The CreateDayMatrix Function

We can ask Darwin to produce a Dayhoff matrix for a specific PAM distance or specific range of PAM distances via the CreateDayMatrix function and the global variable logPAM1.

Calling Sequences:
CreateDayMatrix(logmat, pam)
CreateDayMatrix(logmat, r)
Parameters:

logmat	:	array(real, real)
pam	:	real>0
r=r1..r2	:	range, $0<r_{1} \leq r_{2}$

Returns: DayMatrix or array(DayMatrix)

Synposis: This function computes a similarity matrix (enhanced Dayhoff) from the logarithmic mutation matrix logPAM1 and a specified PAM value or range of PAM values..

These matrices are equivalent to those produced by the CreateDayMatrices function.

> p55 := CreateDayMatrix(logPAM1, 55);

The variable logPAM1 deserves some attention. The entries of this matrix are the logarithm of a 1-PAM mutation matrix. It is particularly economical to compute k-PAM mutation matrices from this transformed matrix as we need only compute

$$M^{k} = e^{k \cdot \log ({\tt logPAM1})}$$

We use this to compute a 55-PAM similarity matrix.

> PrintMatrix( 10000*logPAM1, '%4d' );
-110   5   5   6  12   9  11  12   5   2   5   6   9   2  10  30  14   1
   4 -93   5   2   2  16   4   3   8   1   2  30   2   0   3   5   5   4
   3   4-112  18   2   8   5   6  13   1   1  10   1   1   2  13   8   1
   4   2  22 -95   0   7  28   5   6   0   0   5   0   0   3   7   5   0
   3   1   1   0 -55   0   0   1   1   1   1   0   1   1   0   3   1   1
   4  11   7   5   1-145  18   2  14   1   3  15   6   1   4   5   5   1
   8   5   6  31   0  28-111   2   7   1   1  15   3   0   4   7   5   1
  11   4   9   7   2   4   3 -48   3   0   1   3   1   0   2  10   2   2
   1   4   7   3   1   9   3   1-106   1   1   3   2   2   1   2   3   1
   2   1   2   0   2   2   1   0   2-122  22   2  27   7   1   1   5   2
   6   4   2   0   3   8   2   1   3  36 -82   3  49  22   4   3   4   5
   5  33  13   5   0  23  15   2   8   2   2-118   5   1   4   6   9   1
   3   1   1   0   2   4   1   0   2  10  12   2-142   5   0   2   3   1
   1   0   1   0   3   1   0   0   4   5  10   0   9 -78   0   1   1  10
   6   2   2   2   0   5   3   1   2   1   2   3   0   1 -58   6   5   0
  23   5  17   8   9   9   7   8   6   1   2   7   4   1   8-139  33   2
  11   5  11   6   4   8   5   2   7   6   2   9   7   2   7  33-122   1
   0   1   0   0   1   1   0   0   1   0   1   0   1   3   0   0   0 -44
   1   2   2   1   3   1   1   0  13   1   2   1   2  22   1   2   1  10
  15   2   1   0   8   3   4   1   2  51  14   3  12   5   2   3  14   1

> M55 := exp( 55*logPAM1 ):
> PrintMatrix( 1000*M55, '%4d' );
 560  25  26  28  49  37  42  48  23  19  22  29  35  13  43  93  56   7
  17 612  24  13  10  57  23  14  33   7  10  99  11   4  14  22  21  16
  15  20 550  63   9  32  25  23  47   6   5  36   8   6  10  43  31   4
  19  13  74 606   4  33  94  22  27   3   2  24   4   2  15  30  24   2
  12   3   4   1 742   2   1   3   5   4   4   1   6   6   1  11   6   5
  18  40  26  23   4 463  56  10  45   6  12  47  20   5  17  21  19   7
  31  25  32 102   4  87 560  14  30   7   7  53  12   3  19  29  23   4
  45  20  38  30  13  19  17 772  15   3   4  16   7   3  14  40  15   8
   7  15  24  12   6  28  12   5 564   4   4  14   7  10   6  10  10   6
  14   8   8   3  11  10   7   2   9 538  80  11  88  31   7   9  23   9
  26  18  10   4  18  30  11   5  18 130 658  18 162  88  18  15  21  25
  22 109  46  27   5  74  53  13  35  11  11 541  20   5  19  28  33   5
  10   5   4   2   7  12   5   2   7  34  39   8 466  20   2   7  10   6
   7   3   5   2  12   6   2   2  17  22  38   3  35 663   3   5   7  46
  25  12  10  12   3  20  15   8  12   5   9  14   5   3 731  26  22   2
  72  24  57  34  34  34  30  33  26  10   9  29  18   7  34 486  96   8
  44  25  42  27  21  32  25  12  27  25  14  35  28  10  30  98 526   5
   1   4   1   0   4   2   1   1   4   2   3   1   3  15   1   2   1 785
   5   8  10   5  12   7   4   2  45   8  10   6  10  83   4   9   6  43
  51  12   9   5  33  15  16   6  10 156  58  14  54  24  13  18  47   7