Interface Xqrm_spfct_unmqr_c

[amontoison]

Float32 + transp='n'

8×8 Matrix{Float32}:
  0.765399  -0.583735   0.0       0.0  -0.270955     0.0        0.0   0.0
 -0.142009   0.121727   0.0       0.0  -0.663393    -0.724517   0.0   0.0
 -0.243844  -0.316964  -0.738126  0.0  -0.00596202   0.0        0.0   0.543331
  0.0        0.0        0.0       1.0   0.0          0.0        0.0   0.0
  0.149274  -0.127955   0.0       0.0   0.697331    -0.689257   0.0   0.0
  0.0        0.0        0.0       0.0   0.0          0.0       -1.0   0.0
 -0.491001  -0.638233   0.0       0.0  -0.012005     0.0        0.0  -0.592817
  0.266782   0.346779  -0.674663  0.0   0.00652282   0.0        0.0  -0.59444

Float32 + transp='t'

8×8 Matrix{Float32}:
  0.765399  -0.142009  -0.243844    0.0   0.149274   0.0  -0.491001   0.266782
 -0.583735   0.121727  -0.316964    0.0  -0.127955   0.0  -0.638233   0.346779
  0.0        0.0       -0.738126    0.0   0.0        0.0   0.0       -0.674663
  0.0        0.0        0.0         1.0   0.0        0.0   0.0        0.0
 -0.270955  -0.663393  -0.00596202  0.0   0.697331   0.0  -0.012005   0.00652282
  0.0       -0.724517   0.0         0.0  -0.689257   0.0   0.0        0.0
  0.0        0.0        0.0         0.0   0.0       -1.0   0.0        0.0
  0.0        0.0        0.543331    0.0   0.0        0.0  -0.592817  -0.59444

Float32 + transp='c'

8×8 Matrix{Float32}:
  0.765399  -0.583735   0.0       0.0  -0.270955     0.0        0.0   0.0
 -0.142009   0.121727   0.0       0.0  -0.663393    -0.724517   0.0   0.0
 -0.243844  -0.316964  -0.738126  0.0  -0.00596202   0.0        0.0   0.543331
  0.0        0.0        0.0       1.0   0.0          0.0        0.0   0.0
  0.149274  -0.127955   0.0       0.0   0.697331    -0.689257   0.0   0.0
  0.0        0.0        0.0       0.0   0.0          0.0       -1.0   0.0
 -0.491001  -0.638233   0.0       0.0  -0.012005     0.0        0.0  -0.592817
  0.266782   0.346779  -0.674663  0.0   0.00652282   0.0        0.0  -0.59444

Float64 + transp='n'

8×8 Matrix{Float64}:
  0.00649547  -0.150752    0.0        0.28846    -0.387076   -0.136938   -0.770867   -0.362225
  0.310472    -0.588545    0.0        0.620165    0.328261    0.0854132   0.0607044   0.232124
  0.10971     -0.010901   -0.923031   0.0924533  -0.255888   -0.0135257   0.221378   -0.112437
 -0.646438    -0.363147   -0.152295  -0.0878052   0.448818   -0.307906    0.0264383  -0.349852
 -0.194154     0.660747    0.0        0.646752    0.257743    0.0390146   0.0633068  -0.18833
 -0.31589     -0.159652    0.0        0.0        -0.0979924   0.912631    0.0        -0.179521
 -0.00797196   0.18502    -0.3533    -0.203694    0.475062    0.168065   -0.589768    0.444563
 -0.579743    -0.0508492   0.0        0.23696    -0.416873   -0.127674    0.0231947   0.643849

Float64 + transp='t'

8×8 Matrix{Float64}:
  0.00649547   0.310472    0.10971    -0.646438   -0.194154   -0.31589    -0.00797196  -0.579743
 -0.150752    -0.588545   -0.010901   -0.363147    0.660747   -0.159652    0.18502     -0.0508492
  0.0          0.0        -0.923031   -0.152295    0.0         0.0        -0.3533       0.0
  0.28846      0.620165    0.0924533  -0.0878052   0.646752    0.0        -0.203694     0.23696
 -0.387076     0.328261   -0.255888    0.448818    0.257743   -0.0979924   0.475062    -0.416873
 -0.136938     0.0854132  -0.0135257  -0.307906    0.0390146   0.912631    0.168065    -0.127674
 -0.770867     0.0607044   0.221378    0.0264383   0.0633068   0.0        -0.589768     0.0231947
 -0.362225     0.232124   -0.112437   -0.349852   -0.18833    -0.179521    0.444563     0.643849

