockBandedMatrix` stores the entries in a single vector, ordered by columns.
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For example, if `A` is a `BlockBandedMatrix` with block-bandwidths `(A.l,A.u) == (1,0)`
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and the block sizes `fill(2, N)` where `N = 3` is the number
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of row and column blocks, then `A` has zero structure
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```julia
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[ a_11 a_12
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a_21 a_22
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a_31 a_32 a_33 a_34
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a_41 a_42 a_43 a_44
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a_53 a_54
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a_63 a_64 ]
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```
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and is stored in memory via `A.data` as a single vector by columns, containing:
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```
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[a_11,a_21,a_31,a_41,a_12,a_22,a_32,a_42,a_33,a_43,a_53,a_63,a_34,a_44,a_54,a_64]
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```
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The reasoning behind this storage scheme as that each block still satisfies
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the strided matrix interface, but we can also use BLAS and LAPACK to, for example,
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upper-triangularize a block column all at once.
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A `BandedBlockBandedMatrix` stores the entries as a `PseudoBlockMatrix`,
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with the number of row blocks equal to `A.l + A.u + 1`, and the row
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block sizes are all `A.μ + A.λ + 1`. The column block sizes of the storage is
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the same as the the column block sizes of the `BandedBlockBandedMatrix`. This
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is a block-wise version of the storage of `BandedMatrix`.
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For example, if `A` is a `BandedBlockBandedMatrix` with block-bandwidths `(A.l,A.u) == (1,0)`
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and subblock-bandwidths `(A.λ, A.μ) == (1,0)`, and the block sizes `fill(2, N)` where `N = 3` is the number
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of row and column blocks, then `A` has zero structure
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```julia
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[ a_11
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a_21 a_22
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a_31 a_33
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a_41 a_42 a_43 a_44
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a_53
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a_63 a_64 ]
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```
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and is stored in memory via `A.data` as a `PseudoBlockMatrix`, which has block sizes
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2 x 2, containing entries:
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```
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[a_11 a_22 a_33 a_44;
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a_21 X a_43 X ;
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a_31 a_42 a_53 a_64;
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a_41 X a_63 X ]
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```
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where `X` is an entry that is not used.
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The reasoning behind this storage scheme as that each block still satisfies
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the banded matrix interface.

‎REQUIRE

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BandedMatrices 0.4
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BlockArrays 0.3.1
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Compat 0.41
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FillArrays 0.0.2

‎docs/src/index.md

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subblockbandwidth
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```
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## Implementation
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A `BlockBandedMatrix` stores the entries in a single vector, ordered by columns.
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For example, if `A` is a `BlockBandedMatrix` with block-bandwidths `(A.l,A.u) == (1,0)`
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and the block sizes `fill(2, N)` where `N = 3` is the number
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of row and column blocks, then `A` has zero structure
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```julia
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[ a_11 a_12
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a_21 a_22
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a_31 a_32 a_33 a_34
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a_41 a_42 a_43 a_44
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a_53 a_54
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a_63 a_64 ]
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```
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and is stored in memory via `A.data` as a single vector by columns, containing:
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```
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[a_11,a_21,a_31,a_41,a_12,a_22,a_32,a_42,a_33,a_43,a_53,a_63,a_34,a_44,a_54,a_64]
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```
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The reasoning behind this storage scheme as that each block still satisfies
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the strided matrix interface, but we can also use BLAS and LAPACK to, for example,
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upper-triangularize a block column all at once.
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A `BandedBlockBandedMatrix` stores the entries as a `PseudoBlockMatrix`,
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with the number of row blocks equal to `A.l + A.u + 1`, and the row
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block sizes are all `A.μ + A.λ + 1`. The column block sizes of the storage is
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the same as the the column block sizes of the `BandedBlockBandedMatrix`. This
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is a block-wise version of the storage of `BandedMatrix`.
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For example, if `A` is a `BandedBlockBandedMatrix` with block-bandwidths `(A.l,A.u) == (1,0)`
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and subblock-bandwidths `(A.λ, A.μ) == (1,0)`, and the block sizes `fill(2, N)` where `N = 3` is the number
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of row and column blocks, then `A` has zero structure
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```julia
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[ a_11
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a_21 a_22
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a_31 a_33
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a_41 a_42 a_43 a_44
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a_53
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a_63 a_64 ]
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```
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and is stored in memory via `A.data` as a `PseudoBlockMatrix`, which has block sizes
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2 x 2, containing entries:
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```
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[a_11 a_22 a_33 a_44;
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a_21 X a_43 X ;
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a_31 a_42 a_53 a_64;
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a_41 X a_63 X ]
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```
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where `X` is an entry that is not used.
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The reasoning behind this storage scheme as that each block still satisfies
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the banded matrix interface.

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