Add is_invertible_with_inverse for arb matrices (#1525)

src/arb/ComplexMat.jl

@@ -440,12 +440,18 @@ Given a $n\times n$ matrix of type `acb_mat`, return an
 $n\times n$ matrix $X$ such that $AX$ contains the
 identity matrix. If $A$ cannot be inverted numerically an exception is raised.
 """
-function inv(x::ComplexMat, prec::Int = precision(Balls))
-  ncols(x) != nrows(x) && error("Matrix must be square")
+function inv(x::ComplexMat)
+  fl, z = is_invertible_with_inverse(x)
+  fl && return z
+  error("Matrix singular or cannot be inverted numerically")
+end
+
+function is_invertible_with_inverse(x::ComplexMat)
+  ncols(x) != nrows(x) && return false, x
   z = similar(x)
   r = ccall((:acb_mat_inv, libarb), Cint,
-              (Ref{ComplexMat}, Ref{ComplexMat}, Int), z, x, prec)
-  Bool(r) ? (return z) : error("Matrix cannot be inverted numerically")
+            (Ref{ComplexMat}, Ref{ComplexMat}, Int), z, x, precision(Balls))
+  return Bool(r), z
 end
 
 ###############################################################################

src/arb/RealMat.jl

@@ -398,11 +398,17 @@ $n\times n$ matrix $X$ such that $AX$ contains the
 identity matrix. If $A$ cannot be inverted numerically an exception is raised.
 """
 function inv(x::RealMat)
-  ncols(x) != nrows(x) && error("Matrix must be square")
+  fl, z = is_invertible_with_inverse(x)
+  fl && return z
+  error("Matrix singular or cannot be inverted numerically")
+end
+
+function is_invertible_with_inverse(x::RealMat)
+  ncols(x) != nrows(x) && return false, x
   z = similar(x)
   r = ccall((:arb_mat_inv, libarb), Cint,
               (Ref{RealMat}, Ref{RealMat}, Int), z, x, precision(Balls))
-  Bool(r) ? (return z) : error("Matrix cannot be inverted numerically")
+  return Bool(r), z
 end
 
 ###############################################################################

src/arb/acb_mat.jl

@@ -444,11 +444,17 @@ $n\times n$ matrix $X$ such that $AX$ contains the
 identity matrix. If $A$ cannot be inverted numerically an exception is raised.
 """
 function inv(x::acb_mat)
-  ncols(x) != nrows(x) && error("Matrix must be square")
+  fl, z = is_invertible_with_inverse(x)
+  fl && return z
+  error("Matrix singular or cannot be inverted numerically")
+end
+
+function is_invertible_with_inverse(x::acb_mat)
+  ncols(x) != nrows(x) && return false, x
   z = similar(x)
   r = ccall((:acb_mat_inv, libarb), Cint,
               (Ref{acb_mat}, Ref{acb_mat}, Int), z, x, precision(base_ring(x)))
-  Bool(r) ? (return z) : error("Matrix cannot be inverted numerically")
+  return Bool(r), z
 end
 
 ###############################################################################

src/arb/arb_mat.jl

@@ -402,11 +402,17 @@ $n\times n$ matrix $X$ such that $AX$ contains the
 identity matrix. If $A$ cannot be inverted numerically an exception is raised.
 """
 function inv(x::arb_mat)
-  ncols(x) != nrows(x) && error("Matrix must be square")
+  fl, z = is_invertible_with_inverse(x)
+  fl && return z
+  error("Matrix singular or cannot be inverted numerically")
+end
+
+function is_invertible_with_inverse(x::arb_mat)
+  ncols(x) != nrows(x) && return false, x
   z = similar(x)
   r = ccall((:arb_mat_inv, libarb), Cint,
               (Ref{arb_mat}, Ref{arb_mat}, Int), z, x, precision(base_ring(x)))
-  Bool(r) ? (return z) : error("Matrix cannot be inverted numerically")
+  return Bool(r), z
 end
 
 ###############################################################################

test/arb/ComplexMat-test.jl

@@ -325,6 +325,14 @@ end
 
    @test overlaps(A*C, one(S))
    @test contains(C, B)
+
+   fl, C = is_invertible_with_inverse(A)
+   @test fl && contains(C, B)
+
+   A = CC[1 1; 1 1] 
+   fl, C = is_invertible_with_inverse(A)
+   @test !fl
+   @test_throws ErrorException inv(A)
 end
 
 @testset "ComplexMat.divexact" begin

test/arb/RealMat-test.jl

@@ -294,6 +294,14 @@ end
 
    @test overlaps(A*C, one(S))
    @test contains(C, B)
+
+   fl, C = is_invertible_with_inverse(A)
+   @test fl && contains(C, B)
+
+   A = RR[1 1; 1 1] 
+   fl, C = is_invertible_with_inverse(A)
+   @test !fl
+   @test_throws ErrorException inv(A)
 end
 
 @testset "RealMat.divexact" begin

test/arb/acb_mat-test.jl

@@ -325,6 +325,14 @@ end
 
    @test overlaps(A*C, one(S))
    @test contains(C, B)
+
+   fl, C = is_invertible_with_inverse(A)
+   @test fl && contains(C, B)
+
+   A = CC[1 1; 1 1] 
+   fl, C = is_invertible_with_inverse(A)
+   @test !fl
+   @test_throws ErrorException inv(A)
 end
 
 @testset "acb_mat.divexact" begin

test/arb/arb_mat-test.jl

@@ -294,6 +294,14 @@ end
 
    @test overlaps(A*C, one(S))
    @test contains(C, B)
+
+   fl, C = is_invertible_with_inverse(A)
+   @test fl && contains(C, B)
+
+   A = RR[1 1; 1 1] 
+   fl, C = is_invertible_with_inverse(A)
+   @test !fl
+   @test_throws ErrorException inv(A)
 end
 
 @testset "arb_mat.divexact" begin