cholup#

Purpose#

Performs a Cholesky update of one or more rows on an upper triangular matrix.

Format#

r = cholup(C, x)#

Parameters:

C (KxK matrix) – upper triangular matrix
x (NxK matrix) – the rows to update C with.

Returns:

r (KxK upper triangular matrix) – the updated matrix.

Examples#

// Assign C matrix
C = { 18.87055964 15.3229443  8.04947012,
                0 9.30682813 -2.12009339,
                0          0  7.62878355 };

// Assign x matrix
x = { 1.76644971 7.49445820 9.79114666,
      6.87691156 4.41961438 4.32476921 };

// Call cholup
r = cholup(C, x);

After the above code, R will equal:

    20.162100    16.505444    9.8667614
r = 0.0000000    11.166015    2.9776167
    0.0000000    0.0000000    11.654961

Remarks#

C should be a Cholesky factorization.

cholup(C, x) is equivalent to chol(C'C + x'x), but cholup is numerically much more stable.