feat: extend intrinsic matmul

example/intrinsics/CMakeLists.txt

@@ -1,2 +1,3 @@
 ADD_EXAMPLE(sum)
-ADD_EXAMPLE(dot_product)
+ADD_EXAMPLE(dot_product)
+ADD_EXAMPLE(matmul)

example/intrinsics/example_matmul.f90

@@ -0,0 +1,19 @@
+program example_matmul
+    use stdlib_intrinsics, only: stdlib_matmul
+    complex :: x(2, 2), y(2, 2)
+    real :: r1(50, 100), r2(100, 40), r3(40, 50)
+    real, allocatable :: res(:, :)
+    x = reshape([(0, 0), (1, 0), (1, 0), (0, 0)], [2, 2])
+    y = reshape([(0, 0), (0, 1), (0, -1), (0, 0)], [2, 2]) ! pauli y-matrix
+
+    print *, stdlib_matmul(y, y, y) ! should be y
+    print *, stdlib_matmul(x, x, y, x) ! should be -i x sigma_z
+
+    call random_seed()
+    call random_number(r1)
+    call random_number(r2)
+    call random_number(r3)
+
+    res = stdlib_matmul(r1, r2, r3) ! 50x50 matrix
+    print *, shape(res)
+end program example_matmul

src/CMakeLists.txt

@@ -19,6 +19,7 @@ set(fppFiles
     stdlib_hash_64bit_spookyv2.fypp
     stdlib_intrinsics_dot_product.fypp
     stdlib_intrinsics_sum.fypp
+    stdlib_intrinsics_matmul.fypp
     stdlib_intrinsics.fypp
     stdlib_io.fypp
     stdlib_io_npy.fypp
@@ -32,14 +33,14 @@ set(fppFiles
     stdlib_linalg_kronecker.fypp
     stdlib_linalg_cross_product.fypp
     stdlib_linalg_eigenvalues.fypp
-    stdlib_linalg_solve.fypp    
+    stdlib_linalg_solve.fypp
     stdlib_linalg_determinant.fypp
     stdlib_linalg_qr.fypp
     stdlib_linalg_inverse.fypp
     stdlib_linalg_pinv.fypp
     stdlib_linalg_norms.fypp
     stdlib_linalg_state.fypp
-    stdlib_linalg_svd.fypp 
+    stdlib_linalg_svd.fypp
     stdlib_linalg_cholesky.fypp
     stdlib_linalg_schur.fypp
     stdlib_optval.fypp

src/stdlib_intrinsics.fypp

@@ -146,6 +146,30 @@ module stdlib_intrinsics
         #:endfor
     end interface
     public :: kahan_kernel
+
+    interface stdlib_matmul
+        !! version: experimental
+        !!
+        !!### Summary
+        !! compute the matrix multiplication of more than two matrices with a single function call.
+        !! ([Specification](../page/specs/stdlib_intrinsics.html#stdlib_matmul))
+        !!
+        !!### Description
+        !!
+        !! matrix multiply more than two matrices with a single function call
+        !! the multiplication with the optimal parenthesization for efficiency of computation is done automatically
+        !! Supported data types are `real` and `complex`.
+        !!
+        !! Note: The matrices must be of compatible shapes to be multiplied
+        #:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
+            pure module function stdlib_matmul_${s}$ (m1, m2, m3, m4, m5) result(r)
+                ${t}$, intent(in) :: m1(:,:), m2(:,:)
+                ${t}$, intent(in), optional :: m3(:,:), m4(:,:), m5(:,:)
+                ${t}$, allocatable :: r(:,:)
+            end function stdlib_matmul_${s}$
+        #:endfor
+    end interface stdlib_matmul
+    public :: stdlib_matmul
 
