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Results with Julia v1.2.0
Testing was successful .
Last evaluation was ago and took 44 minutes, 15 seconds.
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Resolving package versions...
Installed FastClosures ──── v0.3.2
Installed LinearOperators ─ v0.6.0
Installed Krylov ────────── v0.3.1
Updating `~/.julia/environments/v1.2/Project.toml`
[ba0b0d4f] + Krylov v0.3.1
Updating `~/.julia/environments/v1.2/Manifest.toml`
[9aa1b823] + FastClosures v0.3.2
[ba0b0d4f] + Krylov v0.3.1
[5c8ed15e] + LinearOperators v0.6.0
[2a0f44e3] + Base64
[8ba89e20] + Distributed
[b77e0a4c] + InteractiveUtils
[8f399da3] + Libdl
[37e2e46d] + LinearAlgebra
[56ddb016] + Logging
[d6f4376e] + Markdown
[de0858da] + Printf
[9a3f8284] + Random
[9e88b42a] + Serialization
[6462fe0b] + Sockets
[2f01184e] + SparseArrays
[8dfed614] + Test
[4ec0a83e] + Unicode
Testing Krylov
Status `/tmp/jl_X5JtN5/Manifest.toml`
[9aa1b823] FastClosures v0.3.2
[ba0b0d4f] Krylov v0.3.1
[5c8ed15e] LinearOperators v0.6.0
[2a0f44e3] Base64 [`@stdlib/Base64`]
[8ba89e20] Distributed [`@stdlib/Distributed`]
[b77e0a4c] InteractiveUtils [`@stdlib/InteractiveUtils`]
[8f399da3] Libdl [`@stdlib/Libdl`]
[37e2e46d] LinearAlgebra [`@stdlib/LinearAlgebra`]
[56ddb016] Logging [`@stdlib/Logging`]
[d6f4376e] Markdown [`@stdlib/Markdown`]
[de0858da] Printf [`@stdlib/Printf`]
[9a3f8284] Random [`@stdlib/Random`]
[9e88b42a] Serialization [`@stdlib/Serialization`]
[6462fe0b] Sockets [`@stdlib/Sockets`]
[2f01184e] SparseArrays [`@stdlib/SparseArrays`]
[8dfed614] Test [`@stdlib/Test`]
[4ec0a83e] Unicode [`@stdlib/Unicode`]
USYMLQ: Relative residual: 1.5e-16
USYMLQ: Relative residual: 7.4e-15
USYMLQ: Relative residual: 3.8e-10
USYMLQ: Relative residual: 2.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 7.8e+01 ... 1.5e-01 1.5e-01 1.6e-02 ]
Aresiduals: [ ]
status: solution xᶜ good enough given atol and rtol
USYMLQ: Relative residual: 1.4e-08
USYMLQ: Relative residual: 1.4e-08
USYMLQ: Relative residual: 3.7e-16
USYMLQ: Relative residual: 0.0e+00
USYMLQ: Relative residual: 0.0e+00
USYMQR: Relative residual: 4.8e-16
USYMQR: Relative residual: 7.4e-15
USYMQR: Relative residual: 3.8e-10
USYMQR: Relative residual: 2.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 7.3e+01 ... 1.5e-01 1.4e-01 5.5e-14 ]
Aresiduals: [ 2.5e+02 2.6e+03 5.8e+02 ... 4.3e+01 1.3e+00 1.3e+00 ]
status: solution good enough given atol and rtol
USYMQR: Relative residual: 1.3e-08
USYMQR: Relative residual: 1.4e-08
USYMQR: Relative residual: 3.7e-16
USYMQR: Relative residual: 0.0e+00
USYMQR: Relative residual: 0.0e+00
QMR: Relative residual: 3.6e-16
QMR: Relative residual: 1.0e-14
QMR: Relative residual: 3.8e-10
QMR: Relative residual: 3.6e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.7e+02 1.7e+02 ... 6.7e-01 7.0e-01 1.0e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
QMR: Relative residual: 1.2e-09
DIOM: Relative residual: 1.3e-16
DIOM: Relative residual: 2.0e-16
DIOM: Relative residual: 3.8e-10
DIOM: Relative residual: 2.2e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 1.0e+02 ... 2.2e-01 2.2e-01 4.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.4e-08
DIOM: Relative residual: 1.4e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+01 4.8e+00 1.1e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 4.8e+01 2.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.0e+00 4.0e-17 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 3.7e-16
CGS: Relative residual: 5.6e-09
CGS: Relative residual: 1.1e-11
CGS: Relative residual: 3.4e-10
CGS: Relative residual: 8.4e-15
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 1.5e+04 8.8e+01 ... 1.2e-03 2.8e-02 6.4e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGS: Relative residual: 1.5e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 2.0e+01 1.7e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGS: Relative residual: 8.3e-17
DQGMRES: Relative residual: 1.4e-16
DQGMRES: Relative residual: 1.0e-16
DQGMRES: Relative residual: 3.8e-10
DQGMRES: Relative residual: 2.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 9.1e+01 ... 2.2e-01 2.2e-01 1.4e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 1.3e-08
DQGMRES: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+01 4.6e+00 1.1e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 2.0e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 4.6e+01 2.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 1.5e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.0e+00 4.0e-17 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 3.7e-16
CG: Relative residual: 1.2e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 6.6e+00 1.4e+00 ... 3.7e-04 7.1e-05 3.2e-18 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 2.8e+01 ]
Aresiduals: [ ]
status: on trust-region boundary
CG: Relative residual: 1.4e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 6.4e+01 9.8e+01 8.4e+01 7.7e+01 5.2e+01 ]
Aresiduals: [ ]
status: on trust-region boundary
Simple stats
solved: true
inconsistent: false
residuals: [ 6.2e+01 1.5e+01 3.3e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CG: Relative residual: 8.3e-17
CG_Lanczos: Relative residual: 1.7e-16
CG_Lanczos: Relative residuals with shifts: 1.5e-16 1.3e-08 3.2e-09 1.1e-08 4.3e-09 1.8e-09
CG Lanczos: system of 10 equations in 10 variables with 6 shifts
0 1.1e+02 1.1e+02 1.1e+02 1.1e+02 1.1e+02 1.1e+02
1 5.6e+00 4.9e+00 4.4e+00 3.9e+00 3.5e+00 3.2e+00
2 9.6e-01 7.0e-01 5.4e-01 4.3e-01 3.4e-01 2.8e-01
3 1.9e-01 1.2e-01 7.6e-02 5.2e-02 3.7e-02 2.8e-02
4 3.9e-02 1.9e-02 1.1e-02 6.4e-03 4.1e-03 2.7e-03
5 7.9e-03 3.2e-03 1.5e-03 7.9e-04 4.5e-04 2.7e-04
6 1.6e-03 5.3e-04 2.1e-04 9.6e-05 4.8e-05 2.6e-05
7 3.1e-04 8.4e-05 2.9e-05 1.1e-05 4.9e-06 2.4e-06
8 5.6e-05 1.3e-05 3.6e-06 1.2e-06 4.8e-07 2.1e-07
9 8.3e-06 1.5e-06 3.6e-07 1.2e-06 4.8e-07 2.1e-07
10 8.3e-19 1.5e-06 3.6e-07 1.2e-06 4.8e-07 2.1e-07
CG Lanczos stats
solved: true
residuals: Array{Float64,2}
flagged: Bool[0, 0, 0, 0, 0, 0]
‖A‖F: 0.0e+00
κ₂(A): 0.0e+00
status: solution good enough given atol and rtol
CG Lanczos stats
