# fillMatrix -- fill a mutable matrix with random numbers

## Synopsis

• Function: fillMatrix
• Usage:
fillMatrix M
fillMatrix(M,n)
• Inputs:
• M,
• n, an integer, if specified, the maximum number of entries to replace
• Optional inputs:
• Density => , default value 1, the fraction of entries of M to be replaced, if n is not specified
• UpperTriangular => , default value false, whether to fill entries only above the diagonal
• Height => an integer, default value 10, a bound on the absolute values of the generated random numbers
• Outputs:
• M
• Consequences:
• some entries of M are replaced with randomly generated numbers, whose size depends on the value of the option Height

## Description

 i1 : printingPrecision = 2 o1 = 2 i2 : fillMatrix(mutableMatrix(RR,5,10)) o2 = | .89 .71 .91 .71 .35 .54 .19 .39 .28 .89 | | .67 .89 .31 .13 .56 .87 .4 .56 .61 .17 | | .29 .23 .074 .25 .25 .42 .62 .87 .97 .97 | | .63 .46 .81 .74 .15 .61 .015 .7 .68 .065 | | .026 .78 .36 .11 .83 .85 .22 .68 .91 .88 | o2 : MutableMatrix i3 : fillMatrix(mutableMatrix(ZZ,5,10),UpperTriangular=>true) o3 = | 0 8 2 1 6 4 2 5 6 7 | | 0 0 2 7 7 0 6 4 4 9 | | 0 0 0 5 4 1 1 9 8 0 | | 0 0 0 0 5 4 1 7 4 9 | | 0 0 0 0 0 4 4 4 2 3 | o3 : MutableMatrix i4 : fillMatrix(mutableMatrix(QQ,5,10),Density=>.2,Height=>1000) o4 = | 0 0 243/835 89/26 0 76/169 0 0 473/389 2/9 | | 0 0 0 0 0 0 0 0 0 0 | | 0 250/159 519/809 0 79/74 0 701/437 0 377/614 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 31/951 38/707 | o4 : MutableMatrix i5 : fillMatrix(mutableMatrix(ZZ,5,10),25,Height=>1000) o5 = | 0 0 0 0 693 0 0 0 0 0 | | 830 622 0 655 817 0 170 0 851 155 | | 948 0 520 0 0 897 0 0 591 0 | | 0 391 0 274 0 968 0 0 0 596 | | 12 0 0 366 0 625 181 0 0 0 | o5 : MutableMatrix