Try to fix #497

Pardiso defaults for highly indefinite matrices.

This commit essentially reverts #89 and introduces a new
kwarg "cache_analysis" (default `false`) to PardisoJL() which, if true would
lead to the behaviour of #89.

Also, allow the user to overwrite all iparms modified by
the extension besides of 12.

Author: j-fu

ext/LinearSolvePardisoExt.jl

@@ -22,7 +22,7 @@ function LinearSolve.init_cacheval(alg::PardisoJL,
         reltol,
         verbose::Bool,
         assumptions::LinearSolve.OperatorAssumptions)
-    @unpack nprocs, solver_type, matrix_type, iparm, dparm = alg
+    @unpack nprocs, solver_type, matrix_type, cache_analysis, iparm, dparm = alg
     A = convert(AbstractMatrix, A)
 
     solver = if Pardiso.PARDISO_LOADED[]
@@ -52,22 +52,6 @@ function LinearSolve.init_cacheval(alg::PardisoJL,
     end
     verbose && Pardiso.set_msglvl!(solver, Pardiso.MESSAGE_LEVEL_ON)
 
-    # pass in vector of tuples like [(iparm::Int, key::Int) ...]
-    if iparm !== nothing
-        for i in iparm
-            Pardiso.set_iparm!(solver, i...)
-        end
-    end
-
-    if dparm !== nothing
-        for d in dparm
-            Pardiso.set_dparm!(solver, d...)
-        end
-    end
-
-    # Make sure to say it's transposed because its CSC not CSR
-    Pardiso.set_iparm!(solver, 12, 1)
-
     #=
     Note: It is recommended to use IPARM(11)=1 (scaling) and IPARM(13)=1 (matchings) for
     highly indefinite symmetric matrices e.g. from interior point optimizations or saddle point problems.
@@ -79,10 +63,10 @@ function LinearSolve.init_cacheval(alg::PardisoJL,
     be changed to Pardiso.ANALYSIS_NUM_FACT in the solver loop otherwise instabilities
     occur in the example https://github.com/SciML/OrdinaryDiffEq.jl/issues/1569
     =#
-    Pardiso.set_iparm!(solver, 11, 0)
-    Pardiso.set_iparm!(solver, 13, 0)
-
-    Pardiso.set_phase!(solver, Pardiso.ANALYSIS)
+    if cache_analysis
+        Pardiso.set_iparm!(solver, 11, 0)
+        Pardiso.set_iparm!(solver, 13, 0)
+    end
 
     if alg.solver_type == 1
         # PARDISO uses a numerical factorization A = LU for the first system and
@@ -92,10 +76,30 @@ function LinearSolve.init_cacheval(alg::PardisoJL,
         Pardiso.set_iparm!(solver, 3, round(Int, abs(log10(reltol)), RoundDown) * 10 + 1)
     end
 
-    Pardiso.pardiso(solver,
-        u,
-        SparseMatrixCSC(size(A)..., getcolptr(A), rowvals(A), nonzeros(A)),
-        b)
+    # pass in vector of tuples like [(iparm::Int, key::Int) ...]
+    if iparm !== nothing
+        for i in iparm
+            Pardiso.set_iparm!(solver, i...)
+        end
+    end
+
+    if dparm !== nothing
+        for d in dparm
+            Pardiso.set_dparm!(solver, d...)
+        end
+    end
+
+    # Make sure to say it's transposed because its CSC not CSR
+    # This is also the only value which should not be overwritten by users
+    Pardiso.set_iparm!(solver, 12, 1)
+
+    if cache_analysis
+        Pardiso.set_phase!(solver, Pardiso.ANALYSIS)
+        Pardiso.pardiso(solver,
+            u,
+            SparseMatrixCSC(size(A)..., getcolptr(A), rowvals(A), nonzeros(A)),
+            b)
+    end
 
     return solver
 end
@@ -105,7 +109,8 @@ function SciMLBase.solve!(cache::LinearSolve.LinearCache, alg::PardisoJL; kwargs
     A = convert(AbstractMatrix, A)
 
     if cache.isfresh
-        Pardiso.set_phase!(cache.cacheval, Pardiso.NUM_FACT)
+        phase = alg.cache_analysis ? Pardiso.NUM_FACT : Pardiso.ANALYSIS_NUM_FACT
+        Pardiso.set_phase!(cache.cacheval, phase)
         Pardiso.pardiso(cache.cacheval, A, eltype(A)[])
         cache.isfresh = false
     end

src/extension_algs.jl

@@ -154,12 +154,14 @@ struct PardisoJL{T1, T2} <: LinearSolve.SciMLLinearSolveAlgorithm
     nprocs::Union{Int, Nothing}
     solver_type::T1
     matrix_type::T2
+    cache_analysis::Bool
     iparm::Union{Vector{Tuple{Int, Int}}, Nothing}
     dparm::Union{Vector{Tuple{Int, Int}}, Nothing}
 
     function PardisoJL(; nprocs::Union{Int, Nothing} = nothing,
             solver_type = nothing,
             matrix_type = nothing,
+            cache_analysis = false,
             iparm::Union{Vector{Tuple{Int, Int}}, Nothing} = nothing,
             dparm::Union{Vector{Tuple{Int, Int}}, Nothing} = nothing)
         ext = Base.get_extension(@__MODULE__, :LinearSolvePardisoExt)
@@ -170,7 +172,8 @@ struct PardisoJL{T1, T2} <: LinearSolve.SciMLLinearSolveAlgorithm
             T2 = typeof(matrix_type)
             @assert T1 <: Union{Int, Nothing, ext.Pardiso.Solver}
             @assert T2 <: Union{Int, Nothing, ext.Pardiso.MatrixType}
-            return new{T1, T2}(nprocs, solver_type, matrix_type, iparm, dparm)
+            return new{T1, T2}(
+                nprocs, solver_type, matrix_type, cache_analysis, iparm, dparm)
         end
     end
 end

test/pardiso/pardiso.jl

@@ -1,4 +1,4 @@
-using LinearSolve, SparseArrays, Random
+using LinearSolve, SparseArrays, Random, LinearAlgebra
 import Pardiso
 