solved: true
residuals: Array{Float64,1}
flagged: false
‖A‖F: 2.1e+00
κ₂(A): 0.0e+00
status: solution good enough given atol and rtol
CG_Lanczos: Relative residual: 2.9e-16
CG_Lanczos: Relative residuals with shifts: 2.0e-16 2.0e-16 1.9e-16 1.8e-16 1.2e-16 9.2e-17 1.9e-16 1.8e-16 1.6e-16 1.2e-16
MINRES: Relative residual: 1.3e-16
MINRES: Relative residual: 1.5e-14
Simple stats
solved: true
inconsistent: false
residuals: [ 5.4e+01 4.4e+00 1.6e+00 ... 3.8e-01 2.7e-01 8.2e-13 ]
Aresiduals: [ 0.0e+00 1.5e+02 8.7e+00 ... 4.3e-01 1.3e-01 5.2e-02 ]
status: found approximate zero-residual solution
MINRES: Relative residual: 4.6e-06
MINRES: Relative residual: 1.2e-05
Simple stats
solved: true
inconsistent: false
residuals: [ 6.2e+01 1.5e+01 3.4e-15 ]
Aresiduals: [ 0.0e+00 1.1e+02 1.4e+01 ]
status: found approximate zero-residual solution
MINRES: Relative residual: 3.1e-16
MINRES-QLP: Relative residual: 5.5e-16
MINRES-QLP: Relative residual: 7.4e-15
Simple stats
solved: true
inconsistent: false
residuals: [ 5.4e+01 4.4e+00 1.6e+00 ... 3.8e-01 2.7e-01 4.1e-13 ]
Aresiduals: [ 1.5e+02 8.7e+00 2.0e+00 ... 4.3e-01 1.3e-01 5.2e-02 ]
status: solution good enough given atol and rtol
MINRES-QLP: Relative residual: 1.3e-08
MINRES-QLP: Relative residual: 8.8e-09
MINRES-QLP: Relative residual: 9.4e-16
SYMMLQ: Relative residual: 4.8e-06
SYMMLQ: Relative residual: 2.6e-15
SYMMLQ stats
solved: true
residuals: [ 5.4e+01 5.4e+01 7.4e+00 ... 4.0e-01 2.1e-01 2.1e-11 ]
residuals (cg): [ 5.4e+01 4.4e+00 1.7e+00 ... 4.0e-01 1.7e-12 1.4e-14 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 6.3e+00
κ₂(A): 1.5e+01
status: found approximate solution
stats =
SYMMLQ stats
solved: true
residuals: [ 6.4e+01 6.4e+01 2.3e+02 ... 2.0e-03 9.0e-04 3.6e-04 ]
residuals (cg): [ 6.4e+01 9.8e+01 8.4e+01 ... 8.8e-06 4.5e-06 2.2e-06 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 4.1e+01
κ₂(A): 8.0e+00
status: found approximate solution
SYMMLQ: Relative residual: 3.5e-06
SYMMLQ: Relative residual: 1.9e-04
SYMMLQ : true error: 6.5e-04
SYMMLQ-CG : true error: 7.1e-06
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ stats
solved: true
residuals: [ 6.2e+01 6.2e+01 2.4e+01 1.8e-14 ]
residuals (cg): [ 6.2e+01 1.5e+01 6.8e-15 2.0e-15 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 3.0e+00
κ₂(A): 1.8e+00
status: found approximate solution
SYMMLQ: Relative residual: 3.1e-16
BILQ: Relative residual: 1.6e-16
BILQ: Relative residual: 1.0e-14
BILQ: Relative residual: 3.8e-10
BILQ: Relative residual: 3.7e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 1.0e+02 ... 2.4e-01 2.3e-01 5.6e-03 ]
Aresiduals: [ ]
status: solution xᶜ good enough given atol and rtol
BILQ: Relative residual: 1.4e-08
CGLS: Relative residual: 1.1e-13
CGLS: Relative residual: 2.3e-13
CGLS: Relative residual: 1.8e-11
CGLS: Relative residual: 7.7e-12
CGLS: Relative residual: 2.3e-11
CGLS: Relative residual: 2.0e-11
CGLS: Relative residual: 6.0e-13
CGLS: Relative residual: 9.1e-14
CGLS: Preconditioned residual: 2.7e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 3.4e-05 3.3e-05 3.4e-07 ]
Aresiduals: [ 1.5e+02 5.6e+02 5.2e+02 ... 6.1e-06 5.5e-06 3.7e-08 ]
status: solution good enough given atol and rtol
CRLS: Relative residual: 1.6e-13
CRLS: Relative residual: 1.2e-13
CRLS: Relative residual: 8.5e-11
CRLS: Relative residual: 1.9e-10
CRLS: Relative residual: 2.0e-11
CRLS: Relative residual: 8.0e-13
CRLS: Relative residual: 9.8e-13
CRLS: Relative residual: 1.6e-13
CRLS: Preconditioned residual: 2.1e-09
Simple stats
solved: true
inconsistent: false
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 1.2e-02 3.1e-04 4.9e-06 ]
Aresiduals: [ 1.5e+02 1.4e+02 1.4e+02 ... 3.9e-03 6.8e-05 7.3e-07 ]
status: solution good enough given atol and rtol
CGNE: residual: 3.8e-15
‖x - xmin‖ = 1.3e-14
CGNE: residual: 6.1e-01
CGNE: residual: 8.9e-17
‖x - xmin‖ = 4.7e-16
CGNE: residual: 3.3e-01
CGNE: residual: 9.4e-16
‖x - xmin‖ = 2.2e-15
CGNE: residual: 5.7e-01
CGNE: residual: 0.0e+00
‖x - xmin‖ = 3.0e-08
CGNE: residual: 0.0e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 4.2e+01 9.8e-10 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGNE: residual: 1.2e-16
‖x - xmin‖ = 2.5e-15
CGNE: residual: 5.6e-16
‖x - xmin‖ = 9.2e-17
CRMR: residual: 5.1e-16
‖x - xmin‖ = 4.6e-15
CRMR: residual: 5.2e-01
CRMR: residual: 2.4e-16
‖x - xmin‖ = 9.5e-16
CRMR: residual: 3.2e-01
CRMR: residual: 1.2e-15
‖x - xmin‖ = 2.8e-15
CRMR: residual: 4.9e-01
CRMR: residual: 0.0e+00
‖x - xmin‖ = 6.2e-08
CRMR: residual: 0.0e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 3.7e+01 6.6e-10 ]
Aresiduals: [ 1.0e+03 1.2e+00 1.0e-08 ]
status: solution good enough given atol and rtol
CRMR: residual: 2.6e-15
‖x - xmin‖ = 1.5e-16
LSLQ: Relative residual: 1.2e-13
LSLQ: Relative residual: 1.2e-13
LSLQ: Relative residual: 2.3e-10
LSLQ: Relative residual: 2.2e-10
LSLQ: Relative residual: 1.1e-08
LSLQ: Relative residual: 2.8e-09
LSLQ: Relative residual: 1.0e-08
LSLQ: Relative residual: 7.5e-10
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 7.8e+04 7.8e+04 7.8e+04 ]
Aresiduals: [ 1.5e+02 1.5e+02 1.0e+03 ... 1.0e-02 2.3e-01 2.1e-05 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 1.8e+00 1.8e+00 ]
Aresiduals: [ 9.0e+00 9.0e+00 3.7e-16 ]
status: found approximate minimum least-squares solution
LSLQ: Relative residual: 9.7e-17
LSQR: Relative residual: 8.2e-14
LSQR: Relative residual: 8.2e-14
LSQR: Relative residual: 2.0e-06
LSQR: Relative residual: 5.3e-11
LSQR: Relative residual: 5.0e-06
LSQR: Relative residual: 3.0e-10
LSQR: Relative residual: 1.9e-06
LSQR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 3.0e+02 2.3e+00 1.3e-02 ]
Aresiduals: [ 1.5e+02 5.6e+02 5.2e+02 ... 2.2e+02 1.2e+00 4.4e-03 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 9.0e+00 2.4e-16 ]
status: found approximate minimum least-squares solution
LSQR: Relative residual: 9.7e-17
LSMR: Relative residual: 8.2e-14
LSMR: Relative residual: 8.2e-14
LSMR: Relative residual: 2.0e-06
LSMR: Relative residual: 5.3e-11
LSMR: Relative residual: 5.0e-06
LSMR: Relative residual: 3.0e-10
LSMR: Relative residual: 1.6e-06