 contains
 

src/stdlib_intrinsics_matmul.fypp

@@ -0,0 +1,226 @@
+#:include "common.fypp"
+#:set I_KINDS_TYPES = list(zip(INT_KINDS, INT_TYPES, INT_KINDS))
+#:set R_KINDS_TYPES = list(zip(REAL_KINDS, REAL_TYPES, REAL_SUFFIX))
+#:set C_KINDS_TYPES = list(zip(CMPLX_KINDS, CMPLX_TYPES, CMPLX_SUFFIX))
+
+submodule (stdlib_intrinsics) stdlib_intrinsics_matmul
+    use stdlib_linalg_blas, only: gemm
+    use stdlib_constants
+    implicit none
+
+contains
+
+    ! Algorithm for the optimal parenthesization of matrices
+    ! Reference: Cormen, "Introduction to Algorithms", 4ed, ch-14, section-2
+    ! Internal use only!
+    pure function matmul_chain_order(p) result(s)
+        integer, intent(in) :: p(:)
+        integer :: s(1:size(p) - 2, 2:size(p) - 1), m(1:size(p) - 1, 1:size(p) - 1)
+        integer :: n, l, i, j, k, q
+        n = size(p) - 1
+        m(:,:) = 0
+        s(:,:) = 0
+
+        do l = 2, n
+            do i = 1, n - l + 1
+                j = i + l - 1
+                m(i,j) = huge(1)
+
+                do k = i, j - 1
+                    q = m(i,k) + m(k+1,j) + p(i)*p(k+1)*p(j+1)
+
+                    if (q < m(i, j)) then
+                        m(i,j) = q
+                        s(i,j) = k
+                    end if
+                end do
+            end do
+        end do
+    end function matmul_chain_order
+
+#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
+
+    pure function matmul_chain_mult_${s}$_3 (m1, m2, m3, start, s, p) result(r)
+        ${t}$, intent(in) :: m1(:,:), m2(:,:), m3(:,:)
+        integer, intent(in) :: start, s(:,2:), p(:)
+        ${t}$, allocatable :: r(:,:), temp(:,:)
+        integer :: ord, m, n, k
+        ord = s(start, start + 2)
+        allocate(r(p(start), p(start + 3)))
+
+        if (ord == start) then
+            ! m1*(m2*m3)
+            m = p(start + 1)
+            n = p(start + 3)
+            k = p(start + 2)
+            allocate(temp(m,n))
+            call gemm('N', 'N', m, n, k, one_${s}$, m2, m, m3, k, zero_${s}$, temp, m)
+            m = p(start)
+            n = p(start + 3)
+            k = p(start + 1)
+            call gemm('N', 'N', m, n, k, one_${s}$, m1, m, temp, k, zero_${s}$, r, m)
+        else if (ord == start + 1) then
+            ! (m1*m2)*m3
+            m = p(start)
+            n = p(start + 2)
+            k = p(start + 1)
+            allocate(temp(m, n))
+            call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, temp, m)
+            m = p(start)
+            n = p(start + 3)
+            k = p(start + 1)
+            call gemm('N', 'N', m, n, k, one_${s}$, temp, m, m3, k, zero_${s}$, r, m)
+        else
+            error stop "stdlib_matmul: error: unexpected s(i,j)"
+        end if
+
+    end function matmul_chain_mult_${s}$_3
+
+    pure function matmul_chain_mult_${s}$_4 (m1, m2, m3, m4, start, s, p) result(r)
+        ${t}$, intent(in) :: m1(:,:), m2(:,:), m3(:,:), m4(:,:)
+        integer, intent(in) :: start, s(:,2:), p(:)
+        ${t}$, allocatable :: r(:,:), temp(:,:), temp1(:,:)
+        integer :: ord, m, n, k
+        ord = s(start, start + 3)
+        allocate(r(p(start), p(start + 4)))
+
+        if (ord == start) then
+            ! m1*(m2*m3*m4)
+            temp = matmul_chain_mult_${s}$_3(m2, m3, m4, start + 1, s, p)
+            m = p(start)
+            n = p(start + 4)
+            k = p(start + 1)
+            call gemm('N', 'N', m, n, k, one_${s}$, m1, m, temp, k, zero_${s}$, r, m)
+        else if (ord == start + 1) then
+            ! (m1*m2)*(m3*m4)
+            m = p(start)
+            n = p(start + 2)
+            k = p(start + 1)
+            allocate(temp(m,n))
+            call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, temp, m)
+
+            m = p(start + 2)
+            n = p(start + 4)
+            k = p(start + 3)
+            allocate(temp1(m,n))
+            call gemm('N', 'N', m, n, k, one_${s}$, m3, m, m4, k, zero_${s}$, temp1, m)
+
+            m = p(start)
+            n = p(start + 4)