 A1 = sparse([1.0 0 -2 3
@@ -13,12 +13,22 @@ n = 4
 e = ones(n)
 e2 = ones(n - 1)
 A2 = spdiagm(-1 => im * e2, 0 => lambda * e, 1 => -im * e2)
+
 b2 = rand(n) + im * zeros(n)
 cache_kwargs = (; verbose = true, abstol = 1e-8, reltol = 1e-8, maxiter = 30)
 
 prob2 = LinearProblem(A2, b2)
 
-for alg in (PardisoJL(), MKLPardisoFactorize(), MKLPardisoIterate())
+for alg in (PardisoJL(), MKLPardisoFactorize())
+    u = solve(prob1, alg; cache_kwargs...).u
+    @test A1 * u ≈ b1
+
+    u = solve(prob2, alg; cache_kwargs...).u
+    @test eltype(u) <: Complex
+    @test A2 * u ≈ b2
+end
+
+for alg in (MKLPardisoIterate(),)
     u = solve(prob1, alg; cache_kwargs...).u
     @test A1 * u ≈ b1
 
@@ -27,6 +37,8 @@ for alg in (PardisoJL(), MKLPardisoFactorize(), MKLPardisoIterate())
     @test_broken A2 * u ≈ b2
 end
 
+
+
 Random.seed!(10)
 A = sprand(n, n, 0.8);
 A2 = 2.0 .* A;
@@ -53,6 +65,25 @@ sol33 = solve(linsolve)
 @test sol12.u ≈ sol32.u
 @test sol13.u ≈ sol33.u
 
+
+# Test for problem from #497
+function makeA()
+    n = 60
+    colptr = [1, 4, 7, 11, 15, 17, 22, 26, 30, 34, 38, 40, 46, 50, 54, 58, 62, 64, 70, 74, 78, 82, 86, 88, 94, 98, 102, 106, 110, 112, 118, 122, 126, 130, 134, 136, 142, 146, 150, 154, 158, 160, 166, 170, 174, 178, 182, 184, 190, 194, 198, 202, 206, 208, 214, 218, 222, 224, 226, 228, 232]
+    rowval = [1, 3, 4, 1, 2, 4, 2, 4, 9, 10, 3, 5, 11, 12, 1, 3, 2, 4, 6, 11, 12, 2, 7, 9, 10, 2, 7, 8, 10, 8, 10, 15, 16, 9, 11, 17, 18, 7, 9, 2, 8, 10, 12, 17, 18, 8, 13, 15, 16, 8, 13, 14, 16, 14, 16, 21, 22, 15, 17, 23, 24, 13, 15, 8, 14, 16, 18, 23, 24, 14, 19, 21, 22, 14, 19, 20, 22, 20, 22, 27, 28, 21, 23, 29, 30, 19, 21, 14, 20, 22, 24, 29, 30, 20, 25, 27, 28, 20, 25, 26, 28, 26, 28, 33, 34, 27, 29, 35, 36, 25, 27, 20, 26, 28, 30, 35, 36, 26, 31, 33, 34, 26, 31, 32, 34, 32, 34, 39, 40, 33, 35, 41, 42, 31, 33, 26, 32, 34, 36, 41, 42, 32, 37, 39, 40, 32, 37, 38, 40, 38, 40, 45, 46, 39, 41, 47, 48, 37, 39, 32, 38, 40, 42, 47, 48, 38, 43, 45, 46, 38, 43, 44, 46, 44, 46, 51, 52, 45, 47, 53, 54, 43, 45, 38, 44, 46, 48, 53, 54, 44, 49, 51, 52, 44, 49, 50, 52, 50, 52, 57, 58, 51, 53, 59, 60, 49, 51, 44, 50, 52, 54, 59, 60, 50, 55, 57, 58, 50, 55, 56, 58, 56, 58, 57, 59, 55, 57, 50, 56, 58, 60]
+    nzval = [-0.64, 1.0, -1.0, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -0.03510101010101016, -0.975, -1.0806825309567203, 1.0, -0.95, -0.025, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0, -0.025, -0.95, -0.3564, -0.64, 1.0, -1.0, 13.792569659442691, 0.8606811145510832, -13.792569659442691, 1.0, 0.03475000000000006, 1.0, -1.0806825309567203, 1.0, 2.370597639417811, -2.3705976394178108, 10.698449178570607, -11.083604432603583, -0.2770901108150896, 1.0]
+    A = SparseMatrixCSC(n, n, colptr, rowval, nzval)
+    return(A)
+end
+
+A=makeA()
+u0=fill(0.1,size(A,2))
+linprob = LinearProblem(A, A*u0)
+u = LinearSolve.solve(linprob, PardisoJL(),verbose=true)
+@test norm(u-u0) < 1.0e-14
+
+
+
 # Testing and demonstrating Pardiso.set_iparm! for MKLPardisoSolver
 solver = Pardiso.MKLPardisoSolver()
 iparm = [