Add Dgetrs (compute a solution based on LU factorization) and test.

Responded to PR comments

cgo/lapack.go

@@ -136,3 +136,27 @@ func (impl Implementation) Dgetrf(m, n int, a []float64, lda int, ipiv []int) (o
 	}
 	return ok
 }
+
+// Dgetrs solves a system of equations using an LU factorization.
+// The system of equations solved is
+//  A * X = B if trans == blas.Trans
+//  A^T * X = B if trans == blas.NoTrans
+// A is a general n×n matrix with stride lda. B is a general matrix of size n×nrhs.
+//
+// On entry b contains the elements of the matrix B. On exit, b contains the
+// elements of X, the solution to the system of equations.
+//
+// a and ipiv contain the LU factorization of A and the permutation indices as
+// computed by Dgetrf. ipiv is zero-indexed.
+func (impl Implementation) Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int) {
+	checkMatrix(n, n, a, lda)
+	checkMatrix(n, nrhs, b, ldb)
+	if len(ipiv) < n {
+		panic(badIpiv)
+	}
+	ipiv32 := make([]int32, len(ipiv))
+	for i, v := range ipiv {
+		ipiv32[i] = int32(v) + 1 // Transform to one-indexed.
+	}
+	clapack.Dgetrs(trans, n, nrhs, a, lda, ipiv32, b, ldb)
+}