Numerical methods for Data Assimilation

Updating of a QR factorization

Packed implementation

  • Consider the factor stored in a distributed packed format as

  • use of the ScaLAPACK routine PDGEQRF modified by stopping the QR factorization after the first columns

  • new observations are stored in a block matrix

Algorithm

Updating of the R factor in an incremental QR factorization

At the first iteration, we factor :

we advance the updating of the R factor as :

Performance results

Updating of a 25600 x 25600 R factor by 51200 new observations (1 x 4 procs).

Nb of rows in L

512

1024

2048

5120

10240

12800

25600

Storage (Gbytes)

0.72

0.75

0.80

0.96

1.22

1.35

2.00

Flops overhead

1.50

1.31

1.22

1.16

1.14

1.14

1.13

Facto. time (sec)

7577

5824

5255

5077

5001

4894

4981

Gflops

3.33

3.61

3.59

3.47

3.44

3.50

3.40

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