Use faster algorithm for complex matmul, test=develop (#26231)

python/paddle/incubate/complex/tensor/linalg.py

@@ -56,20 +56,20 @@ def matmul(x, y, transpose_x=False, transpose_y=False, alpha=1.0, name=None):
                 # [1.+5.j 5.+9.j]         
     """
     # x = a + bi, y = c + di
-    # mm(x, y) = mm(a, c) - mm(b, d) + (mm(a, d) + mm(b, c))i
+    # P1 = ac; P2 = (a + b)(c + d); P3 = bd; then mm(x, y) = (P1-P3) + (P2-P1-P3)j
     complex_variable_exists([x, y], "matmul")
     a, b = (x.real, x.imag) if is_complex(x) else (x, None)
     c, d = (y.real, y.imag) if is_complex(y) else (y, None)
-    ac = layers.matmul(a, c, transpose_x, transpose_y, alpha, name)
+    P1 = layers.matmul(a, c, transpose_x, transpose_y, alpha, name)
     if is_real(b) and is_real(d):
-        bd = layers.matmul(b, d, transpose_x, transpose_y, alpha, name)
-        real = ac - bd
-        imag = layers.matmul(a, d, transpose_x, transpose_y, alpha, name) + \
-               layers.matmul(b, c, transpose_x, transpose_y, alpha, name)
+        P2 = layers.matmul(a + b, c + d, transpose_x, transpose_y, alpha, name)
+        P3 = layers.matmul(b, d, transpose_x, transpose_y, alpha, name)
+        real = P1 - P3
+        imag = P2 - P1 - P3
     elif is_real(b):
-        real = ac
+        real = P1
         imag = layers.matmul(b, c, transpose_x, transpose_y, alpha, name)
     else:
-        real = ac
+        real = P1
         imag = layers.matmul(a, d, transpose_x, transpose_y, alpha, name)
     return ComplexVariable(real, imag)