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/usr/share/scalapack/LS.dat is in scalapack-test-common 1.8.0-9build1.

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The actual contents of the file can be viewed below.

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'ScaLAPACK LS solve input file'
'MPI machine'
'LS.out'			output file name (if any)
6				device out
3				number of problems sizes
15 7 31    			values of M
5 21 31    			values of N
2				number of NB's
2 3 5				values of NB
2				number of NRHS's
2 3 5				values of NRHS
2				number of NBRHS's
1 2				values of NBRHS
4				number of process grids (ordered pairs P & Q)
1 1 4 2 2 3 8			values of P
1 4 1 2 3 2 1			values of Q
4.0				threshold