We have a problem inverting a matrix which has the following eigenvalues:
eigen(tcross, only.values=TRUE)
$values
[1] 7.917775e+20 2.130980e+16 7.961620e+13 8.241041e+12 2.258325e+12
[6] 3.869428e+11 6.791041e+10 2.485352e+09 9.863098e+08 9.819373e+05
[11] 3.263408e+05 2.929853e+05 2.920419e+05 2.714355e+05 8.733435e+04
[16] 8.127136e+04 6.543883e+04 5.335074e+04 3.773311e+04 2.904373e+04
[21] 2.418297e+04 1.387422e+04 8.925090e+03 5.538344e+03 4.831908e+03
[26] 1.133571e+03 9.882477e+02 7.725812e+02 5.081682e+02 3.010545e+02
[31] 1.801611e+02 1.319787e+02 1.050521e+02 7.096471e+01 5.576549e+01
[36] 4.192645e+01 3.549810e+01 2.638731e+01 2.444429e+01 1.735139e+01
[41] 1.058796e+01 7.425778e+00 7.209576e+00 4.689665e+00 3.181650e+00
[46] 3.002956e+00 1.959247e+00 1.551665e+00 1.079589e+00 1.064981e+00
[51] 5.409617e-01 4.076501e-01 2.010129e-01 1.302394e-01 4.029787e-02
[56] 2.599448e-02 1.061294e-02 1.634286e-03 4.095303e-09 1.021885e-10
[61] 2.124763e-11 6.906665e-12 2.850103e-12 9.440867e-13 6.269723e-13
[66] 1.043794e-13 -1.300171e-13 -7.220665e-13 -4.166945e-12 -6.145350e-12
[71] -2.776804e-11 -5.269669e-11 -7.154246e-10 -1.490515e-09 -1.294256e-08
[76] -1.224821e-02 -3.278657e+00 -4.620100e+01 -9.781843e+02 -1.303929e+04
[81] -5.545949e+04 -8.077540e+04 -8.577861e+04 -1.329961e+05 -1.450908e+05
[86] -3.022353e+05 -4.015776e+05
As yout can see, the eigenvalues spread very much (between e+20 and e-13).
We presume, that it has something to do with R's floating point precision,
which I read is about 22-digits in mantissa as default. Can this precision
be set to values above 22? The problem occurs especially when trying to
perform 2SLS with the 'systemfit' package. There appears always an error
message like the following from the inverting routine:
solve(tcross)
Error in solve.default(tcross) : Lapack routine dgesv: system is exactly
singular
is there another source of error? We would like to embed R-routines in a
non-commercial web application for which we need to employ 'systemfit'
together with individual, user-submitted data. So the problem needs a
general solution and not a special one for this particular matrix.
Thanks in advance
Roy
PS: The 'gmp' package is definitely not the solution. I already tried it.
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Roy Nitze wrote:
We have a problem inverting a matrix which has the following eigenvalues:


>>eigen(tcross, only.values=TRUE)

$values
[1] 7.917775e+20 2.130980e+16 7.961620e+13 8.241041e+12 2.258325e+12
[6] 3.869428e+11 6.791041e+10 2.485352e+09 9.863098e+08 9.819373e+05
[11] 3.263408e+05 2.929853e+05 2.920419e+05 2.714355e+05 8.733435e+04
[16] 8.127136e+04 6.543883e+04 5.335074e+04 3.773311e+04 2.904373e+04
[21] 2.418297e+04 1.387422e+04 8.925090e+03 5.538344e+03 4.831908e+03
[26] 1.133571e+03 9.882477e+02 7.725812e+02 5.081682e+02 3.010545e+02
[31] 1.801611e+02 1.319787e+02 1.050521e+02 7.096471e+01 5.576549e+01
[36] 4.192645e+01 3.549810e+01 2.638731e+01 2.444429e+01 1.735139e+01
[41] 1.058796e+01 7.425778e+00 7.209576e+00 4.689665e+00 3.181650e+00
[46] 3.002956e+00 1.959247e+00 1.551665e+00 1.079589e+00 1.064981e+00
[51] 5.409617e-01 4.076501e-01 2.010129e-01 1.302394e-01 4.029787e-02
[56] 2.599448e-02 1.061294e-02 1.634286e-03 4.095303e-09 1.021885e-10
[61] 2.124763e-11 6.906665e-12 2.850103e-12 9.440867e-13 6.269723e-13
[66] 1.043794e-13 -1.300171e-13 -7.220665e-13 -4.166945e-12 -6.145350e-12
[71] -2.776804e-11 -5.269669e-11 -7.154246e-10 -1.490515e-09 -1.294256e-08
[76] -1.224821e-02 -3.278657e+00 -4.620100e+01 -9.781843e+02 -1.303929e+04
[81] -5.545949e+04 -8.077540e+04 -8.577861e+04 -1.329961e+05 -1.450908e+05
[86] -3.022353e+05 -4.015776e+05

As yout can see, the eigenvalues spread very much (between e+20 and e-13).
We presume, that it has something to do with R's floating point precision,
which I read is about 22-digits in mantissa as default.

