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https://github.com/TREX-CoE/qmckl.git
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Created a function to provide the derivative functions along with Doc. #17
This commit is contained in:
vijay gopal chilkuri
parent
55d749f5c6
commit
cb70c1f568
@ -1105,6 +1105,360 @@ end function qmckl_distance_rescaled_f
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#+end_src
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*** Test :noexport:
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* Rescaled Distance Derivatives
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** ~qmckl_distance_rescaled_deriv_e~
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:PROPERTIES:
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:Name: qmckl_distance_rescaled_deriv_e
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:CRetType: qmckl_exit_code
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:FRetType: qmckl_exit_code
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:END:
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~qmckl_distance_rescaled_deriv_e~ computes the matrix of the gradient and laplacian of the
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rescaled distance with respect to the electron coordinates. The derivative is a rank 3 tensor.
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The first dimension has a dimension of 4 of which the first three coordinates
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contains the gradient vector and the last index is the laplacian.
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\[
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C_{ij} = \left( 1 - \exp{-\kappa C_{ij}}\right)/\kappa
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\]
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Here the gradient is defined as follows:
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\[
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\nabla (C_{ij}(\mathbf{r}_{ee})) = \left(\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta x},\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta y},\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta z} \right)
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\]
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and the laplacian is defined as follows:
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\[
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\triangle (C_{ij}(r_{ee})) = \frac{\delta^2}{\delta x^2} + \frac{\delta^2}{\delta y^2} + \frac{\delta^2}{\delta z^2}
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\]
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Using the above three formulae, the expression for the gradient and laplacian is
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as follows:
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\[
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\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta x} = \frac{|(x_i - x_j)|}{r_{ij}} (1 - \kappa R_{ij})
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\]
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\[
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\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta y} = \frac{|(y_i - y_j)|}{r_{ij}} (1 - \kappa R_{ij})
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\]
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\[
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\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta z} = \frac{|(z_i - z_j)|}{r_{ij}} (1 - \kappa R_{ij})
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\]
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\[
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\Delta(C_{ij}(r_{ee}) = \left[ \frac{2}{r_{ij}} - \kappa \right] (1-\kappa R_{ij})
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\]
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If the input array is normal (~'N'~), the xyz coordinates are in
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the leading dimension: ~[n][3]~ in C and ~(3,n)~ in Fortran.
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#+NAME: qmckl_distance_rescaled_deriv_e_args
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| qmckl_context | context | in | Global state |
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| char | transa | in | Array ~A~ is ~'N'~: Normal, ~'T'~: Transposed |
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| char | transb | in | Array ~B~ is ~'N'~: Normal, ~'T'~: Transposed |
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| int64_t | m | in | Number of points in the first set |
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| int64_t | n | in | Number of points in the second set |
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| double | A[][lda] | in | Array containing the $m \times 3$ matrix $A$ |
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| int64_t | lda | in | Leading dimension of array ~A~ |
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| double | B[][ldb] | in | Array containing the $n \times 3$ matrix $B$ |
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| int64_t | ldb | in | Leading dimension of array ~B~ |
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| double | C[4][n][ldc] | out | Array containing the $4 \times m \times n$ matrix $C$ |
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| int64_t | ldc | in | Leading dimension of array ~C~ |
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| double | rescale_factor_kappa | in | Factor for calculating rescaled distances derivatives |
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*** Requirements
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- ~context~ is not ~QMCKL_NULL_CONTEXT~
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- ~m > 0~
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- ~n > 0~
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- ~lda >= 3~ if ~transa == 'N'~
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- ~lda >= m~ if ~transa == 'T'~
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- ~ldb >= 3~ if ~transb == 'N'~
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- ~ldb >= n~ if ~transb == 'T'~
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- ~ldc >= m~
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- ~A~ is allocated with at least $3 \times m \times 8$ bytes
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- ~B~ is allocated with at least $3 \times n \times 8$ bytes
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- ~C~ is allocated with at least $4 \times m \times n \times 8$ bytes
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*** C header
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#+CALL: generate_c_header(table=qmckl_distance_rescaled_deriv_e_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src c :tangle (eval h_func) :comments org
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qmckl_exit_code qmckl_distance_rescaled_deriv_e (
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const qmckl_context context,
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const char transa,
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const char transb,
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const int64_t m,
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const int64_t n,
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const double* A,
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const int64_t lda,
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const double* B,
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const int64_t ldb,
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double* const C,
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const int64_t ldc,
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const double rescale_factor_kappa);
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#+end_src
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*** Source
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#+begin_src f90 :tangle (eval f)
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integer function qmckl_distance_rescaled_deriv_e_f(context, transa, transb, m, n, &
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A, LDA, B, LDB, C, LDC, rescale_factor_kappa) &
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result(info)
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use qmckl
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implicit none
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integer(qmckl_context) , intent(in) :: context
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character , intent(in) :: transa, transb
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integer*8 , intent(in) :: m, n
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integer*8 , intent(in) :: lda
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real*8 , intent(in) :: A(lda,*)
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integer*8 , intent(in) :: ldb
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real*8 , intent(in) :: B(ldb,*)
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integer*8 , intent(in) :: ldc
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real*8 , intent(out) :: C(4,ldc,*)
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real*8 , intent(in) :: rescale_factor_kappa