LSMR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 6.8e+04 1.8e+01 1.3e-02 ]
Aresiduals: [ 1.5e+02 1.4e+02 1.4e+02 ... 7.2e+01 1.2e+00 4.4e-03 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 9.0e+00 2.4e-16 ]
status: found approximate minimum least-squares solution
LSMR: Relative residual: 9.7e-17
CRAIG: residual: 1.7e-15
‖x - xmin‖ = 4.5e-15
CRAIG: residual: 1.0e+31
Simple stats
solved: false
inconsistent: false
residuals: [ 2.0e+01 1.2e+01 2.8e+16 2.0e+32 ]
Aresiduals: [ ]
status: condition number exceeds tolerance
CRAIG: residual: 2.4e-16
‖x - xmin‖ = 8.5e-16
CRAIG: residual: 6.0e+30
CRAIG: residual: 3.4e-15
‖x - xmin‖ = 7.8e-15
CRAIG: residual: 1.4e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 4.2e+01 7.1e-07 ]
Aresiduals: [ ]
status: solution good enough for the tolerances given
Simple stats
solved: true
inconsistent: false
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ ]
status: solution good enough for the tolerances given
CRAIG: Relative residual: 9.7e-17
CRAIGMR: residual: 1.8e-15 least-squares: 1.7e-15
‖x - xmin‖ = 4.4e-15
CRAIGMR: residual: 5.2e-01 least-squares: 3.7e-16
CRAIGMR: residual: 2.4e-16 least-squares: 1.7e-16
‖x - xmin‖ = 1.0e-15
CRAIGMR: residual: 3.2e-01 least-squares: 0.0e+00
CRAIGMR: residual: 3.2e-15 least-squares: 3.1e-15
‖x - xmin‖ = 7.4e-15
CRAIGMR: residual: 4.9e-01 least-squares: 1.1e-16
Simple stats
solved: false
inconsistent: true
residuals: [ 7.4e+01 3.7e+01 ]
Aresiduals: [ 1.4e+01 4.5e-14 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: false
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 5.1e+00 2.4e-16 ]
status: found approximate minimum-norm solution
CRAIGMR: Relative residual: 5.6e-17
CR: Relative residual: 1.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 6.6e+00 1.4e+00 ... 3.6e-04 7.0e-05 1.2e-06 ]
Aresiduals: [ 6.5e+02 2.9e+01 5.2e+00 ... 1.2e-03 1.9e-04 1.0e-17 ]
status: solution good enough given atol and rtol
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 5.6e+01 ]
Aresiduals: [ 6.5e+02 1.6e+02 ]
status: on trust-region boundary
CR: Relative residual: 2.9e-01
CR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 6.4e+01 2.3e+01 1.2e+01 7.9e+00 5.5e+00 4.0e+00 3.3e+00 ]
Aresiduals: [ 4.1e+02 1.3e+02 5.5e+01 2.9e+01 1.9e+01 1.3e+01 6.0e+00 ]
status: on trust-region boundary
Simple stats
solved: false
inconsistent: false
residuals: [ 2.0e+01 5.7e+01 5.5e+01 ... 5.5e+01 5.5e+01 5.5e+01 ]
Aresiduals: [ 3.4e+02 4.6e+01 2.1e-14 ... 8.9e-62 3.2e-62 1.6e-77 ]
status: maximum number of iterations exceeded
CR: Relative residual: 1.2e-16
Tests of multi-precision methods:
cg ✔
cgls ✔
usymqr ✔
cgne ✔
cgs ✔
crmr ✔
cg_lanczos ✔
dqgmres ✔
diom ✔
cr ✔
lslq ✔
lsqr ✔
lsmr ✔
craig ✔
craigmr ✔
crls ✔
symmlq ✔
minres ✔
cg_lanczos_shift_seq ✔
bilq ✔
minres_qlp ✔
qmr ✔
usymlq ✔
Tests of variants:
cg_lanczos ✔
cg_lanczos_shift_seq ✔
cg ✔
cgls ✔
cgne ✔
cr ✔
craig ✔
craigmr ✔
crls ✔
crmr ✔
lslq ✔
lsmr ✔
bilq ✔
lsqr ✔
minres ✔
symmlq ✔
dqgmres ✔
diom ✔
cgs ✔
usymqr ✔
minres_qlp ✔
qmr ✔
usymlq ✔
Testing Krylov tests passed
Results with Julia v1.3.0
Testing was successful .
Last evaluation was ago and took 39 minutes, 59 seconds.
Click here to download the log file.
Click here to show the log contents.
Resolving package versions...
Installed FastClosures ──── v0.3.2
Installed LinearOperators ─ v0.6.0
Installed Krylov ────────── v0.3.1
Updating `~/.julia/environments/v1.3/Project.toml`
[ba0b0d4f] + Krylov v0.3.1
Updating `~/.julia/environments/v1.3/Manifest.toml`
[9aa1b823] + FastClosures v0.3.2
[ba0b0d4f] + Krylov v0.3.1
[5c8ed15e] + LinearOperators v0.6.0
[2a0f44e3] + Base64
[8ba89e20] + Distributed
[b77e0a4c] + InteractiveUtils
[8f399da3] + Libdl
[37e2e46d] + LinearAlgebra
[56ddb016] + Logging
[d6f4376e] + Markdown
[de0858da] + Printf
[9a3f8284] + Random
[9e88b42a] + Serialization
[6462fe0b] + Sockets
[2f01184e] + SparseArrays
[8dfed614] + Test
[4ec0a83e] + Unicode
Testing Krylov
Status `/tmp/jl_yYqpBI/Manifest.toml`
[9aa1b823] FastClosures v0.3.2
[ba0b0d4f] Krylov v0.3.1
[5c8ed15e] LinearOperators v0.6.0
[2a0f44e3] Base64 [`@stdlib/Base64`]
[8ba89e20] Distributed [`@stdlib/Distributed`]
[b77e0a4c] InteractiveUtils [`@stdlib/InteractiveUtils`]
[8f399da3] Libdl [`@stdlib/Libdl`]
[37e2e46d] LinearAlgebra [`@stdlib/LinearAlgebra`]
[56ddb016] Logging [`@stdlib/Logging`]
[d6f4376e] Markdown [`@stdlib/Markdown`]
[de0858da] Printf [`@stdlib/Printf`]
[9a3f8284] Random [`@stdlib/Random`]
[9e88b42a] Serialization [`@stdlib/Serialization`]
[6462fe0b] Sockets [`@stdlib/Sockets`]
[2f01184e] SparseArrays [`@stdlib/SparseArrays`]
[8dfed614] Test [`@stdlib/Test`]
[4ec0a83e] Unicode [`@stdlib/Unicode`]
USYMLQ: Relative residual: 1.5e-16
USYMLQ: Relative residual: 7.4e-15
USYMLQ: Relative residual: 3.8e-10
USYMLQ: Relative residual: 2.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 7.8e+01 ... 1.5e-01 1.5e-01 1.6e-02 ]
Aresiduals: [ ]
status: solution xᶜ good enough given atol and rtol
USYMLQ: Relative residual: 1.4e-08
USYMLQ: Relative residual: 1.2e-08
USYMLQ: Relative residual: 3.7e-16
USYMLQ: Relative residual: 0.0e+00
USYMLQ: Relative residual: 0.0e+00
USYMQR: Relative residual: 4.8e-16
USYMQR: Relative residual: 7.4e-15
USYMQR: Relative residual: 3.8e-10
USYMQR: Relative residual: 2.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 7.3e+01 ... 1.5e-01 1.4e-01 5.5e-14 ]
Aresiduals: [ 2.5e+02 2.6e+03 5.8e+02 ... 4.3e+01 1.3e+00 1.3e+00 ]
status: solution good enough given atol and rtol
USYMQR: Relative residual: 1.3e-08
USYMQR: Relative residual: 1.1e-08
USYMQR: Relative residual: 3.7e-16
USYMQR: Relative residual: 0.0e+00
USYMQR: Relative residual: 0.0e+00
QMR: Relative residual: 3.6e-16
QMR: Relative residual: 1.0e-14
QMR: Relative residual: 3.8e-10
QMR: Relative residual: 3.6e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.7e+02 1.7e+02 ... 6.7e-01 7.0e-01 1.0e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
QMR: Relative residual: 1.2e-09
DIOM: Relative residual: 1.3e-16
DIOM: Relative residual: 2.0e-16
DIOM: Relative residual: 3.8e-10
DIOM: Relative residual: 2.2e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 1.0e+02 ... 2.2e-01 2.2e-01 4.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.4e-08
