51 KiB
Inter-particle distances
Functions for the computation of distances between particles.
Squared distance
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:
\[ C_{ij} = \sum_{k=1}^3 (A_{k,i}-B_{k,j})^2 \]
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
transa |
char |
in | Array A is 'N' : Normal, 'T' : Transposed |
transb |
char |
in | Array B is 'N' : Normal, 'T' : Transposed |
m |
int64_t |
in | Number of points in the first set |
n |
int64_t |
in | Number of points in the second set |
A |
double[][lda] |
in | Array containing the $m \times 3$ matrix $A$ |
lda |
int64_t |
in | Leading dimension of array A |
B |
double[][ldb] |
in | Array containing the $n \times 3$ matrix $B$ |
ldb |
int64_t |
in | Leading dimension of array B |
C |
double[n][ldc] |
out | Array containing the $m \times n$ matrix $C$ |
ldc |
int64_t |
in | Leading dimension of array C |
Requirements:
context
is notQMCKL_NULL_CONTEXT
m > 0
n > 0
lda >= 3
iftransa == 'N'
lda >= m
iftransa == 'T'
ldb >= 3
iftransb == 'N'
ldb >= n
iftransb == 'T'
ldc >= m
A
is allocated with at least $3 \times m \times 8$ bytesB
is allocated with at least $3 \times n \times 8$ bytesC
is allocated with at least $m \times n \times 8$ bytes
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 );
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 = QMCKL_SUCCESS
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 (transb == 'T' .or. transb == '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. LDB < 3) then
info = QMCKL_INVALID_ARG_7
return
endif
if (iand(transab,2) == 2 .and. LDB < n) 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
Performance
This function is more efficient when A
and B
are
transposed.
Distance
qmckl_distance
qmckl_distance
computes the matrix of the distances between all
pairs of points in two sets, one point within each set:
\[ C_{ij} = \sqrt{\sum_{k=1}^3 (A_{k,i}-B_{k,j})^2} \]
If the input array is normal ('N'
), the xyz coordinates are in
the leading dimension: [n][3]
in C and (3,n)
in Fortran.
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
transa |
char |
in | Array A is 'N' : Normal, 'T' : Transposed |
transb |
char |
in | Array B is 'N' : Normal, 'T' : Transposed |
m |
int64_t |
in | Number of points in the first set |
n |
int64_t |
in | Number of points in the second set |
A |
double[][lda] |
in | Array containing the $m \times 3$ matrix $A$ |
lda |
int64_t |
in | Leading dimension of array A |
B |
double[][ldb] |
in | Array containing the $n \times 3$ matrix $B$ |
ldb |
int64_t |
in | Leading dimension of array B |
C |
double[n][ldc] |
out | Array containing the $m \times n$ matrix $C$ |
ldc |
int64_t |
in | Leading dimension of array C |
Requirements
context
is notQMCKL_NULL_CONTEXT
m > 0
n > 0
lda >= 3
iftransa == 'N'
lda >= m
iftransa == 'T'
ldb >= 3
iftransb == 'N'
ldb >= n
iftransb == 'T'
ldc >= m
A
is allocated with at least $3 \times m \times 8$ bytesB
is allocated with at least $3 \times n \times 8$ bytesC
is allocated with at least $m \times n \times 8$ bytes
C header
qmckl_exit_code qmckl_distance (
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 );
Source
integer function qmckl_distance_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 = QMCKL_SUCCESS
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 (transb == 'T' .or. transb == 't') then
transab = transab + 2
else
transab = -100
endif
if (transab < 0) then
info = QMCKL_INVALID_ARG_1
return
endif
! check for LDA
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
! check for LDB
if (iand(transab,1) == 0 .and. LDB < 3) then
info = QMCKL_INVALID_ARG_9
return
endif
if (iand(transab,1) == 1 .and. LDB < n) then
info = QMCKL_INVALID_ARG_9
return
endif
! check for LDC
if (LDC < m) then
info = QMCKL_INVALID_ARG_11
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
C(:,j) = dsqrt(C(:,j))
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
C(:,j) = dsqrt(C(:,j))
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
C(:,j) = dsqrt(C(:,j))
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
C(:,j) = dsqrt(C(:,j))
end do
end select
end function qmckl_distance_f
Performance
This function is more efficient when A
and B
are transposed.
