Fixed a bug in the matrix BLAS bindings that caused BLAS to return an invalid

argument error.  The error occurred when general matrix multiply expressions
were transposed and didn't result in a square matrix.  E.g. mat = trans(a*b)
where mat isn't square.

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%403368

dlib/matrix/matrix_blas_bindings.h

@@ -488,7 +488,7 @@ namespace dlib
             if (transpose == false)
                 cblas_gemm(Order, CblasNoTrans, CblasNoTrans, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc);
             else
-                cblas_gemm(Order, CblasTrans, CblasTrans, M, N, K, alpha, B, ldb, A, lda, beta, C, ldc);
+                cblas_gemm(Order, CblasTrans, CblasTrans, N, M, K, alpha, B, ldb, A, lda, beta, C, ldc);
 
         } DLIB_END_BLAS_BINDING
 
@@ -516,7 +516,7 @@ namespace dlib
             if (transpose == false)
                 cblas_gemm(Order, TransA, TransB, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc);
             else
-                cblas_gemm(Order, TransA, TransB, M, N, K, alpha, B, ldb, A, lda, beta, C, ldc);
+                cblas_gemm(Order, TransA, TransB, N, M, K, alpha, B, ldb, A, lda, beta, C, ldc);
 
         } DLIB_END_BLAS_BINDING
 
@@ -544,7 +544,7 @@ namespace dlib
             if (transpose == false)
                 cblas_gemm(Order, TransA, TransB, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc);
             else
-                cblas_gemm(Order, TransA, TransB, M, N, K, alpha, B, ldb, A, lda, beta, C, ldc);
+                cblas_gemm(Order, TransA, TransB, N, M, K, alpha, B, ldb, A, lda, beta, C, ldc);
 
         } DLIB_END_BLAS_BINDING
 
@@ -570,7 +570,7 @@ namespace dlib
             if (transpose == false)
                 cblas_gemm(Order, CblasTrans, CblasTrans, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc);
             else
-                cblas_gemm(Order, CblasNoTrans, CblasNoTrans, M, N, K, alpha, B, ldb, A, lda, beta, C, ldc);
+                cblas_gemm(Order, CblasNoTrans, CblasNoTrans, N, M, K, alpha, B, ldb, A, lda, beta, C, ldc);
         } DLIB_END_BLAS_BINDING
 
         // --------------------------------------

dlib/test/matrix3.cpp

@@ -272,6 +272,43 @@ namespace
                 check_equal(temp, temp3);
             }
 
+            dlog << LTRACE << "1.17.1";
+            {
+                matrix<type> m1, m2;
+
+                m1 = matrix_cast<type>(randm(rows, cols, rnd));
+                m2 = matrix_cast<type>(randm(cols, rows + 8, rnd));
+                check_equal(tmp(m1*m2), m1*m2);
+                check_equal(tmp(trans(m1*m2)), trans(m1*m2));
+
+                m1 = trans(m1);
+                check_equal(tmp(trans(m1)*m2), trans(m1)*m2);
+                check_equal(tmp(trans(trans(m1)*m2)), trans(trans(m1)*m2));
+
+                m2 = trans(m2);
+                check_equal(tmp(trans(m1)*trans(m2)), trans(m1)*trans(m2));
+                check_equal(tmp(trans(trans(m1)*trans(m2))), trans(trans(m1)*trans(m2)));
+
+                m1 = trans(m1);
+                check_equal(tmp(m1*trans(m2)), m1*trans(m2));
+                check_equal(tmp(trans(m1*trans(m2))), trans(m1*trans(m2)));
+            }
+
+            dlog << LTRACE << "1.17.5";
+            {
+                matrix<type,1,0> r;
+                matrix<type,0,1> c;
+
+                r = matrix_cast<type>(randm(1, rows+9, rnd));
+                c = matrix_cast<type>(randm(rows, 1, rnd));
+
+                check_equal(tmp(c*r), c*r);
+                check_equal(tmp(trans(c*r)), trans(c*r));
+
+                check_equal(tmp(trans(r)*trans(c)), trans(r)*trans(c));
+                check_equal(tmp(trans(trans(r)*trans(c))), trans(trans(r)*trans(c)));
+            }
+
             dlog << LTRACE << "1.18";
 
             // GEMV tests