add solve_lu test

Author: perazz

example/linalg/CMakeLists.txt

@@ -20,5 +20,6 @@ ADD_EXAMPLE(blas_gemv)
 ADD_EXAMPLE(lapack_getrf)
 ADD_EXAMPLE(solve1)
 ADD_EXAMPLE(solve2)
+ADD_EXAMPLE(solve3)
 ADD_EXAMPLE(determinant)
 ADD_EXAMPLE(determinant2)

example/linalg/example_solve3.f90

@@ -0,0 +1,30 @@
+program example_solve3
+  use stdlib_linalg_constants, only: sp
+  use stdlib_linalg, only: solve_lu, linalg_state_type 
+  implicit none
+
+  integer(ilp) :: test
+  complex(sp), allocatable :: A(:,:),b(:),x(:)
+
+  ! Solve a system of 3 complex linear equations: 
+  !  2x +      iy + 2z = (5-i)
+  ! -ix + (4-3i)y + 6z = i
+  !  4x +      3y +  z = 1
+
+  ! Note: Fortran is column-major! -> transpose 
+  A = transpose(reshape([(2.0, 0.0),(0.0, 1.0),(2.0,0.0), &
+                         (0.0,-1.0),(4.0,-3.0),(6.0,0.0), &
+                         (4.0, 0.0),(3.0, 0.0),(1.0,0.0)] , [3,3])) 
+  b = [(5.0,-1.0),(0.0,1.0),(1.0,0.0)]
+  
+  ! Pre-allocate x
+  allocate(x,source=b)
+
+  ! Call system many times avoiding reallocation 
+  do test=1,100
+     call solve_lu(A,b,x)
+     print "(i2,'-th solution: ',*(1x,f12.6))", test,x
+  end do
+
+end program example_solve3
+