Less than that. It depends a bit on the platform and the exact
calculation, but you can't count on more than 15-16 decimal digits
precision.

Can this precision
be set to values above 22?

No. R generally uses the floating point hardware type "double
precision", and it's a fixed size.

The problem occurs especially when trying to
perform 2SLS with the 'systemfit' package. There appears always an error
message like the following from the inverting routine:

solve(tcross)
Error in solve.default(tcross) : Lapack routine dgesv: system is exactly
singular

You will have to find a different solution to the problem. To machine
precision, that matrix looks singular. This usually indicates that it's
not the right matrix to try to invert.

Duncan Murdoch

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Peter Dalgaard wrote:
Duncan Murdoch <murdoch (AT) stats (DOT) uwo.cawrites:


>>You will have to find a different solution to the problem. To machine
>>precision, that matrix looks singular. This usually indicates that it's
>>not the right matrix to try to invert.

It might be a scaling issue though: If you're measuring age in days
and hormone concentrations in Molar, then you'll get that sort of
eigenvalue ratios in a fairly benign way.

Remember the old joke.

The patient to his doctor: "It hurts when I do this."

The doctor: "So don't do that."

Duncan Murdoch

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8/5/05, Roy Nitze <rnitze (AT) wiwi (DOT) uni-bielefeld.dewrote:
We have a problem inverting a matrix which has the following eigenvalues:

eigen(tcross, only.values=TRUE)
$values
[1] 7.917775e+20 2.130980e+16 7.961620e+13 8.241041e+12 2.258325e+12
[6] 3.869428e+11 6.791041e+10 2.485352e+09 9.863098e+08 9.819373e+05
[11] 3.263408e+05 2.929853e+05 2.920419e+05 2.714355e+05 8.733435e+04
[16] 8.127136e+04 6.543883e+04 5.335074e+04 3.773311e+04 2.904373e+04
[21] 2.418297e+04 1.387422e+04 8.925090e+03 5.538344e+03 4.831908e+03
[26] 1.133571e+03 9.882477e+02 7.725812e+02 5.081682e+02 3.010545e+02
[31] 1.801611e+02 1.319787e+02 1.050521e+02 7.096471e+01 5.576549e+01
[36] 4.192645e+01 3.549810e+01 2.638731e+01 2.444429e+01 1.735139e+01
[41] 1.058796e+01 7.425778e+00 7.209576e+00 4.689665e+00 3.181650e+00
[46] 3.002956e+00 1.959247e+00 1.551665e+00 1.079589e+00 1.064981e+00
[51] 5.409617e-01 4.076501e-01 2.010129e-01 1.302394e-01 4.029787e-02
[56] 2.599448e-02 1.061294e-02 1.634286e-03 4.095303e-09 1.021885e-10
[61] 2.124763e-11 6.906665e-12 2.850103e-12 9.440867e-13 6.269723e-13
[66] 1.043794e-13 -1.300171e-13 -7.220665e-13 -4.166945e-12 -6.145350e-12
[71] -2.776804e-11 -5.269669e-11 -7.154246e-10 -1.490515e-09 -1.294256e-08
[76] -1.224821e-02 -3.278657e+00 -4.620100e+01 -9.781843e+02 -1.303929e+04
[81] -5.545949e+04 -8.077540e+04 -8.577861e+04 -1.329961e+05 -1.450908e+05
[86] -3.022353e+05 -4.015776e+05

As yout can see, the eigenvalues spread very much (between e+20 and e-13).
We presume, that it has something to do with R's floating point precision,
which I read is about 22-digits in mantissa as default. Can this precision
be set to values above 22? The problem occurs especially when trying to
perform 2SLS with the 'systemfit' package. There appears always an error
message like the following from the inverting routine:

solve(tcross)
Error in solve.default(tcross) : Lapack routine dgesv: system is exactly
singular

is there another source of error? We would like to embed R-routines in a
non-commercial web application for which we need to employ 'systemfit'
together with individual, user-submitted data. So the problem needs a
general solution and not a special one for this particular matrix.

It appears that you are using the crossproduct but not taking
advantage of the symmetry.

The condition number of the crossproduct is the square of the
condition number of the original matrix so you are making your
conditioning problems much worse by taking the crossproduct. I
suggest that you use a QR or SVD decomposition of the original model
matrix instead. You will still end up with a very ill-conditioned
problem but now quite as bad as the one you have now.

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