GO:0052811:   1-phosphatidylinositol-3-phosphate 4-kinase activity
Catalysis of the reaction: a 1-phosphatidyl-1D-myo-inositol 4-phosphate + ATP = a 1-phosphatidyl-1D-myo-inositol 3,4-bisphosphate + ADP + 2 H(+).