Float64 + transp='c'

8×8 Matrix{Float64}:
  0.00649547  -0.150752    0.0        0.28846    -0.387076   -0.136938   -0.770867   -0.362225
  0.310472    -0.588545    0.0        0.620165    0.328261    0.0854132   0.0607044   0.232124
  0.10971     -0.010901   -0.923031   0.0924533  -0.255888   -0.0135257   0.221378   -0.112437
 -0.646438    -0.363147   -0.152295  -0.0878052   0.448818   -0.307906    0.0264383  -0.349852
 -0.194154     0.660747    0.0        0.646752    0.257743    0.0390146   0.0633068  -0.18833
 -0.31589     -0.159652    0.0        0.0        -0.0979924   0.912631    0.0        -0.179521
 -0.00797196   0.18502    -0.3533    -0.203694    0.475062    0.168065   -0.589768    0.444563
 -0.579743    -0.0508492   0.0        0.23696    -0.416873   -0.127674    0.0231947   0.643849

ComplexF32 + transp='n'

8×8 Matrix{ComplexF32}:
 -0.813029-0.582223im         0.0+0.0im       0.0+0.0im        0.0+0.0im              0.0+0.0im             0.0+0.0im              0.0+0.0im                 0.0+0.0im
       0.0+0.0im        -0.510879-0.282436im  0.0+0.0im        0.0+0.0im       -0.0899323-0.103586im        0.0+0.0im          0.18427+0.257582im       0.220833+0.700959im
       0.0+0.0im              0.0+0.0im       1.0+0.0im        0.0+0.0im              0.0+0.0im             0.0+0.0im              0.0+0.0im                 0.0+0.0im
       0.0+0.0im              0.0+0.0im       0.0+0.0im  -0.148556-0.597834im         0.0+0.0im        0.124377+0.777854im         0.0+0.0im                 0.0+0.0im
       0.0+0.0im        -0.381157-0.504905im  0.0+0.0im        0.0+0.0im       -0.0433391-0.142205im        0.0+0.0im         0.068806+0.336253im      0.0770988-0.673755im
       0.0+0.0im              0.0+0.0im       0.0+0.0im  -0.539919-0.573597im         0.0+0.0im       -0.382615-0.482784im         0.0+0.0im                 0.0+0.0im
       0.0+0.0im        -0.314262-0.328527im  0.0+0.0im        0.0+0.0im       -0.0428204-0.097879im        0.0+0.0im        -0.276821-0.839801im      8.9407f-8-4.47035f-8im
       0.0+0.0im       -0.0906571-0.210032im  0.0+0.0im        0.0+0.0im        0.0551322+0.97192im         0.0+0.0im       4.47035f-8-7.45058f-9im  -2.38419f-7+0.0im

ComplexF32 + transp='t'

8×8 Matrix{ComplexF32}:
 -0.813029-0.582223im         0.0+0.0im       0.0+0.0im        0.0+0.0im              0.0+0.0im             0.0+0.0im              0.0+0.0im                 0.0+0.0im
       0.0+0.0im        -0.510879-0.282436im  0.0+0.0im        0.0+0.0im       -0.0899323-0.103586im        0.0+0.0im          0.18427+0.257582im       0.220833+0.700959im
       0.0+0.0im              0.0+0.0im       1.0+0.0im        0.0+0.0im              0.0+0.0im             0.0+0.0im              0.0+0.0im                 0.0+0.0im
       0.0+0.0im              0.0+0.0im       0.0+0.0im  -0.148556-0.597834im         0.0+0.0im        0.124377+0.777854im         0.0+0.0im                 0.0+0.0im
       0.0+0.0im        -0.381157-0.504905im  0.0+0.0im        0.0+0.0im       -0.0433391-0.142205im        0.0+0.0im         0.068806+0.336253im      0.0770988-0.673755im
       0.0+0.0im              0.0+0.0im       0.0+0.0im  -0.539919-0.573597im         0.0+0.0im       -0.382615-0.482784im         0.0+0.0im                 0.0+0.0im
       0.0+0.0im        -0.314262-0.328527im  0.0+0.0im        0.0+0.0im       -0.0428204-0.097879im        0.0+0.0im        -0.276821-0.839801im      8.9407f-8-4.47035f-8im
       0.0+0.0im       -0.0906571-0.210032im  0.0+0.0im        0.0+0.0im        0.0551322+0.97192im         0.0+0.0im       4.47035f-8-7.45058f-9im  -2.38419f-7+0.0im

