add qless tutorial

docs/src/tutorials/qless.md

@@ -0,0 +1,58 @@
+```@example qless1
+using QRMumps, LinearAlgebra, SparseArrays, Printf
+
+irn = [1, 3, 5, 2, 3, 5, 1, 4, 4, 5, 2, 1, 3]
+jcn = [1, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7]
+val = [1.0, 2.0, 3.0, 1.0, 1.0, 2.0, 4.0, 1.0, 5.0, 1.0, 3.0, 6.0, 1.0]
+
+A = sparse(irn, jcn, val, 5, 7)
+b = [40.0, 10.0, 44.0, 98.0, 87.0]
+y_star = [0.0, 1.0, 2.0, 3.0, 4.0]
+y₁ = similar(b,7)
+y₂ = similar(b)
+
+qrm_init()
+
+spmat = qrm_spmat_init(A)
+spfct = qrm_spfct_init(spmat)
+qrm_analyse!(spmat, spfct; transp='t')
+qrm_set(spfct, "qrm_keeph", 0)
+qrm_factorize!(spmat, spfct, transp='t')
+
+qrm_solve!(spfct, b, y₁; transp='t')
+qrm_solve!(spfct, y₁, y₂; transp='n')
+
+error_norm = norm(y₂ - y_star)
+
+@printf("Error norm ‖y* - y‖ = %10.5e\n", error_norm)
+```
+
+```@example qless2
+using QRMumps, LinearAlgebra, SparseArrays, Printf
+
+irn = [1, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7]
+jcn = [1, 3, 5, 2, 3, 5, 1, 4, 4, 5, 2, 1, 3]
+val = [1.0, 2.0, 3.0, 1.0, 1.0, 2.0, 4.0, 1.0, 3.0, 1.0, 3.0, 2.0, 1.0]
+
+A = sparse(irn, jcn, val, 7, 5)
+b = [22.0, 2.0, 13.0, 8.0, 17.0, 6.0, 5.0]
+x_star = [1.0, 2.0, 3.0, 4.0, 5.0]
+
+qrm_init()
+
+spmat = qrm_spmat_init(A)
+spfct = qrm_spfct_init(spmat)
+
+qrm_set(spfct, "qrm_keeph", 0)
+
+qrm_analyse!(spmat, spfct)
+qrm_factorize!(spmat, spfct)
+
+z = A'*b
+x₁ = qrm_solve(spfct, z; transp = 't')
+x₂ = qrm_solve(spfct, x₁; transp = 'n')
+
+error_norm = norm(x₂ - x_star)
+
+@printf("Error norm ‖x* - x‖ = %10.5e\n", error_norm)
+```