Alignment fourth routine

Last routines which attempts to line up children under parents and put spouses and siblings "close" to each other, to the extent possible within the constraints of page width.

Usage

alignped4(rval, spouse, level, width, align, precision = 2)

Arguments

rval: A list with components n, nid, pos, and fam.
spouse: A boolean matrix with one row per level representing if the subject is a spouse or not.
level: Vector of the level of each subject
width: For a packed output, the minimum width of the plot, in inches.
align: For a packed Pedigree, align children under parents TRUE, to the extent possible given the page width, or align to to the left margin FALSE. This argument can be a two element vector, giving the alignment parameters, or a logical value. If TRUE, the default is c(1.5, 2), or if numeric the routine alignped4() will be called.
precision: The number of decimal places to round the solution to.

Value

The updated position matrix

Details

The alignped4() routine is the final step of alignment. The current code does necessary setup and then calls the quadprog::solve.QP() function.

There are two important parameters for the function:

The maximum width specified. The smallest possible width is the maximum number of subjects on a line. If the user suggestion is too low it is increased to that amount plus one (to give just a little wiggle room).
The align vector of 2 alignment parameters a and b. For each set of siblings x with parents at p_1 and p_2 the alignment penalty is:

$$(1/k^a)\sum_{i=1}^{k} (x_i - (p_1 + p_2)/2)^2$$

where k is the number of siblings in the set.

Using the fact that when a = 1 :

$$\sum(x_i-c)^2 = \sum(x_i-\mu)^2 + k(c-\mu)^2$$

then moving a sibship with k sibs one unit to the left or right of optimal will incur the same cost as moving one with only 1 or two sibs out of place.

If a = 0 then large sibships are harder to move than small ones. With the default value a = 1.5, they are slightly easier to move than small ones. The rationale for the default is as long as the parents are somewhere between the first and last siblings the result looks fairly good, so we are more flexible with the spacing of a large family. By tethering all the sibs to a single spot they tend to be kept close to each other.

The alignment penalty for spouses is $b(x_1 - x_2)^2$, which tends to keep them together. The size of b controls the relative importance of sib-parent and spouse-spouse closeness.

We start by adding in these penalties. The total number of parameters in the alignment problem (what we hand to quadprog) is the set of sum(n) positions. A work array myid keeps track of the parameter number for each position so that it is easy to find. There is one extra penalty added at the end. Because the penalty amount would be the same if all the final positions were shifted by a constant, the penalty matrix will not be positive definite; solve.QP() does not like this. We add a tiny amount of leftward pull to the widest line.
If there are k subjects on a line there will be k+1 constraints for that line. The first point must be $\ge 0$, each subsequent one must be at least 1 unit to the right, and the final point must be $\le$ the max width.

Examples

data(sampleped)
ped <- Pedigree(sampleped)
align(ped)
#> $`1`
#> $`1`$n
#> [1]  2 10 16 14
#> 
#> $`1`$nid
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   35   36    0    0    0    0    0    0    0     0     0     0     0     0
#> [2,]    1    2    3    4   37   38    5    6    7     8     0     0     0     0
#> [3,]    9   10   11   12   14   39   40   41   14    15    12    18    17    16
#> [4,]   21   22   23   24   27   28   25   26   29    30    31    32    33    34
#>      [,15] [,16]
#> [1,]     0     0
#> [2,]     0     0
#> [3,]    19    20
#> [4,]     0     0
#> 
#> $`1`$pos
#>      [,1] [,2] [,3] [,4] [,5] [,6]  [,7]  [,8]  [,9] [,10] [,11] [,12] [,13]
#> [1,]  3.8  4.8  0.0  0.0 0.00 0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
#> [2,]  0.0  1.0  2.8  3.8 4.80 5.80 11.25 12.25 14.01 15.01  0.00  0.00  0.00
#> [3,]  0.0  1.0  2.0  3.0 4.00 5.00  6.00  7.00  8.00  9.00 10.00 11.00 12.00
#> [4,]  0.0  1.0  2.0  3.0 6.01 7.01  8.01  9.01 10.01 11.01 12.01 13.01 14.01
#>      [,14] [,15] [,16]
#> [1,]  0.00     0     0
#> [2,]  0.00     0     0
#> [3,] 13.00    14    15
#> [4,] 15.01     0     0
#> 
#> $`1`$fam
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
#> [2,]    0    0    1    0    0    1    0    0    0     0     0     0     0     0
#> [3,]    1    3    3    3    3    5    5    5    0     7     0     7     0     7
#> [4,]    1    1    1    1    9    9   11   11   13    15    15    15    15    15
#>      [,15] [,16]
#> [1,]     0     0
#> [2,]     0     0
#> [3,]     7     9
#> [4,]     0     0
#> 
#> $`1`$spouse
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]    1    0    0    0    0    0    0    0    0     0     0     0     0     0
#> [2,]    1    0    1    0    1    0    1    0    1     0     0     0     0     0
#> [3,]    1    0    0    0    0    0    0    0    1     0     1     0     1     0
#> [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
#>      [,15] [,16]
#> [1,]     0     0
#> [2,]     0     0
#> [3,]     1     0
#> [4,]     0     0
#> 
#> 
#> $`2`
#> $`2`$n
#> [1] 2 7 5
#> 
#> $`2`$nid
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    1    2    0    0    0    0    0
#> [2,]    3    4    5    6    7    9    8
#> [3,]   10   11   12   13   14    0    0
#> 
#> $`2`$pos
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]  2.7  3.7  0.0  0.0  0.0    0    0
#> [2,]  0.0  1.0  2.0  3.0  4.0    5    6
#> [3,]  0.0  1.0  4.5  5.5  6.5    0    0
#> 
#> $`2`$fam
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    0    0    0    0    0    0    0
#> [2,]    0    1    1    1    1    0    1
#> [3,]    1    1    6    6    6    0    0
#> 
#> $`2`$spouse
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    1    0    0    0    0    0    0
#> [2,]    1    0    0    0    0    1    0
#> [3,]    0    0    0    0    0    0    0
#> 
#>

Usage

Arguments

Value

Details

See also

Examples