ComplexF32 + transp='c'

8×8 Matrix{ComplexF32}:
 -0.813029+0.582223im         0.0+0.0im       0.0+0.0im        0.0+0.0im              0.0+0.0im             0.0+0.0im              0.0+0.0im                 0.0+0.0im
       0.0+0.0im        -0.510879+0.282436im  0.0+0.0im        0.0+0.0im        -0.381157+0.504905im        0.0+0.0im        -0.314262+0.328527im     -0.0906571+0.210032im
       0.0+0.0im              0.0+0.0im       1.0+0.0im        0.0+0.0im              0.0+0.0im             0.0+0.0im              0.0+0.0im                 0.0+0.0im
       0.0+0.0im              0.0+0.0im       0.0+0.0im  -0.148556+0.597834im         0.0+0.0im       -0.539919+0.573597im         0.0+0.0im                 0.0+0.0im
       0.0+0.0im       -0.0899323+0.103586im  0.0+0.0im        0.0+0.0im       -0.0433391+0.142205im        0.0+0.0im       -0.0428203+0.097879im      0.0551321-0.97192im
       0.0+0.0im              0.0+0.0im       0.0+0.0im   0.124377-0.777854im         0.0+0.0im       -0.382615+0.482784im         0.0+0.0im                 0.0+0.0im
       0.0+0.0im          0.18427-0.257582im  0.0+0.0im        0.0+0.0im         0.068806-0.336253im        0.0+0.0im        -0.276821+0.839801im     4.84288f-8+5.58794f-9im
       0.0+0.0im         0.220833-0.700959im  0.0+0.0im        0.0+0.0im        0.0770988+0.673755im        0.0+0.0im       8.19564f-8+2.98023f-8im  -2.38419f-7+2.98023f-8im

ComplexF64 + transp='n'

8×8 Matrix{ComplexF64}:
         0.0+4.72188e-19im        0.0+0.0im       0.0+0.0im  0.0+0.0im           0.0+0.0im            -0.445512-0.895276im     -5.55112e-17+1.11022e-16im        0.0+0.0im
 5.55112e-17+1.66533e-16im  -0.572767-0.400613im  0.0+0.0im  0.0+0.0im     -0.383545-0.180022im     2.77556e-17+0.0im             0.0391816-0.574801im           0.0+0.0im
         0.0+0.0im                0.0+0.0im       1.0+0.0im  0.0+0.0im           0.0+0.0im                  0.0+0.0im                   0.0+0.0im                0.0+0.0im
         0.0+0.0im                0.0+0.0im       0.0+0.0im  1.0+0.0im           0.0+0.0im                  0.0+0.0im                   0.0+0.0im                0.0+0.0im
         0.0+0.0im                0.0+0.0im       0.0+0.0im  0.0+0.0im      0.804078-0.0496436im            0.0+0.0im             -0.248288-0.53791im            0.0+0.0im
 5.45315e-17-1.69206e-16im  -0.128626-0.703493im  0.0+0.0im  0.0+0.0im      0.142908+0.38866im              0.0+1.11156e-17im     -0.422173+0.372617im           0.0+0.0im
   -0.998168-0.0605078im          0.0+0.0im       0.0+0.0im  0.0+0.0im  -4.16334e-17+2.08167e-17im          0.0+0.0im           1.11022e-16-6.93889e-17im        0.0+0.0im
         0.0+0.0im                0.0+0.0im       0.0+0.0im  0.0+0.0im           0.0+0.0im                  0.0+0.0im                   0.0+0.0im          -0.837483-0.546464im

ComplexF64 + transp='t'