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integer*8 :: i,j
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real*8 :: x, y, z, dist, dist_inv
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real*8 :: rescale_factor_kappa_inv, rij
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integer :: transab
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rescale_factor_kappa_inv = 1.0d0/rescale_factor_kappa;
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info = QMCKL_SUCCESS
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if (context == QMCKL_NULL_CONTEXT) then
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info = QMCKL_INVALID_CONTEXT
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return
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endif
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if (m <= 0_8) then
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info = QMCKL_INVALID_ARG_4
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return
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endif
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if (n <= 0_8) then
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info = QMCKL_INVALID_ARG_5
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return
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endif
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if (transa == 'N' .or. transa == 'n') then
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transab = 0
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else if (transa == 'T' .or. transa == 't') then
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transab = 1
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else
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transab = -100
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endif
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if (transb == 'N' .or. transb == 'n') then
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continue
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else if (transa == 'T' .or. transa == 't') then
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transab = transab + 2
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else
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transab = -100
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endif
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! check for LDA
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if (transab < 0) then
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info = QMCKL_INVALID_ARG_1
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return
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endif
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if (iand(transab,1) == 0 .and. LDA < 3) then
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info = QMCKL_INVALID_ARG_7
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return
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endif
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if (iand(transab,1) == 1 .and. LDA < m) then
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info = QMCKL_INVALID_ARG_7
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return
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endif
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if (iand(transab,2) == 0 .and. LDA < 3) then
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info = QMCKL_INVALID_ARG_7
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return
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endif
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if (iand(transab,2) == 2 .and. LDA < m) then
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info = QMCKL_INVALID_ARG_7
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return
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endif
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! check for LDB
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if (iand(transab,1) == 0 .and. LDB < 3) then
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info = QMCKL_INVALID_ARG_9
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return
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endif
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if (iand(transab,1) == 1 .and. LDB < n) then
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info = QMCKL_INVALID_ARG_9
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return
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endif
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if (iand(transab,2) == 0 .and. LDB < 3) then
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info = QMCKL_INVALID_ARG_9
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return
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endif
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if (iand(transab,2) == 2 .and. LDB < n) then
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info = QMCKL_INVALID_ARG_9
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return
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endif
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! check for LDC
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if (LDC < m) then
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info = QMCKL_INVALID_ARG_11
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return
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endif
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select case (transab)
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case(0)
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do j=1,n
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do i=1,m
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x = A(1,i) - B(1,j)
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y = A(2,i) - B(2,j)
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z = A(3,i) - B(3,j)
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dist = dsqrt(x*x + y*y + z*z)
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dist_inv = 1.0d0/dist
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rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
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C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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end do
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end do
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case(1)
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do j=1,n
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do i=1,m
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x = A(i,1) - B(1,j)
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y = A(i,2) - B(2,j)
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z = A(i,3) - B(3,j)
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dist = dsqrt(x*x + y*y + z*z)
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dist_inv = 1.0d0/dist
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rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
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C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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end do
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end do
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case(2)
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do j=1,n
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do i=1,m
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x = A(1,i) - B(j,1)
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y = A(2,i) - B(j,2)
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z = A(3,i) - B(j,3)
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dist = dsqrt(x*x + y*y + z*z)
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dist_inv = 1.0d0/dist
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rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
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C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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end do
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end do
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case(3)
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do j=1,n
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do i=1,m
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x = A(i,1) - B(j,1)
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y = A(i,2) - B(j,2)
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z = A(i,3) - B(j,3)
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dist = dsqrt(x*x + y*y + z*z)
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dist_inv = 1.0d0/dist
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rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
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C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
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end do
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end do
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end select
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end function qmckl_distance_rescaled_deriv_e_f
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#+end_src
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*** Performance
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This function is more efficient when ~A~ and ~B~ are transposed.