Rescaled Distance
qmckl_distance_rescaled
qmckl_distance_rescaled
computes the matrix of the rescaled distances between all
pairs of points in two sets, one point within each set:
\[ C_{ij} = \frac{ 1 - e^{-\kappa r_{ij}}}{\kappa} \]
If the input array is normal ('N'
), the xyz coordinates are in
the leading dimension: [n][3]
in C and (3,n)
in Fortran.
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
transa |
char |
in | Array A is 'N' : Normal, 'T' : Transposed |
transb |
char |
in | Array B is 'N' : Normal, 'T' : Transposed |
m |
int64_t |
in | Number of points in the first set |
n |
int64_t |
in | Number of points in the second set |
A |
double[][lda] |
in | Array containing the $m \times 3$ matrix $A$ |
lda |
int64_t |
in | Leading dimension of array A |
B |
double[][ldb] |
in | Array containing the $n \times 3$ matrix $B$ |
ldb |
int64_t |
in | Leading dimension of array B |
C |
double[n][ldc] |
out | Array containing the $m \times n$ matrix $C$ |
ldc |
int64_t |
in | Leading dimension of array C |
rescale_factor_kappa |
double |
in | Factor for calculating rescaled distances |
Requirements
context
is notQMCKL_NULL_CONTEXT
m > 0
n > 0
lda >= 3
iftransa == 'N'
lda >= m
iftransa == 'T'
ldb >= 3
iftransb == 'N'
ldb >= n
iftransb == 'T'
ldc >= m
A
is allocated with at least $3 \times m \times 8$ bytesB
is allocated with at least $3 \times n \times 8$ bytesC
is allocated with at least $m \times n \times 8$ bytes
C header
qmckl_exit_code qmckl_distance_rescaled (
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,
const double rescale_factor_kappa );
Source
integer function qmckl_distance_rescaled_f(context, transa, transb, m, n, &
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) &
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,*)
real*8 , intent(in) :: rescale_factor_kappa
integer*8 :: i,j
real*8 :: x, y, z, dist, rescale_factor_kappa_inv
integer :: transab
rescale_factor_kappa_inv = 1.0d0/rescale_factor_kappa;
info = QMCKL_SUCCESS
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 (transb == 'T' .or. transb == 't') then
transab = transab + 2
else
transab = -100
endif
! check for LDA
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
! check for LDB
if (iand(transab,2) == 0 .and. LDB < 3) then
info = QMCKL_INVALID_ARG_9
return
endif
if (iand(transab,2) == 2 .and. LDB < n) then
info = QMCKL_INVALID_ARG_9
return
endif
! check for LDC
if (LDC < m) then
info = QMCKL_INVALID_ARG_11
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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
end do
end do
end select
end function qmckl_distance_rescaled_f
Performance
This function is more efficient when A
and B
are transposed.
Rescaled Distance Derivatives
qmckl_distance_rescaled_gl
qmckl_distance_rescaled_gl
computes the matrix of the gradient and Laplacian of the
rescaled distance with respect to the electron coordinates. The derivative is a rank 3 tensor.