DIOM: Relative residual: 6.9e-09
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+01 4.8e+00 1.1e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 4.8e+01 2.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.0e+00 4.0e-17 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 3.7e-16
CGS: Relative residual: 5.6e-09
CGS: Relative residual: 1.1e-11
CGS: Relative residual: 3.4e-10
CGS: Relative residual: 8.4e-15
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 1.5e+04 8.8e+01 ... 1.2e-03 2.8e-02 6.4e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGS: Relative residual: 1.5e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 2.0e+01 1.7e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGS: Relative residual: 8.3e-17
DQGMRES: Relative residual: 1.4e-16
DQGMRES: Relative residual: 1.0e-16
DQGMRES: Relative residual: 3.8e-10
DQGMRES: Relative residual: 2.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 9.1e+01 ... 2.2e-01 2.2e-01 1.4e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 1.3e-08
DQGMRES: Relative residual: 1.1e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+01 4.6e+00 1.1e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 2.0e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 4.6e+01 2.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 1.5e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.0e+00 4.0e-17 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 3.7e-16
CG: Relative residual: 1.2e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 6.6e+00 1.4e+00 ... 3.7e-04 7.1e-05 3.2e-18 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 2.8e+01 ]
Aresiduals: [ ]
status: on trust-region boundary
CG: Relative residual: 1.4e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 6.4e+01 9.8e+01 8.4e+01 7.7e+01 5.2e+01 ]
Aresiduals: [ ]
status: on trust-region boundary
Simple stats
solved: true
inconsistent: false
residuals: [ 6.2e+01 1.5e+01 3.3e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CG: Relative residual: 8.3e-17
CG_Lanczos: Relative residual: 1.7e-16
CG_Lanczos: Relative residuals with shifts: 1.5e-16 1.3e-08 3.2e-09 1.1e-08 4.3e-09 1.8e-09
CG Lanczos: system of 10 equations in 10 variables with 6 shifts
0 1.1e+02 1.1e+02 1.1e+02 1.1e+02 1.1e+02 1.1e+02
1 5.6e+00 4.9e+00 4.4e+00 3.9e+00 3.5e+00 3.2e+00
2 9.6e-01 7.0e-01 5.4e-01 4.3e-01 3.4e-01 2.8e-01
3 1.9e-01 1.2e-01 7.6e-02 5.2e-02 3.7e-02 2.8e-02
4 3.9e-02 1.9e-02 1.1e-02 6.4e-03 4.1e-03 2.7e-03
5 7.9e-03 3.2e-03 1.5e-03 7.9e-04 4.5e-04 2.7e-04
6 1.6e-03 5.3e-04 2.1e-04 9.6e-05 4.8e-05 2.6e-05
7 3.1e-04 8.4e-05 2.9e-05 1.1e-05 4.9e-06 2.4e-06
8 5.6e-05 1.3e-05 3.6e-06 1.2e-06 4.8e-07 2.1e-07
9 8.3e-06 1.5e-06 3.6e-07 1.2e-06 4.8e-07 2.1e-07
10 8.3e-19 1.5e-06 3.6e-07 1.2e-06 4.8e-07 2.1e-07
CG Lanczos stats
solved: true
residuals: Array{Float64,2}
flagged: Bool[0, 0, 0, 0, 0, 0]
‖A‖F: 0.0e+00
κ₂(A): 0.0e+00
status: solution good enough given atol and rtol
CG Lanczos stats
solved: true
residuals: Array{Float64,1}
flagged: false
‖A‖F: 2.1e+00
κ₂(A): 0.0e+00
status: solution good enough given atol and rtol
CG_Lanczos: Relative residual: 2.9e-16
CG_Lanczos: Relative residuals with shifts: 2.0e-16 2.0e-16 1.9e-16 1.8e-16 1.2e-16 9.2e-17 1.9e-16 1.8e-16 1.6e-16 1.2e-16
MINRES: Relative residual: 1.3e-16
MINRES: Relative residual: 1.5e-14
Simple stats
solved: true
inconsistent: false
residuals: [ 5.4e+01 4.4e+00 1.6e+00 ... 3.8e-01 2.7e-01 8.2e-13 ]
Aresiduals: [ 0.0e+00 1.5e+02 8.7e+00 ... 4.3e-01 1.3e-01 5.2e-02 ]
status: found approximate zero-residual solution
MINRES: Relative residual: 4.6e-06
MINRES: Relative residual: 1.2e-05
Simple stats
solved: true
inconsistent: false
residuals: [ 6.2e+01 1.5e+01 3.4e-15 ]
Aresiduals: [ 0.0e+00 1.1e+02 1.4e+01 ]
status: found approximate zero-residual solution
MINRES: Relative residual: 3.1e-16
MINRES-QLP: Relative residual: 5.5e-16
MINRES-QLP: Relative residual: 7.4e-15
Simple stats
solved: true
inconsistent: false
residuals: [ 5.4e+01 4.4e+00 1.6e+00 ... 3.8e-01 2.7e-01 4.1e-13 ]
Aresiduals: [ 1.5e+02 8.7e+00 2.0e+00 ... 4.3e-01 1.3e-01 5.2e-02 ]
status: solution good enough given atol and rtol
MINRES-QLP: Relative residual: 1.3e-08
MINRES-QLP: Relative residual: 8.8e-09
MINRES-QLP: Relative residual: 9.4e-16
SYMMLQ: Relative residual: 4.8e-06
SYMMLQ: Relative residual: 2.6e-15
SYMMLQ stats
solved: true
residuals: [ 5.4e+01 5.4e+01 7.4e+00 ... 4.0e-01 2.1e-01 2.1e-11 ]
residuals (cg): [ 5.4e+01 4.4e+00 1.7e+00 ... 4.0e-01 1.7e-12 1.4e-14 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 6.3e+00
κ₂(A): 1.5e+01
status: found approximate solution
stats =
SYMMLQ stats
solved: true
residuals: [ 6.4e+01 6.4e+01 2.3e+02 ... 2.0e-03 9.0e-04 3.6e-04 ]
residuals (cg): [ 6.4e+01 9.8e+01 8.4e+01 ... 8.8e-06 4.5e-06 2.2e-06 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 4.1e+01
κ₂(A): 8.0e+00
status: found approximate solution
SYMMLQ: Relative residual: 3.5e-06
SYMMLQ: Relative residual: 1.9e-04
SYMMLQ : true error: 6.5e-04
SYMMLQ-CG : true error: 7.1e-06
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ stats
solved: true
residuals: [ 6.2e+01 6.2e+01 2.4e+01 1.8e-14 ]
residuals (cg): [ 6.2e+01 1.5e+01 6.8e-15 2.0e-15 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 3.0e+00
κ₂(A): 1.8e+00
status: found approximate solution
SYMMLQ: Relative residual: 3.1e-16
BILQ: Relative residual: 1.6e-16
BILQ: Relative residual: 1.0e-14
BILQ: Relative residual: 3.8e-10
BILQ: Relative residual: 3.7e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 1.0e+02 ... 2.4e-01 2.3e-01 5.6e-03 ]
Aresiduals: [ ]
status: solution xᶜ good enough given atol and rtol
BILQ: Relative residual: 1.4e-08
CGLS: Relative residual: 1.1e-13
CGLS: Relative residual: 2.3e-13
CGLS: Relative residual: 1.8e-11
CGLS: Relative residual: 7.7e-12
CGLS: Relative residual: 2.3e-11
CGLS: Relative residual: 2.0e-11
CGLS: Relative residual: 6.0e-13
CGLS: Relative residual: 9.1e-14
CGLS: Preconditioned residual: 2.7e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 3.4e-05 3.3e-05 3.4e-07 ]