8×8 Matrix{ComplexF64}:
         0.0+4.72188e-19im        0.0+0.0im       0.0+0.0im  0.0+0.0im           0.0+0.0im            -0.445512-0.895276im     -5.55112e-17+1.11022e-16im        0.0+0.0im
 5.55112e-17+1.66533e-16im  -0.572767-0.400613im  0.0+0.0im  0.0+0.0im     -0.383545-0.180022im     2.77556e-17+0.0im             0.0391816-0.574801im           0.0+0.0im
         0.0+0.0im                0.0+0.0im       1.0+0.0im  0.0+0.0im           0.0+0.0im                  0.0+0.0im                   0.0+0.0im                0.0+0.0im
         0.0+0.0im                0.0+0.0im       0.0+0.0im  1.0+0.0im           0.0+0.0im                  0.0+0.0im                   0.0+0.0im                0.0+0.0im
         0.0+0.0im                0.0+0.0im       0.0+0.0im  0.0+0.0im      0.804078-0.0496436im            0.0+0.0im             -0.248288-0.53791im            0.0+0.0im
 5.45315e-17-1.69206e-16im  -0.128626-0.703493im  0.0+0.0im  0.0+0.0im      0.142908+0.38866im              0.0+1.11156e-17im     -0.422173+0.372617im           0.0+0.0im
   -0.998168-0.0605078im          0.0+0.0im       0.0+0.0im  0.0+0.0im  -4.16334e-17+2.08167e-17im          0.0+0.0im           1.11022e-16-6.93889e-17im        0.0+0.0im
         0.0+0.0im                0.0+0.0im       0.0+0.0im  0.0+0.0im           0.0+0.0im                  0.0+0.0im                   0.0+0.0im          -0.837483-0.546464im

ComplexF64 + transp='c'

8×8 Matrix{ComplexF64}:
 1.11022e-16+0.0im          5.55112e-17-1.66533e-16im  0.0+0.0im  0.0+0.0im        0.0+0.0im        2.77556e-17+0.0im             -0.998168+0.0605078im          0.0+0.0im
         0.0+0.0im            -0.572767+0.400613im     0.0+0.0im  0.0+0.0im        0.0+0.0im          -0.128626+0.703493im              0.0+0.0im                0.0+0.0im
         0.0+0.0im                  0.0+0.0im          1.0+0.0im  0.0+0.0im        0.0+0.0im                0.0+0.0im                   0.0+0.0im                0.0+0.0im
         0.0+0.0im                  0.0+0.0im          0.0+0.0im  1.0+0.0im        0.0+0.0im                0.0+0.0im                   0.0+0.0im                0.0+0.0im
 2.94365e-17-2.38335e-17im    -0.383545+0.180022im     0.0+0.0im  0.0+0.0im   0.804078+0.0496436im     0.142908-0.38866im      -6.43664e-18+3.71928e-17im        0.0+0.0im
   -0.445512+0.895276im     2.77556e-17+0.0im          0.0+0.0im  0.0+0.0im        0.0+0.0im                0.0-2.77556e-17im           0.0+0.0im                0.0+0.0im
         0.0-1.11022e-16im    0.0391816+0.574801im     0.0+0.0im  0.0+0.0im  -0.248288+0.53791im      -0.422173-0.372617im      1.11022e-16+8.32667e-17im        0.0+0.0im
         0.0+0.0im                  0.0+0.0im          0.0+0.0im  0.0+0.0im        0.0+0.0im                0.0+0.0im                   0.0+0.0im          -0.837483+0.546464im

[amontoison]

@abuttari
I implemented qrm_spfct_unmqr in #99 and I have a comment for you.

In the real case, you could easily support transp='c' and dispatch to transp='t'.
In the complex case, if transp='t' is not supported, it should return an error.
The flag transp is just ignored when it's not supported and we have the result with transp='n'.
I can do that directly in the Julia interface but it could be relevant for other C or Fortran users.

A quick question, what the difference with qrm_apply?
In general we have another argument side for unmqr.

[abuttari]

unmqr now return an error if called with transp=t.

apply is currently only an alias for unmqr for backward compatibility. In the latest version I have renamed a few routines because "apply" (renamed into unmqr) and "solve" (renamed into trsm) don't seem accurate enough.

Yes in LAPACK unmqr there is also a "side" argument but this feature is currently lacking in qrm. It will we added if the need arises.