Skip to content

Commit

Permalink
sagemathgh-38360: Reintroducing tight complex interval inverse
Browse files Browse the repository at this point in the history 
    
This provides a (hopefully) correct implementation of computing a tight
enclosure for the inverse of a complex interval. It fixes sagemath#37963.

There is some history to this:
Commit 84ab655 from sagemath#19964 introduced a tight enclosure but had some
bugs such as ticket sagemath#37927.
Thus, the that commit (and the subsequent partial fixes) were reverted
in commit 8d59b12, see pull request sagemath#37941.
This is a new implementation of Rokne-Lancaster that I wrote from
scratch.

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

sagemath#37941
    
URL: sagemath#38360
Reported by: Matthias Goerner
Reviewer(s): Marc Culler, Nathan Dunfield
  • Loading branch information
Release Manager committed Jul 20, 2024
2 parents fb0e10a + 32568ca commit ed68bff
Show file tree
Hide file tree
Showing 9 changed files with 470 additions and 67 deletions.
2 changes: 1 addition & 1 deletion src/sage/dynamics/arithmetic_dynamics/projective_ds.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -6103,7 +6103,7 @@ def reduced_form(self, **kwds):
sage: f.reduced_form(prec=30, smallest_coeffs=False)
Traceback (most recent call last):
...
ValueError: accuracy of Newton's root not within tolerance(0.00009... > 1e-06), increase precision
ValueError: accuracy of Newton's root not within tolerance(0.00008... > 1e-06), increase precision
sage: f.reduced_form(smallest_coeffs=False)
(
Dynamical System of Projective Space of dimension 1 over Rational Field
Expand Down
2 changes: 1 addition & 1 deletion src/sage/matrix/matrix0.pyx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1974,7 +1974,7 @@ cdef class Matrix(sage.structure.element.Matrix):
sage: K = (A - e).kernel()
sage: P = K.basis_matrix()
sage: P.str()
'[ 1.000000000000000? + 0.?e-17*I -2.116651487479748? + 0.0255565807096352?*I -0.2585224251020429? + 0.288602340904754?*I -0.4847545623533090? - 1.871890760086142?*I]'
'[ 1.000000000000000? + 0.?e-17*I -2.116651487479748? + 0.0255565807096352?*I -0.2585224251020429? + 0.2886023409047535?*I -0.4847545623533090? - 1.871890760086142?*I]'
Use single-row delimiters where appropriate::
Expand Down
46 changes: 24 additions & 22 deletions src/sage/matrix/matrix2.pyx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -10589,23 +10589,24 @@ cdef class Matrix(Matrix1):
....: [-1, 1, -6, -6, 5]])
sage: Q, R = A.QR()
sage: Q
[ -0.4588314677411235? -0.1260506983326509? 0.3812120831224489? -0.394573711338418? -0.687440062597?]
[ -0.4588314677411235? 0.4726901187474409? -0.05198346588033394? 0.717294125164660? -0.220962877263?]
[ 0.2294157338705618? 0.6617661662464172? 0.6619227988762521? -0.180872093737548? 0.1964114464561?]
[ 0.6882472016116853? 0.1890760474989764? -0.2044682991293135? 0.096630296654307? -0.662888631790?]
[ -0.4588314677411235? -0.1260506983326509? 0.3812120831224489? -0.394573711338418? -0.6874400625964?]
[ -0.4588314677411235? 0.4726901187474409? -0.05198346588033394? 0.7172941251646595? -0.2209628772631?]
[ 0.2294157338705618? 0.6617661662464172? 0.6619227988762521? -0.1808720937375480? 0.1964114464561?]
[ 0.6882472016116853? 0.1890760474989764? -0.2044682991293135? 0.0966302966543065? -0.6628886317894?]
[ -0.2294157338705618? 0.5357154679137663? -0.609939332995919? -0.536422031427112? 0.0245514308070?]
sage: R
[ 4.358898943540674? -0.4588314677411235? 13.07669683062202? 6.194224814505168? 2.982404540317303?]
[ 0 1.670171752907625? 0.5987408170800917? -1.292019657909672? 6.207996892883057?]
[ 0 0 5.444401659866974? 5.468660610611130? -0.682716185228386?]
[ 0 0 0 1.027626039419836? -3.61930014968662?]
[ 0 0 0 0 0.02455143080702?]
[ 0 0 5.444401659866974? 5.468660610611130? -0.6827161852283857?]
[ 0 0 0 1.027626039419836? -3.619300149686620?]
[ 0 0 0 0 0.024551430807012?]

sage: Q.conjugate_transpose()*Q
[1.000000000000000? 0.?e-18 0.?e-17 0.?e-15 0.?e-12]
[ 0.?e-18 1.000000000000000? 0.?e-16 0.?e-15 0.?e-12]
[ 0.?e-17 0.?e-16 1.000000000000000? 0.?e-15 0.?e-12]
[ 0.?e-15 0.?e-15 0.?e-15 1.000000000000000? 0.?e-12]
[ 0.?e-12 0.?e-12 0.?e-12 0.?e-12 1.000000000000?]
[1.000000000000000? 0.?e-18 0.?e-17 0.?e-16 0.?e-13]
[ 0.?e-18 1.000000000000000? 0.?e-17 0.?e-16 0.?e-13]
[ 0.?e-17 0.?e-17 1.000000000000000? 0.?e-16 0.?e-13]
[ 0.?e-16 0.?e-16 0.?e-16 1.000000000000000? 0.?e-13]
[ 0.?e-13 0.?e-13 0.?e-13 0.?e-13 1.0000000000000?]
sage: Q * R == A
True