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** C interface :noexport:
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#+CALL: generate_c_interface(table=qmckl_distance_rescaled_deriv_e_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src f90 :tangle (eval f) :comments org :exports none
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integer(c_int32_t) function qmckl_distance_rescaled_deriv_e &
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(context, transa, transb, m, n, A, lda, B, ldb, C, ldc, rescale_factor_kappa) &
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bind(C) result(info)
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use, intrinsic :: iso_c_binding
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implicit none
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integer (c_int64_t) , intent(in) , value :: context
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character , intent(in) , value :: transa
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character , intent(in) , value :: transb
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integer (c_int64_t) , intent(in) , value :: m
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integer (c_int64_t) , intent(in) , value :: n
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real (c_double ) , intent(in) :: A(lda,*)
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integer (c_int64_t) , intent(in) , value :: lda
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real (c_double ) , intent(in) :: B(ldb,*)
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integer (c_int64_t) , intent(in) , value :: ldb
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real (c_double ) , intent(out) :: C(4,ldc,n)
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integer (c_int64_t) , intent(in) , value :: ldc
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real (c_double ) , intent(in) , value :: rescale_factor_kappa
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integer(c_int32_t), external :: qmckl_distance_rescaled_deriv_e_f
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info = qmckl_distance_rescaled_deriv_e_f &
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(context, transa, transb, m, n, A, lda, B, ldb, C, ldc, rescale_factor_kappa)
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end function qmckl_distance_rescaled_deriv_e
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#+end_src
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#+CALL: generate_f_interface(table=qmckl_distance_rescaled_deriv_e_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
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#+RESULTS:
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#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
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interface
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integer(c_int32_t) function qmckl_distance_rescaled_deriv_e &
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(context, transa, transb, m, n, A, lda, B, ldb, C, ldc, rescale_factor_kappa) &
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bind(C)
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use, intrinsic :: iso_c_binding
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import
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implicit none
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integer (c_int64_t) , intent(in) , value :: context
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character , intent(in) , value :: transa
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character , intent(in) , value :: transb
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integer (c_int64_t) , intent(in) , value :: m
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integer (c_int64_t) , intent(in) , value :: n
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real (c_double ) , intent(in) :: A(lda,*)
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integer (c_int64_t) , intent(in) , value :: lda
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real (c_double ) , intent(in) :: B(ldb,*)
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integer (c_int64_t) , intent(in) , value :: ldb
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real (c_double ) , intent(out) :: C(4,ldc,n)
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integer (c_int64_t) , intent(in) , value :: ldc
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real (c_double ) , intent(in) , value :: rescale_factor_kappa
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end function qmckl_distance_rescaled_deriv_e
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end interface
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#+end_src
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* End of files :noexport:
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#+begin_src c :comments link :tangle (eval c_test)
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