To achieve the spectral reproduction technology of halftone prints manuscript, the number of primary ink and the ink composition used in the manuscript should be specified before hand. However, there are still many problems to be solved in the primary ink spectral prediction for prints manuscript, and existing methods of spectral prediction have many disadvantages. To solve this problem, the algorithm of primary ink spectral prediction based on constrained non negative matrix factorization ISPNMF, and the optimizing algorithm for black ink spectral prediction have been put forward innovatively. The short comings of multiple optimal solutions and local minima of the basic non-negative matrix factorization were overcome, and the unique global optimal solution was realized by the algorithm of ISPNMF. The interference of prediction black inkcaused by the colored inks mixed absorption was eliminated by the optimizing algorithm for black ink spectral prediction, and the optimized result was close to the actual black ink spectrum. The accuracy of the algorithm was verified by using the samples of simulating different brands ink. In the experiments, Konica Minolta C1085 and HP indigo 5600, two kinds of four-color digital printing machine, with its toner and ink paste mimicking different brands of ink, were used. And the IT8.7/3 color card was printed in 230 g white cardboard, then X-rite I1 Pro2 was used to obtain the spectral reflectance data of two proofs as the experimental samples, to explore and verify the accuracy and practicability of the algorithms. The experimental results showed that, the number and spectrum of primary inks used in the printed manuscript can be accurately predicted in the linear empirical space. The GFC of prediction results of color inks were all up to 99.9%, and the SAD were all less than 0.045. The GFC of prediction results of black inks, which were optimized, were also up to 99.9%. The algorithms can not only predict theprimary ink of prints manuscript accurately, but also can match the actualprimary ink precisely. It is of great significance to the realization of the spectral replication of prints manuscript.