+            k = p(start + 2)
+            call gemm('N', 'N', m, n, k, one_${s}$, temp, m, temp1, k, zero_${s}$, r, m)
+        else if (ord == start + 2) then
+            ! (m1*m2*m3)*m4
+            temp = matmul_chain_mult_${s}$_3(m1, m2, m3, start, s, p)
+            m = p(start)
+            n = p(start + 4)
+            k = p(start + 3)
+            call gemm('N', 'N', m, n, k, one_${s}$, temp, m, m4, k, zero_${s}$, r, m)
+        else
+            error stop "stdlib_matmul: error: unexpected s(i,j)"
+        end if
+
+    end function matmul_chain_mult_${s}$_4
+
+    pure module function stdlib_matmul_${s}$ (m1, m2, m3, m4, m5) result(r)
+        ${t}$, intent(in) :: m1(:,:), m2(:,:)
+        ${t}$, intent(in), optional :: m3(:,:), m4(:,:), m5(:,:)
+        ${t}$, allocatable :: r(:,:), temp(:,:), temp1(:,:)
+        integer :: p(6), num_present, m, n, k
+        integer, allocatable :: s(:,:)
+
+        p(1) = size(m1, 1)
+        p(2) = size(m2, 1)
+        p(3) = size(m2, 2)
+
+        num_present = 2
+        if (present(m3)) then
+            p(3) = size(m3, 1)
+            p(4) = size(m3, 2)
+            num_present = num_present + 1
+        end if
+        if (present(m4)) then
+            p(4) = size(m4, 1)
+            p(5) = size(m4, 2)
+            num_present = num_present + 1
+        end if
+        if (present(m5)) then
+            p(5) = size(m5, 1)
+            p(6) = size(m5, 2)
+            num_present = num_present + 1
+        end if
+
+        allocate(r(p(1), p(num_present + 1)))
+
+        if (num_present == 2) then
+            m = p(1)
+            n = p(3)
+            k = p(2)
+            call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, r, m)
+            return
+        end if
+
+        ! Now num_present >= 3
+        allocate(s(1:num_present - 1, 2:num_present))
+
+        s = matmul_chain_order(p(1: num_present + 1))
+
+        if (num_present == 3) then
+            r = matmul_chain_mult_${s}$_3(m1, m2, m3, 1, s, p(1:4))
+            return
+        else if (num_present == 4) then
+            r = matmul_chain_mult_${s}$_4(m1, m2, m3, m4, 1, s, p(1:5))
+            return
+        end if
+
+        ! Now num_present is 5
+
+        select case (s(1, 5))
+            case (1)
+                ! m1*(m2*m3*m4*m5)
+                temp = matmul_chain_mult_${s}$_4(m2, m3, m4, m5, 2, s, p)
+                m = p(1)
+                n = p(6)
+                k = p(2)
+                call gemm('N', 'N', m, n, k, one_${s}$, m1, m, temp, k, zero_${s}$, r, m)
+            case (2)
+                ! (m1*m2)*(m3*m4*m5)
+                m = p(1)
+                n = p(3)
+                k = p(2)
+                allocate(temp(m,n))
+                call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, temp, m)
+
+                temp1 = matmul_chain_mult_${s}$_3(m3, m4, m5, 3, s, p)
+
+                k = n
+                n = p(6)
+                call gemm('N', 'N', m, n, k, one_${s}$, temp, m, temp1, k, zero_${s}$, r, m)
+            case (3)
+                ! (m1*m2*m3)*(m4*m5)
+                temp = matmul_chain_mult_${s}$_3(m1, m2, m3, 3, s, p)
+
+                m = p(4)
+                n = p(6)
+                k = p(5)
+                allocate(temp1(m,n))
+                call gemm('N', 'N', m, n, k, one_${s}$, m4, m, m5, k, zero_${s}$, temp1, m)
+
+                k = m
+                m = p(1)
+                call gemm('N', 'N', m, n, k, one_${s}$, temp, m, temp1, k, zero_${s}$, r, m)
+            case (4)
+                ! (m1*m2*m3*m4)*m5
+                temp = matmul_chain_mult_${s}$_4(m1, m2, m3, m4, 1, s, p)
+                m = p(1)
+                n = p(6)
+                k = p(5)
+                call gemm('N', 'N', m, n, k, one_${s}$, temp, m, m5, k, zero_${s}$, r, m)
+            case default
+                error stop "stdlib_matmul: error: unexpected s(i,j)"
+        end select
+
+    end function stdlib_matmul_${s}$
+
+#:endfor
+end submodule stdlib_intrinsics_matmul