The first dimension has a dimension of 4 of which the first three coordinates
contains the gradient vector and the last index is the Laplacian.
\[ C(r_{ij}) = \left( 1 - \exp(-\kappa\, r_{ij})\right)/\kappa \]
Here the gradient is defined as follows:
\[ \nabla_i C(r_{ij}) = \left(\frac{\partial C(r_{ij})}{\partial x_i},\frac{\partial C(r_{ij})}{\partial y_i},\frac{\partial C(r_{ij})}{\partial z_i} \right) \] and the Laplacian is defined as follows:
\[ \Delta_i C(r_{ij}) = \frac{\partial^2}{\partial x_i^2} + \frac{\partial^2}{\partial y_i^2} + \frac{\partial^2}{\partial z_i^2} \]
Using the above three formulas, the expression for the gradient and Laplacian is:
\[ \frac{\partial C(r_{ij})}{\partial x_i} = \frac{|(x_i - x_j)|}{r_{ij}} \exp (- \kappa \, r_{ij}) \]
\[ \Delta C_{ij}(r_{ij}) = \left[ \frac{2}{r_{ij}} - \kappa \right] \exp (- \kappa \, r_{ij}) \]
If the input array is normal ('N'
), the xyz coordinates are in
the leading dimension: [n][3]
in C and (3,n)
in Fortran.
Variable | Type | In/Out | Description |
---|---|---|---|
context |
qmckl_context |
in | Global state |
transa |
char |
in | Array A is 'N' : Normal, 'T' : Transposed |
transb |
char |
in | Array B is 'N' : Normal, 'T' : Transposed |
m |
int64_t |
in | Number of points in the first set |
n |
int64_t |
in | Number of points in the second set |
A |
double[][lda] |
in | Array containing the $m \times 3$ matrix $A$ |
lda |
int64_t |
in | Leading dimension of array A |
B |
double[][ldb] |
in | Array containing the $n \times 3$ matrix $B$ |
ldb |
int64_t |
in | Leading dimension of array B |
C |
double[4][n][ldc] |
out | Array containing the $4 \times m \times n$ matrix $C$ |
ldc |
int64_t |
in | Leading dimension of array C |
rescale_factor_kappa |
double |
in | Factor for calculating rescaled distances derivatives |
Requirements:
context
is notQMCKL_NULL_CONTEXT
m > 0
n > 0
lda >= 3
iftransa == 'N'
lda >= m
iftransa == 'T'
ldb >= 3
iftransb == 'N'
ldb >= n
iftransb == 'T'
ldc >= m
A
is allocated with at least $3 \times m \times 8$ bytesB
is allocated with at least $3 \times n \times 8$ bytesC
is allocated with at least $4 \times m \times n \times 8$ bytes
qmckl_exit_code qmckl_distance_rescaled_gl (
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,
const double rescale_factor_kappa );
integer function qmckl_distance_rescaled_gl_f(context, transa, transb, m, n, &
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) &
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(4,ldc,*)
real*8 , intent(in) :: rescale_factor_kappa
integer*8 :: i,j
real*8 :: x, y, z, dist, dist_inv
real*8 :: rij
integer :: transab
info = QMCKL_SUCCESS
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 (transb == 'T' .or. transb == 't') then
transab = transab + 2
else
transab = -100
endif
! check for LDA
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
! check for LDB
if (iand(transab,2) == 0 .and. LDB < 3) then
info = QMCKL_INVALID_ARG_9
return
endif
if (iand(transab,2) == 2 .and. LDB < n) then
info = QMCKL_INVALID_ARG_9
return
endif
! check for LDC
if (LDC < m) then
info = QMCKL_INVALID_ARG_11
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)
dist = dsqrt(x*x + y*y + z*z)
! Avoid floating-point exception
if (dist == 0.d0) then
dist = 69.d0/rescale_factor_kappa
endif
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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)
dist = dsqrt(x*x + y*y + z*z)
! Avoid floating-point exception
if (dist == 0.d0) then
dist = 69.d0/rescale_factor_kappa
endif
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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)
dist = dsqrt(x*x + y*y + z*z)
! Avoid floating-point exception
if (dist == 0.d0) then
dist = 69.d0/rescale_factor_kappa
endif
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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)
dist = dsqrt(x*x + y*y + z*z)
! Avoid floating-point exception
if (dist == 0.d0) then
dist = 69.d0/rescale_factor_kappa
endif
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
end do
end do
end select
end function qmckl_distance_rescaled_gl_f
This function is more efficient when A
and B
are transposed.