Inter-particle distances

1. Squared distance
- 1.1. qmckl_distance_sq

1 Squared distance

1.1 `qmckl_distance_sq`

qmckl_distance_sq computes the matrix of the squared distances between all pairs of points in two sets, one point within each set:

\[ C_{ij} = \sum_{k=1}^3 (A_{k,i}-B_{k,j})^2 \]

qmckl_context	context	in	Global state
char	transa	in	Array `A` is `'N'`: Normal, `'T'`: Transposed
char	transb	in	Array `B` is `'N'`: Normal, `'T'`: Transposed
int64_t	m	in	Number of points in the first set
int64_t	n	in	Number of points in the second set
double	A[][lda]	in	Array containing the \(m \times 3\) matrix \(A\)
int64_t	lda	in	Leading dimension of array `A`
double	B[][ldb]	in	Array containing the \(n \times 3\) matrix \(B\)
int64_t	ldb	in	Leading dimension of array `B`
double	C[n][ldc]	out	Array containing the \(m \times n\) matrix \(C\)
int64_t	ldc	in	Leading dimension of array `C`

1.1.1 Requirements

context is not QMCKL_NULL_CONTEXT
m > 0
n > 0
lda >= 3 if transa == 'N'
lda >= m if transa == 'T'
ldb >= 3 if transb == 'N'
ldb >= n if transb == 'T'
ldc >= m
A is allocated with at least \(3 \times m \times 8\) bytes
B is allocated with at least \(3 \times n \times 8\) bytes
C is allocated with at least \(m \times n \times 8\) bytes

1.1.2 C header

qmckl_exit_code qmckl_distance_sq (
              const qmckl_context context,
      const char transa,
      const char transb,
      const int64_t m,
      const int64_t n,
      const double* A,
      const int64_t lda,
      const double* B,
      const int64_t ldb,
      double* const C,
      const int64_t ldc );

1.1.3 Source

integer function qmckl_distance_sq_f(context, transa, transb, m, n, A, LDA, B, LDB, C, LDC) result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  character  , intent(in)  :: transa, transb
  integer*8  , intent(in)  :: m, n
  integer*8  , intent(in)  :: lda
  real*8     , intent(in)  :: A(lda,*)
  integer*8  , intent(in)  :: ldb
  real*8     , intent(in)  :: B(ldb,*)
  integer*8  , intent(in)  :: ldc
  real*8     , intent(out) :: C(ldc,*)

  integer*8 :: i,j
  real*8    :: x, y, z
  integer   :: transab

  info = 0

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (m <= 0_8) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  if (n <= 0_8) then
     info = QMCKL_INVALID_ARG_5
     return
  endif

  if (transa == 'N' .or. transa == 'n') then
     transab = 0
  else if (transa == 'T' .or. transa == 't') then
     transab = 1
  else
     transab = -100
  endif

  if (transb == 'N' .or. transb == 'n') then
     continue
  else if (transa == 'T' .or. transa == 't') then
     transab = transab + 2
  else
     transab = -100
  endif

  if (transab < 0) then
     info = QMCKL_INVALID_ARG_1
     return 
  endif

  if (iand(transab,1) == 0 .and. LDA < 3) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,1) == 1 .and. LDA < m) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,2) == 0 .and. LDA < 3) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,2) == 2 .and. LDA < m) then
     info = QMCKL_INVALID_ARG_7
     return
  endif


  select case (transab)

  case(0)

     do j=1,n
        do i=1,m
           x = A(1,i) - B(1,j)
           y = A(2,i) - B(2,j)
           z = A(3,i) - B(3,j)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  case(1)

     do j=1,n
        do i=1,m
           x = A(i,1) - B(1,j)
           y = A(i,2) - B(2,j)
           z = A(i,3) - B(3,j)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  case(2)

     do j=1,n
        do i=1,m
           x = A(1,i) - B(j,1)
           y = A(2,i) - B(j,2)
           z = A(3,i) - B(j,3)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  case(3)

     do j=1,n
        do i=1,m
           x = A(i,1) - B(j,1)
           y = A(i,2) - B(j,2)
           z = A(i,3) - B(j,3)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  end select

end function qmckl_distance_sq_f

1.1.4 Performance

This function might be more efficient when A and B are transposed.