Expand All @@ -10621,24 +10622,25 @@ cdef class Matrix(Matrix1):
sage: Q, R = A.QR()
sage: Q
[ -0.7302967433402215? 0.2070566455055649? + 0.5383472783144687?*I 0.2463049809998642? - 0.0764456358723292?*I 0.2381617683194332? - 0.1036596032779695?*I]
[ 0.0912870929175277? -0.2070566455055649? - 0.3778783780476559?*I 0.3786559533863032? - 0.1952221495524667?*I 0.701244450214469? - 0.364371165098660?*I]
[ 0.6390096504226938? + 0.0912870929175277?*I 0.1708217325420910? + 0.6677576817554466?*I -0.03411475806452072? + 0.04090198741767143?*I 0.3140171085506763? - 0.0825191718705412?*I]
[ 0.0912870929175277? -0.2070566455055649? - 0.3778783780476559?*I 0.3786559533863033? - 0.1952221495524667?*I 0.701244450214469? - 0.3643711650986595?*I]
[ 0.6390096504226938? + 0.0912870929175277?*I 0.1708217325420910? + 0.6677576817554466?*I -0.03411475806452072? + 0.04090198741767143?*I 0.3140171085506764? - 0.0825191718705412?*I]
[ 0.1825741858350554? + 0.0912870929175277?*I -0.03623491296347385? + 0.0724698259269477?*I 0.8632284069415110? + 0.06322839976356195?*I -0.4499694867611521? - 0.0116119181208918?*I]
sage: R
[ 10.95445115010333? 0.?e-18 - 1.917028951268082?*I 5.385938482134133? - 2.190890230020665?*I -0.2738612787525831? - 2.190890230020665?*I]
[ 0 4.829596256417300? + 0.?e-17*I -0.869637911123373? - 5.864879483945125?*I 0.993871898426712? - 0.3054085521207082?*I]
[ 0 4.829596256417300? + 0.?e-18*I -0.869637911123373? - 5.864879483945125?*I 0.993871898426712? - 0.3054085521207082?*I]
[ 0 0 12.00160760935814? + 0.?e-16*I -0.2709533402297273? + 0.4420629644486323?*I]
[ 0 0 0 1.942963944258992? + 0.?e-16*I]
sage: Q.conjugate_transpose()*Q
[1.000000000000000? + 0.?e-19*I 0.?e-18 + 0.?e-17*I 0.?e-17 + 0.?e-17*I 0.?e-16 + 0.?e-16*I]
[ 0.?e-18 + 0.?e-17*I 1.000000000000000? + 0.?e-17*I 0.?e-17 + 0.?e-17*I 0.?e-16 + 0.?e-16*I]
[ 0.?e-17 + 0.?e-17*I 0.?e-17 + 0.?e-17*I 1.000000000000000? + 0.?e-16*I 0.?e-16 + 0.?e-16*I]
[ 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I 1.000000000000000? + 0.?e-15*I]
[ 0.?e-17 + 0.?e-17*I 0.?e-17 + 0.?e-17*I 1.000000000000000? + 0.?e-17*I 0.?e-16 + 0.?e-16*I]
[ 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I 1.000000000000000? + 0.?e-16*I]

sage: Q*R - A
[ 0.?e-17 0.?e-17 + 0.?e-17*I 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I]
[ 0.?e-18 0.?e-17 + 0.?e-17*I 0.?e-16 + 0.?e-16*I 0.?e-15 + 0.?e-15*I]
[ 0.?e-18 0.?e-17 + 0.?e-17*I 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I]
[0.?e-17 + 0.?e-18*I 0.?e-17 + 0.?e-17*I 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I]
[0.?e-18 + 0.?e-18*I 0.?e-18 + 0.?e-17*I 0.?e-16 + 0.?e-16*I 0.?e-15 + 0.?e-16*I]
[0.?e-18 + 0.?e-18*I 0.?e-18 + 0.?e-18*I 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I]

A rank-deficient rectangular matrix, with both values of the ``full`` keyword. ::

Expand Down Expand Up @@ -12328,9 +12330,9 @@ cdef class Matrix(Matrix1):
sage: # needs sage.combinat sage.libs.pari
sage: _, T = A.is_similar(B, transformation=True)
sage: T
[ 1.0000000000000? + 0.?e-13*I 0.?e-13 + 0.?e-13*I 0.?e-13 + 0.?e-13*I]
[-0.6666666666667? + 0.?e-13*I 0.16666666666667? + 0.?e-14*I -0.8333333333334? + 0.?e-13*I]
[ 0.6666666666667? + 0.?e-13*I 0.?e-13 + 0.?e-13*I -0.333333333334? + 0.?e-13*I]
[ 1.00000000000000? + 0.?e-14*I 0.?e-14 + 0.?e-14*I 0.?e-14 + 0.?e-14*I]
[-0.66666666666667? + 0.?e-15*I 0.166666666666667? + 0.?e-15*I -0.83333333333334? + 0.?e-14*I]
[ 0.66666666666667? + 0.?e-14*I 0.?e-14 + 0.?e-14*I -0.33333333333333? + 0.?e-14*I]
sage: T.change_ring(QQ)
[ 1 0 0]
[-2/3 1/6 -5/6]
Expand Down
Loading

0 comments on commit ed68bff

Please sign in to comment.