add messages for fallbacks

Author: jClugstor

src/default.jl

@@ -517,7 +517,8 @@ end
             newex = quote
                 sol = SciMLBase.solve!(cache, $(algchoice_to_alg(alg)), args...; kwargs...)
                 if sol.retcode === ReturnCode.Failure && alg.safetyfallback
-                    ## TODO: Add verbosity logging here about using the fallback
+                    @SciMLMessage("LU factorization failed, falling back to QR factorization. `A` is potentially rank-deficient.", 
+                        cache.verbose, :default_lu_fallback, :error_control)
                     sol = SciMLBase.solve!(
                         cache, QRFactorization(ColumnNorm()), args...; kwargs...)
                     SciMLBase.build_linear_solution(alg, sol.u, sol.resid, sol.cache;
@@ -537,7 +538,8 @@ end
 
                 sol = SciMLBase.solve!(cache, $(algchoice_to_alg(alg)), args...; kwargs...)
                 if sol.retcode === ReturnCode.Failure && alg.safetyfallback
-                    ## TODO: Add verbosity logging here about using the fallback
+                    @SciMLMessage("LU factorization failed, falling back to QR factorization. `A` is potentially rank-deficient.",
+                        cache.verbose, :default_lu_fallback, :error_control)
                     sol = SciMLBase.solve!(
                         cache, QRFactorization(ColumnNorm()), args...; kwargs...)
                     SciMLBase.build_linear_solution(alg, sol.u, sol.resid, sol.cache;
@@ -557,7 +559,8 @@ end
 
                 sol = SciMLBase.solve!(cache, $(algchoice_to_alg(alg)), args...; kwargs...)
                 if sol.retcode === ReturnCode.Failure && alg.safetyfallback
-                    ## TODO: Add verbosity logging here about using the fallback
+                    @SciMLMessage("LU factorization failed, falling back to QR factorization. `A` is potentially rank-deficient.",
+                        cache.verbose, :default_lu_fallback, :error_control)
                     sol = SciMLBase.solve!(
                         cache, QRFactorization(ColumnNorm()), args...; kwargs...)
                     SciMLBase.build_linear_solution(alg, sol.u, sol.resid, sol.cache;
@@ -577,7 +580,8 @@ end
 
                 sol = SciMLBase.solve!(cache, $(algchoice_to_alg(alg)), args...; kwargs...)
                 if sol.retcode === ReturnCode.Failure && alg.safetyfallback
-                    ## TODO: Add verbosity logging here about using the fallback
+                    @SciMLMessage("LU factorization failed, falling back to QR factorization. `A` is potentially rank-deficient.",
+                        cache.verbose, :default_lu_fallback, :error_control)
                     sol = SciMLBase.solve!(
                         cache, QRFactorization(ColumnNorm()), args...; kwargs...)
                     SciMLBase.build_linear_solution(alg, sol.u, sol.resid, sol.cache;
@@ -597,7 +601,8 @@ end
 
                 sol = SciMLBase.solve!(cache, $(algchoice_to_alg(alg)), args...; kwargs...)
                 if sol.retcode === ReturnCode.Failure && alg.safetyfallback
-                    ## TODO: Add verbosity logging here about using the fallback
+                    @SciMLMessage("LU factorization failed, falling back to QR factorization. `A` is potentially rank-deficient.",
+                        cache.verbose, :default_lu_fallback, :error_control)
                     sol = SciMLBase.solve!(
                         cache, QRFactorization(ColumnNorm()), args...; kwargs...)
                     SciMLBase.build_linear_solution(alg, sol.u, sol.resid, sol.cache;