Aresiduals: [ 1.5e+02 5.6e+02 5.2e+02 ... 6.1e-06 5.5e-06 3.7e-08 ]
status: solution good enough given atol and rtol
CRLS: Relative residual: 1.6e-13
CRLS: Relative residual: 1.2e-13
CRLS: Relative residual: 8.5e-11
CRLS: Relative residual: 1.9e-10
CRLS: Relative residual: 2.0e-11
CRLS: Relative residual: 8.0e-13
CRLS: Relative residual: 9.8e-13
CRLS: Relative residual: 1.6e-13
CRLS: Preconditioned residual: 2.1e-09
Simple stats
solved: true
inconsistent: false
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 1.2e-02 3.1e-04 4.9e-06 ]
Aresiduals: [ 1.5e+02 1.4e+02 1.4e+02 ... 3.9e-03 6.8e-05 7.3e-07 ]
status: solution good enough given atol and rtol
CGNE: residual: 3.8e-15
‖x - xmin‖ = 1.3e-14
CGNE: residual: 6.1e-01
CGNE: residual: 8.9e-17
‖x - xmin‖ = 4.7e-16
CGNE: residual: 3.3e-01
CGNE: residual: 9.4e-16
‖x - xmin‖ = 2.2e-15
CGNE: residual: 5.7e-01
CGNE: residual: 0.0e+00
‖x - xmin‖ = 3.0e-08
CGNE: residual: 0.0e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 4.2e+01 9.8e-10 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGNE: residual: 1.2e-16
‖x - xmin‖ = 2.5e-15
CGNE: residual: 5.6e-16
‖x - xmin‖ = 9.2e-17
CRMR: residual: 5.1e-16
‖x - xmin‖ = 4.6e-15
CRMR: residual: 5.2e-01
CRMR: residual: 2.4e-16
‖x - xmin‖ = 9.5e-16
CRMR: residual: 3.2e-01
CRMR: residual: 1.2e-15
‖x - xmin‖ = 2.8e-15
CRMR: residual: 4.9e-01
CRMR: residual: 0.0e+00
‖x - xmin‖ = 6.2e-08
CRMR: residual: 0.0e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 3.7e+01 6.6e-10 ]
Aresiduals: [ 1.0e+03 1.2e+00 1.0e-08 ]
status: solution good enough given atol and rtol
CRMR: residual: 2.6e-15
‖x - xmin‖ = 1.5e-16
LSLQ: Relative residual: 1.2e-13
LSLQ: Relative residual: 1.2e-13
LSLQ: Relative residual: 2.3e-10
LSLQ: Relative residual: 2.2e-10
LSLQ: Relative residual: 1.1e-08
LSLQ: Relative residual: 2.8e-09
LSLQ: Relative residual: 1.0e-08
LSLQ: Relative residual: 7.5e-10
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 7.8e+04 7.8e+04 7.8e+04 ]
Aresiduals: [ 1.5e+02 1.5e+02 1.0e+03 ... 1.0e-02 2.3e-01 2.1e-05 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 1.8e+00 1.8e+00 ]
Aresiduals: [ 9.0e+00 9.0e+00 3.7e-16 ]
status: found approximate minimum least-squares solution
LSLQ: Relative residual: 9.7e-17
LSQR: Relative residual: 8.2e-14
LSQR: Relative residual: 8.2e-14
LSQR: Relative residual: 2.0e-06
LSQR: Relative residual: 5.3e-11
LSQR: Relative residual: 5.0e-06
LSQR: Relative residual: 3.0e-10
LSQR: Relative residual: 1.9e-06
LSQR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 3.0e+02 2.3e+00 1.3e-02 ]
Aresiduals: [ 1.5e+02 5.6e+02 5.2e+02 ... 2.2e+02 1.2e+00 4.4e-03 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 9.0e+00 2.4e-16 ]
status: found approximate minimum least-squares solution
LSQR: Relative residual: 9.7e-17
LSMR: Relative residual: 8.2e-14
LSMR: Relative residual: 8.2e-14
LSMR: Relative residual: 2.0e-06
LSMR: Relative residual: 5.3e-11
LSMR: Relative residual: 5.0e-06
LSMR: Relative residual: 3.0e-10
LSMR: Relative residual: 1.6e-06
LSMR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 6.8e+04 1.8e+01 1.3e-02 ]
Aresiduals: [ 1.5e+02 1.4e+02 1.4e+02 ... 7.2e+01 1.2e+00 4.4e-03 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 9.0e+00 2.4e-16 ]
status: found approximate minimum least-squares solution
LSMR: Relative residual: 9.7e-17
CRAIG: residual: 1.7e-15
‖x - xmin‖ = 4.5e-15
CRAIG: residual: 1.0e+31
Simple stats
solved: false
inconsistent: false
residuals: [ 2.0e+01 1.2e+01 2.8e+16 2.0e+32 ]
Aresiduals: [ ]
status: condition number exceeds tolerance
CRAIG: residual: 2.4e-16
‖x - xmin‖ = 8.5e-16
CRAIG: residual: 6.0e+30
CRAIG: residual: 3.4e-15
‖x - xmin‖ = 7.8e-15
CRAIG: residual: 1.4e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 4.2e+01 7.1e-07 ]
Aresiduals: [ ]
status: solution good enough for the tolerances given
Simple stats
solved: true
inconsistent: false
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ ]
status: solution good enough for the tolerances given
CRAIG: Relative residual: 9.7e-17
CRAIGMR: residual: 1.8e-15 least-squares: 1.7e-15
‖x - xmin‖ = 4.4e-15
CRAIGMR: residual: 5.2e-01 least-squares: 3.7e-16
CRAIGMR: residual: 2.4e-16 least-squares: 1.7e-16
‖x - xmin‖ = 1.0e-15
CRAIGMR: residual: 3.2e-01 least-squares: 0.0e+00
CRAIGMR: residual: 3.2e-15 least-squares: 3.1e-15
‖x - xmin‖ = 7.4e-15
CRAIGMR: residual: 4.9e-01 least-squares: 1.1e-16
Simple stats
solved: false
inconsistent: true
residuals: [ 7.4e+01 3.7e+01 ]
Aresiduals: [ 1.4e+01 4.5e-14 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: false
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 5.1e+00 2.4e-16 ]
status: found approximate minimum-norm solution
CRAIGMR: Relative residual: 5.6e-17
CR: Relative residual: 1.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 6.6e+00 1.4e+00 ... 3.6e-04 7.0e-05 1.2e-06 ]
Aresiduals: [ 6.5e+02 2.9e+01 5.2e+00 ... 1.2e-03 1.9e-04 1.0e-17 ]
status: solution good enough given atol and rtol
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 5.6e+01 ]
Aresiduals: [ 6.5e+02 1.6e+02 ]
status: on trust-region boundary
CR: Relative residual: 2.9e-01
CR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 6.4e+01 2.3e+01 1.2e+01 7.9e+00 5.5e+00 4.0e+00 3.3e+00 ]
Aresiduals: [ 4.1e+02 1.3e+02 5.5e+01 2.9e+01 1.9e+01 1.3e+01 6.0e+00 ]
status: on trust-region boundary
Simple stats
solved: false
inconsistent: false
residuals: [ 2.0e+01 5.7e+01 5.5e+01 ... 5.5e+01 5.5e+01 5.5e+01 ]
Aresiduals: [ 3.4e+02 4.6e+01 2.1e-14 ... 8.9e-62 3.2e-62 1.6e-77 ]
status: maximum number of iterations exceeded
CR: Relative residual: 1.2e-16
Tests of multi-precision methods:
cg ✔
cgls ✔
usymqr ✔
cgne ✔
cgs ✔
crmr ✔
cg_lanczos ✔
dqgmres ✔
diom ✔
cr ✔
lslq ✔
lsqr ✔
lsmr ✔
craig ✔
craigmr ✔
crls ✔
symmlq ✔
minres ✔
cg_lanczos_shift_seq ✔
bilq ✔
minres_qlp ✔
qmr ✔
usymlq ✔
Tests of variants:
cg_lanczos ✔
cg_lanczos_shift_seq ✔
cg ✔
cgls ✔
cgne ✔
cr ✔
craig ✔
craigmr ✔
crls ✔
crmr ✔
lslq ✔
lsmr ✔
bilq ✔
lsqr ✔
minres ✔
symmlq ✔
dqgmres ✔
diom ✔
cgs ✔
usymqr ✔
minres_qlp ✔
qmr ✔
usymlq ✔
Testing Krylov tests passed
Results with Julia v1.3.1-pre-7704df0a5a
Testing was successful .
