nakatamaho/mplapack

on macOS xlinstC_dd CLS: Least squares driver routines fails

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on macOS xlinstC_dd CLS: Least squares driver routines fails

CLS: Least squares driver routines
Matrix types (1-3: full rank, 4-6: rank deficient):
1 and 4. Normal scaling
2 and 5. Scaled near overflow
3 and 6. Scaled near underflow
Test ratios:
(1-2: CGELS, 3-6: CGELSY, 7-10: CGELSS, 11-14: CGELSD, 15-16:
1: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS )
2: norm( (A*X-B)' A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS )
if TRANS='N' and M.GE.N or TRANS='T' and M.LT.N, otherwise
check if X is in the row space of A or A' (overdetermined case)
3: norm(svd(A)-svd(R)) / ( min(M,N) * norm(svd(R)) * EPS )
4: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS )
5: norm( (A
X-B)' *A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS )
6: Check if X is in the row space of A or A'
7-10: same as 3-6 11-14: same as 3-6
Messages:
M= 1, N= 2, NRHS= 1, NB= 1, type 1, test( 3)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 1, type 1, test( 7)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 1, type 1, test(11)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test( 3)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test( 7)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test(11)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test( 3)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test( 7)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test(11)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test( 3)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test( 7)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 3, type 1, test(11)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 20, type 1, test( 3)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 20, type 1, test( 7)=1.5936698060288872e+15
M= 1, N= 2, NRHS= 1, NB= 20, type 1, test(11)=1.5936698060288872e+15
...
M= 50, N= 50, NRHS= 15, NB= 20, type 6, test( 7)=1.0752410344628826e+13
M= 50, N= 50, NRHS= 15, NB= 20, type 6, test(11)=1.0752410344628900e+13
CLS drivers: 7425 out of 105840 tests failed to pass the threshold