Description Usage Arguments Value Note Author(s) References See Also Examples

Solves the linear system A*X=B where A is an almost block diagonal matrix of the form:

TopBlock

... Array(1) ... ... ...

... ... Array(2) ... ...

...

... ... ... Array(Nblocks)...

... ... ... BotBlock

The method is based on Gauss elimination with alternate row and column elimination with partial pivoting, producing a stable decomposition of the matrix A without introducing fill-in.

uses FORTRAN subroutine colrow

1 | ```
Solve.block(Top, AR, Bot, B, overlap)
``` |

`Top ` |
the first block of the almost block diagonal matrix |

`AR ` |
intermediary blocks; |

`Bot ` |
the last block of the almost block diagonal matrix |

`B ` |
Right-hand side of the equations, a vector with length = number
of rows of |

`overlap ` |
the number of columns in which successive blocks
overlap, and where |

matrix with the solution, X, of the block diagonal system of equations Ax=B, the number of columns of this matrix = number of columns of B.

A similar function but that requires a totally different input can now
also be found in the `Matrix`

package

Karline Soetaert <karline.soetaert@nioz.nl>

J. C. Diaz , G. Fairweather , P. Keast, 1983. FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination, ACM Transactions on Mathematical Software (TOMS), v.9 n.3, p.358-375

`Solve.tridiag`

to solve a tridiagonal system of linear equations.

`Solve.banded`

to solve a banded system of linear equations.

`Solve`

the generalised inverse solution,

`solve`

the R default

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | ```
# Solve the following system: Ax=B, where A is block diagonal, and
# 0.0 -0.98 -0.79 -0.15 Top
# -1.00 0.25 -0.87 0.35 Top
# 0.78 0.31 -0.85 0.89 -0.69 -0.98 -0.76 -0.82 blk1
# 0.12 -0.01 0.75 0.32 -1.00 -0.53 -0.83 -0.98
# -0.58 0.04 0.87 0.38 -1.00 -0.21 -0.93 -0.84
# -0.21 -0.91 -0.09 -0.62 -1.99 -1.12 -1.21 0.07
# 0.78 -0.93 -0.76 0.48 -0.87 -0.14 -1.00 -0.59 blk2
# -0.99 0.21 -0.73 -0.48 -0.93 -0.91 0.10 -0.89
# -0.68 -0.09 -0.58 -0.21 0.85 -0.39 0.79 -0.71
# 0.39 -0.99 -0.12 -0.75 -0.68 -0.99 0.50 -0.88
# 0.71 -0.64 0.0 0.48 Bot
# 0.08 100.0 50.00 15.00 Bot
B <- c(-1.92, -1.27, -2.12, -2.16, -2.27, -6.08,
-3.03, -4.62, -1.02, -3.52, 0.55, 165.08)
AA <- matrix (nrow = 12, ncol = 12, 0)
AA[1,1:4] <- c( 0.0, -0.98, -0.79, -0.15)
AA[2,1:4] <- c(-1.00, 0.25, -0.87, 0.35)
AA[3,1:8] <- c( 0.78, 0.31, -0.85, 0.89, -0.69, -0.98, -0.76, -0.82)
AA[4,1:8] <- c( 0.12, -0.01, 0.75, 0.32, -1.00, -0.53, -0.83, -0.98)
AA[5,1:8] <- c(-0.58, 0.04, 0.87, 0.38, -1.00, -0.21, -0.93, -0.84)
AA[6,1:8] <- c(-0.21, -0.91, -0.09, -0.62, -1.99, -1.12, -1.21, 0.07)
AA[7,5:12] <- c( 0.78, -0.93, -0.76, 0.48, -0.87, -0.14, -1.00, -0.59)
AA[8,5:12] <- c(-0.99, 0.21, -0.73, -0.48, -0.93, -0.91, 0.10, -0.89)
AA[9,5:12] <- c(-0.68, -0.09, -0.58, -0.21, 0.85, -0.39, 0.79, -0.71)
AA[10,5:12]<- c( 0.39, -0.99, -0.12, -0.75, -0.68, -0.99, 0.50, -0.88)
AA[11,9:12]<- c( 0.71, -0.64, 0.0, 0.48)
AA[12,9:12]<- c( 0.08, 100.0, 50.00, 15.00)
## Block diagonal input.
Top <- matrix(nrow = 2, ncol = 4, data = AA[1:2 , 1:4] )
Bot <- matrix(nrow = 2, ncol = 4, data = AA[11:12, 9:12])
Blk1 <- matrix(nrow = 4, ncol = 8, data = AA[3:6 , 1:8] )
Blk2 <- matrix(nrow = 4, ncol = 8, data = AA[7:10 , 5:12])
AR <- array(dim = c(4, 8, 2), data = c(Blk1, Blk2))
overlap <- 4
# answer = (1, 1,....1)
Solve.block(Top, AR, Bot, B, overlap = 4)
# Now with 3 different B values
B3 <- cbind(B, 2*B, 3*B)
Solve.block(Top, AR, Bot, B3, overlap = 4)
``` |

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

Please suggest features or report bugs in the GitHub issue tracker.

All documentation is copyright its authors; we didn't write any of that.

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.