Last evaluation was ago and took 42 minutes, 33 seconds.
Click here to download the log file.
Click here to show the log contents.
Resolving package versions...
Installed FastClosures ──── v0.3.2
Installed LinearOperators ─ v0.6.0
Installed Krylov ────────── v0.3.1
Updating `~/.julia/environments/v1.3/Project.toml`
[ba0b0d4f] + Krylov v0.3.1
Updating `~/.julia/environments/v1.3/Manifest.toml`
[9aa1b823] + FastClosures v0.3.2
[ba0b0d4f] + Krylov v0.3.1
[5c8ed15e] + LinearOperators v0.6.0
[2a0f44e3] + Base64
[8ba89e20] + Distributed
[b77e0a4c] + InteractiveUtils
[8f399da3] + Libdl
[37e2e46d] + LinearAlgebra
[56ddb016] + Logging
[d6f4376e] + Markdown
[de0858da] + Printf
[9a3f8284] + Random
[9e88b42a] + Serialization
[6462fe0b] + Sockets
[2f01184e] + SparseArrays
[8dfed614] + Test
[4ec0a83e] + Unicode
Testing Krylov
Status `/tmp/jl_Je0615/Manifest.toml`
[9aa1b823] FastClosures v0.3.2
[ba0b0d4f] Krylov v0.3.1
[5c8ed15e] LinearOperators v0.6.0
[2a0f44e3] Base64 [`@stdlib/Base64`]
[8ba89e20] Distributed [`@stdlib/Distributed`]
[b77e0a4c] InteractiveUtils [`@stdlib/InteractiveUtils`]
[8f399da3] Libdl [`@stdlib/Libdl`]
[37e2e46d] LinearAlgebra [`@stdlib/LinearAlgebra`]
[56ddb016] Logging [`@stdlib/Logging`]
[d6f4376e] Markdown [`@stdlib/Markdown`]
[de0858da] Printf [`@stdlib/Printf`]
[9a3f8284] Random [`@stdlib/Random`]
[9e88b42a] Serialization [`@stdlib/Serialization`]
[6462fe0b] Sockets [`@stdlib/Sockets`]
[2f01184e] SparseArrays [`@stdlib/SparseArrays`]
[8dfed614] Test [`@stdlib/Test`]
[4ec0a83e] Unicode [`@stdlib/Unicode`]
USYMLQ: Relative residual: 1.5e-16
USYMLQ: Relative residual: 7.4e-15
USYMLQ: Relative residual: 3.8e-10
USYMLQ: Relative residual: 2.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 7.8e+01 ... 1.5e-01 1.5e-01 1.6e-02 ]
Aresiduals: [ ]
status: solution xᶜ good enough given atol and rtol
USYMLQ: Relative residual: 1.4e-08
USYMLQ: Relative residual: 9.7e-09
USYMLQ: Relative residual: 3.7e-16
USYMLQ: Relative residual: 0.0e+00
USYMLQ: Relative residual: 0.0e+00
USYMQR: Relative residual: 4.8e-16
USYMQR: Relative residual: 7.4e-15
USYMQR: Relative residual: 3.8e-10
USYMQR: Relative residual: 2.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 7.3e+01 ... 1.5e-01 1.4e-01 5.5e-14 ]
Aresiduals: [ 2.5e+02 2.6e+03 5.8e+02 ... 4.3e+01 1.3e+00 1.3e+00 ]
status: solution good enough given atol and rtol
USYMQR: Relative residual: 1.3e-08
USYMQR: Relative residual: 1.3e-08
USYMQR: Relative residual: 3.7e-16
USYMQR: Relative residual: 0.0e+00
USYMQR: Relative residual: 0.0e+00
QMR: Relative residual: 3.6e-16
QMR: Relative residual: 1.0e-14
QMR: Relative residual: 3.8e-10
QMR: Relative residual: 3.6e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.7e+02 1.7e+02 ... 6.7e-01 7.0e-01 1.0e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
QMR: Relative residual: 1.2e-09
DIOM: Relative residual: 1.3e-16
DIOM: Relative residual: 2.0e-16
DIOM: Relative residual: 3.8e-10
DIOM: Relative residual: 2.2e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 1.0e+02 ... 2.2e-01 2.2e-01 4.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.4e-08
DIOM: Relative residual: 1.2e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+01 4.8e+00 1.1e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 4.8e+01 2.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 1.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.0e+00 4.0e-17 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DIOM: Relative residual: 3.7e-16
CGS: Relative residual: 5.6e-09
CGS: Relative residual: 1.1e-11
CGS: Relative residual: 3.4e-10
CGS: Relative residual: 8.4e-15
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 1.5e+04 8.8e+01 ... 1.2e-03 2.8e-02 6.4e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGS: Relative residual: 1.5e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 2.0e+01 1.7e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGS: Relative residual: 8.3e-17
DQGMRES: Relative residual: 1.4e-16
DQGMRES: Relative residual: 1.0e-16
DQGMRES: Relative residual: 3.8e-10
DQGMRES: Relative residual: 2.4e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 9.1e+01 ... 2.2e-01 2.2e-01 1.4e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 1.3e-08
DQGMRES: Relative residual: 1.0e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+01 4.6e+00 1.1e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 2.0e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.0e+02 4.6e+01 2.3e-14 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 1.5e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.0e+00 4.0e-17 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
DQGMRES: Relative residual: 3.7e-16
CG: Relative residual: 1.2e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 6.6e+00 1.4e+00 ... 3.7e-04 7.1e-05 3.2e-18 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 2.8e+01 ]
Aresiduals: [ ]
status: on trust-region boundary
CG: Relative residual: 1.4e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 6.4e+01 9.8e+01 8.4e+01 7.7e+01 5.2e+01 ]
Aresiduals: [ ]
status: on trust-region boundary
Simple stats
solved: true
inconsistent: false
residuals: [ 6.2e+01 1.5e+01 3.3e-15 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CG: Relative residual: 8.3e-17
CG_Lanczos: Relative residual: 1.7e-16
CG_Lanczos: Relative residuals with shifts: 1.5e-16 1.3e-08 3.2e-09 1.1e-08 4.3e-09 1.8e-09
CG Lanczos: system of 10 equations in 10 variables with 6 shifts
0 1.1e+02 1.1e+02 1.1e+02 1.1e+02 1.1e+02 1.1e+02
1 5.6e+00 4.9e+00 4.4e+00 3.9e+00 3.5e+00 3.2e+00
2 9.6e-01 7.0e-01 5.4e-01 4.3e-01 3.4e-01 2.8e-01
3 1.9e-01 1.2e-01 7.6e-02 5.2e-02 3.7e-02 2.8e-02
4 3.9e-02 1.9e-02 1.1e-02 6.4e-03 4.1e-03 2.7e-03
5 7.9e-03 3.2e-03 1.5e-03 7.9e-04 4.5e-04 2.7e-04
6 1.6e-03 5.3e-04 2.1e-04 9.6e-05 4.8e-05 2.6e-05
7 3.1e-04 8.4e-05 2.9e-05 1.1e-05 4.9e-06 2.4e-06
8 5.6e-05 1.3e-05 3.6e-06 1.2e-06 4.8e-07 2.1e-07
9 8.3e-06 1.5e-06 3.6e-07 1.2e-06 4.8e-07 2.1e-07
10 8.3e-19 1.5e-06 3.6e-07 1.2e-06 4.8e-07 2.1e-07
CG Lanczos stats
solved: true
residuals: Array{Float64,2}
flagged: Bool[0, 0, 0, 0, 0, 0]
‖A‖F: 0.0e+00
κ₂(A): 0.0e+00
status: solution good enough given atol and rtol
CG Lanczos stats
solved: true
residuals: Array{Float64,1}
flagged: false
‖A‖F: 2.1e+00
κ₂(A): 0.0e+00
status: solution good enough given atol and rtol
CG_Lanczos: Relative residual: 2.9e-16
CG_Lanczos: Relative residuals with shifts: 2.0e-16 2.0e-16 1.9e-16 1.8e-16 1.2e-16 9.2e-17 1.9e-16 1.8e-16 1.6e-16 1.2e-16
MINRES: Relative residual: 1.3e-16
MINRES: Relative residual: 1.5e-14
Simple stats
solved: true
inconsistent: false
residuals: [ 5.4e+01 4.4e+00 1.6e+00 ... 3.8e-01 2.7e-01 8.2e-13 ]
Aresiduals: [ 0.0e+00 1.5e+02 8.7e+00 ... 4.3e-01 1.3e-01 5.2e-02 ]
status: found approximate zero-residual solution
MINRES: Relative residual: 4.6e-06
MINRES: Relative residual: 1.2e-05
Simple stats
solved: true
inconsistent: false
residuals: [ 6.2e+01 1.5e+01 3.4e-15 ]
Aresiduals: [ 0.0e+00 1.1e+02 1.4e+01 ]
status: found approximate zero-residual solution
MINRES: Relative residual: 3.1e-16
MINRES-QLP: Relative residual: 5.5e-16
MINRES-QLP: Relative residual: 7.4e-15
Simple stats
solved: true
inconsistent: false
residuals: [ 5.4e+01 4.4e+00 1.6e+00 ... 3.8e-01 2.7e-01 4.1e-13 ]
Aresiduals: [ 1.5e+02 8.7e+00 2.0e+00 ... 4.3e-01 1.3e-01 5.2e-02 ]
status: solution good enough given atol and rtol
MINRES-QLP: Relative residual: 1.3e-08
MINRES-QLP: Relative residual: 8.8e-09
MINRES-QLP: Relative residual: 9.4e-16
SYMMLQ: Relative residual: 4.8e-06
SYMMLQ: Relative residual: 2.6e-15
SYMMLQ stats
solved: true
residuals: [ 5.4e+01 5.4e+01 7.4e+00 ... 4.0e-01 2.1e-01 2.1e-11 ]
residuals (cg): [ 5.4e+01 4.4e+00 1.7e+00 ... 4.0e-01 1.7e-12 1.4e-14 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 6.3e+00
κ₂(A): 1.5e+01
status: found approximate solution
stats =
SYMMLQ stats
solved: true
residuals: [ 6.4e+01 6.4e+01 2.3e+02 ... 2.0e-03 9.0e-04 3.6e-04 ]
residuals (cg): [ 6.4e+01 9.8e+01 8.4e+01 ... 8.8e-06 4.5e-06 2.2e-06 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 4.1e+01
κ₂(A): 8.0e+00
status: found approximate solution
SYMMLQ: Relative residual: 3.5e-06
SYMMLQ: Relative residual: 1.9e-04
SYMMLQ : true error: 6.5e-04
SYMMLQ-CG : true error: 7.1e-06
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ : err up-bnd : 6.9e-04
SYMMLQ-CG : err up-bnd : 2.6e-04
SYMMLQ stats
solved: true
residuals: [ 6.2e+01 6.2e+01 2.4e+01 1.8e-14 ]
residuals (cg): [ 6.2e+01 1.5e+01 6.8e-15 2.0e-15 ]
errors: [ ]
errors(cg): [ ]
‖A‖F: 3.0e+00
κ₂(A): 1.8e+00
status: found approximate solution
SYMMLQ: Relative residual: 3.1e-16
BILQ: Relative residual: 1.6e-16
BILQ: Relative residual: 1.0e-14
BILQ: Relative residual: 3.8e-10
BILQ: Relative residual: 3.7e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 2.1e+02 2.1e+02 1.0e+02 ... 2.4e-01 2.3e-01 5.6e-03 ]
Aresiduals: [ ]
status: solution xᶜ good enough given atol and rtol
BILQ: Relative residual: 1.4e-08
CGLS: Relative residual: 1.1e-13
CGLS: Relative residual: 2.3e-13
CGLS: Relative residual: 1.8e-11
CGLS: Relative residual: 7.7e-12
CGLS: Relative residual: 2.3e-11
CGLS: Relative residual: 2.0e-11
CGLS: Relative residual: 6.0e-13
CGLS: Relative residual: 9.1e-14
CGLS: Preconditioned residual: 2.7e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 3.4e-05 3.3e-05 3.4e-07 ]
Aresiduals: [ 1.5e+02 5.6e+02 5.2e+02 ... 6.1e-06 5.5e-06 3.7e-08 ]
status: solution good enough given atol and rtol
CRLS: Relative residual: 1.6e-13
CRLS: Relative residual: 1.2e-13
CRLS: Relative residual: 8.5e-11
CRLS: Relative residual: 1.9e-10
CRLS: Relative residual: 2.0e-11
CRLS: Relative residual: 8.0e-13
CRLS: Relative residual: 9.8e-13
CRLS: Relative residual: 1.6e-13
CRLS: Preconditioned residual: 2.1e-09
Simple stats
solved: true
inconsistent: false
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 1.2e-02 3.1e-04 4.9e-06 ]
Aresiduals: [ 1.5e+02 1.4e+02 1.4e+02 ... 3.9e-03 6.8e-05 7.3e-07 ]
status: solution good enough given atol and rtol
CGNE: residual: 3.8e-15
‖x - xmin‖ = 1.3e-14
CGNE: residual: 6.1e-01
CGNE: residual: 8.9e-17
‖x - xmin‖ = 4.7e-16
CGNE: residual: 3.3e-01
CGNE: residual: 9.4e-16
‖x - xmin‖ = 2.2e-15
CGNE: residual: 5.7e-01
CGNE: residual: 0.0e+00
‖x - xmin‖ = 3.0e-08
CGNE: residual: 0.0e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 4.2e+01 9.8e-10 ]
Aresiduals: [ ]
status: solution good enough given atol and rtol
CGNE: residual: 1.2e-16
‖x - xmin‖ = 2.5e-15
CGNE: residual: 5.6e-16
‖x - xmin‖ = 9.2e-17
CRMR: residual: 5.1e-16
‖x - xmin‖ = 4.6e-15
CRMR: residual: 5.2e-01
CRMR: residual: 2.4e-16
‖x - xmin‖ = 9.5e-16
CRMR: residual: 3.2e-01
CRMR: residual: 1.2e-15
‖x - xmin‖ = 2.8e-15
CRMR: residual: 4.9e-01
CRMR: residual: 0.0e+00
‖x - xmin‖ = 6.2e-08
CRMR: residual: 0.0e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 3.7e+01 6.6e-10 ]
Aresiduals: [ 1.0e+03 1.2e+00 1.0e-08 ]
status: solution good enough given atol and rtol
CRMR: residual: 2.6e-15
‖x - xmin‖ = 1.5e-16
LSLQ: Relative residual: 1.2e-13
LSLQ: Relative residual: 1.2e-13
LSLQ: Relative residual: 2.3e-10
LSLQ: Relative residual: 2.2e-10
LSLQ: Relative residual: 1.1e-08
LSLQ: Relative residual: 2.8e-09
LSLQ: Relative residual: 1.0e-08
LSLQ: Relative residual: 7.5e-10
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 7.8e+04 7.8e+04 7.8e+04 ]
Aresiduals: [ 1.5e+02 1.5e+02 1.0e+03 ... 1.0e-02 2.3e-01 2.1e-05 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 1.8e+00 1.8e+00 ]
Aresiduals: [ 9.0e+00 9.0e+00 3.7e-16 ]
status: found approximate minimum least-squares solution
LSLQ: Relative residual: 9.7e-17
LSQR: Relative residual: 8.2e-14
LSQR: Relative residual: 8.2e-14
LSQR: Relative residual: 2.0e-06
LSQR: Relative residual: 5.3e-11
LSQR: Relative residual: 5.0e-06
LSQR: Relative residual: 3.0e-10
LSQR: Relative residual: 1.9e-06
LSQR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 3.0e+02 2.3e+00 1.3e-02 ]
Aresiduals: [ 1.5e+02 5.6e+02 5.2e+02 ... 2.2e+02 1.2e+00 4.4e-03 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 9.0e+00 2.4e-16 ]
status: found approximate minimum least-squares solution
LSQR: Relative residual: 9.7e-17
LSMR: Relative residual: 8.2e-14
LSMR: Relative residual: 8.2e-14
LSMR: Relative residual: 2.0e-06
LSMR: Relative residual: 5.3e-11
LSMR: Relative residual: 5.0e-06
LSMR: Relative residual: 3.0e-10
LSMR: Relative residual: 1.6e-06
LSMR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: true
residuals: [ 7.8e+04 7.8e+04 7.8e+04 ... 6.8e+04 1.8e+01 1.3e-02 ]
Aresiduals: [ 1.5e+02 1.4e+02 1.4e+02 ... 7.2e+01 1.2e+00 4.4e-03 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: true
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 9.0e+00 2.4e-16 ]
status: found approximate minimum least-squares solution
LSMR: Relative residual: 9.7e-17
CRAIG: residual: 1.7e-15
‖x - xmin‖ = 4.5e-15
CRAIG: residual: 1.0e+31
Simple stats
solved: false
inconsistent: false
residuals: [ 2.0e+01 1.2e+01 2.8e+16 2.0e+32 ]
Aresiduals: [ ]
status: condition number exceeds tolerance
CRAIG: residual: 2.4e-16
‖x - xmin‖ = 8.5e-16
CRAIG: residual: 6.0e+30
CRAIG: residual: 3.4e-15
‖x - xmin‖ = 7.8e-15
CRAIG: residual: 1.4e+00
Simple stats
solved: true
inconsistent: false
residuals: [ 7.4e+01 4.2e+01 7.1e-07 ]
Aresiduals: [ ]
status: solution good enough for the tolerances given
Simple stats
solved: true
inconsistent: false
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ ]
status: solution good enough for the tolerances given
CRAIG: Relative residual: 9.7e-17
CRAIGMR: residual: 1.8e-15 least-squares: 1.7e-15
‖x - xmin‖ = 4.4e-15
CRAIGMR: residual: 5.2e-01 least-squares: 3.7e-16
CRAIGMR: residual: 2.4e-16 least-squares: 1.7e-16
‖x - xmin‖ = 1.0e-15
CRAIGMR: residual: 3.2e-01 least-squares: 0.0e+00
CRAIGMR: residual: 3.2e-15 least-squares: 3.1e-15
‖x - xmin‖ = 7.4e-15
CRAIGMR: residual: 4.9e-01 least-squares: 1.1e-16
Simple stats
solved: false
inconsistent: true
residuals: [ 7.4e+01 3.7e+01 ]
Aresiduals: [ 1.4e+01 4.5e-14 ]
status: found approximate minimum least-squares solution
Simple stats
solved: true
inconsistent: false
residuals: [ 1.8e+00 8.8e-17 ]
Aresiduals: [ 5.1e+00 2.4e-16 ]
status: found approximate minimum-norm solution
CRAIGMR: Relative residual: 5.6e-17
CR: Relative residual: 1.3e-16
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 6.6e+00 1.4e+00 ... 3.6e-04 7.0e-05 1.2e-06 ]
Aresiduals: [ 6.5e+02 2.9e+01 5.2e+00 ... 1.2e-03 1.9e-04 1.0e-17 ]
status: solution good enough given atol and rtol
Simple stats
solved: true
inconsistent: false
residuals: [ 1.1e+02 5.6e+01 ]
Aresiduals: [ 6.5e+02 1.6e+02 ]
status: on trust-region boundary
CR: Relative residual: 2.9e-01
CR: Relative residual: 1.3e-08
Simple stats
solved: true
inconsistent: false
residuals: [ 6.4e+01 2.3e+01 1.2e+01 7.9e+00 5.5e+00 4.0e+00 3.3e+00 ]
Aresiduals: [ 4.1e+02 1.3e+02 5.5e+01 2.9e+01 1.9e+01 1.3e+01 6.0e+00 ]
status: on trust-region boundary
Simple stats
solved: false
inconsistent: false
residuals: [ 2.0e+01 5.7e+01 5.5e+01 ... 5.5e+01 5.5e+01 5.5e+01 ]
Aresiduals: [ 3.4e+02 4.6e+01 2.1e-14 ... 8.9e-62 3.2e-62 1.6e-77 ]
status: maximum number of iterations exceeded
CR: Relative residual: 1.2e-16
Tests of multi-precision methods:
cg ✔
cgls ✔
usymqr ✔
cgne ✔
cgs ✔
crmr ✔
cg_lanczos ✔
dqgmres ✔
diom ✔
cr ✔
lslq ✔
lsqr ✔
lsmr ✔
craig ✔
craigmr ✔
crls ✔
symmlq ✔
minres ✔
cg_lanczos_shift_seq ✔
bilq ✔
minres_qlp ✔
qmr ✔
usymlq ✔
Tests of variants:
cg_lanczos ✔
cg_lanczos_shift_seq ✔
cg ✔
cgls ✔
cgne ✔
cr ✔
craig ✔
craigmr ✔
crls ✔
crmr ✔
lslq ✔
lsmr ✔
bilq ✔
lsqr ✔
minres ✔
symmlq ✔
dqgmres ✔
diom ✔
cgs ✔
usymqr ✔
minres_qlp ✔
qmr ✔
usymlq ✔
Testing Krylov tests passed