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< h1 class = "title" > Inter-particle distances< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org41f5cd4" > 1. Squared distance< / a >
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< ul >
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< li > < a href = "#orga341d9b" > 1.1. < code > qmckl_distance_sq< / code > < / a >
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< ul >
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< li > < a href = "#org8e3601b" > 1.1.1. Performance< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
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< li > < a href = "#org1dd726e" > 2. Distance< / a >
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< ul >
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< li > < a href = "#org50962f3" > 2.1. < code > qmckl_distance< / code > < / a >
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< ul >
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< li > < a href = "#org5c62cbe" > 2.1.1. Requirements< / a > < / li >
< li > < a href = "#orgb166008" > 2.1.2. C header< / a > < / li >
< li > < a href = "#org341b437" > 2.1.3. Source< / a > < / li >
< li > < a href = "#orgaee353c" > 2.1.4. Performance< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
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< li > < a href = "#org508d7b6" > 3. Rescaled Distance< / a >
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< ul >
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< li > < a href = "#org41c1072" > 3.1. < code > qmckl_distance_rescaled< / code > < / a >
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< ul >
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< li > < a href = "#org1a3fcea" > 3.1.1. Requirements< / a > < / li >
< li > < a href = "#org41fbb84" > 3.1.2. C header< / a > < / li >
< li > < a href = "#org98b3fc8" > 3.1.3. Source< / a > < / li >
< li > < a href = "#org6a8051b" > 3.1.4. Performance< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
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< li > < a href = "#org0aa544a" > 4. Rescaled Distance Derivatives< / a >
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< ul >
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< li > < a href = "#orgbeb1322" > 4.1. < code > qmckl_distance_rescaled_deriv_e< / code > < / a > < / li >
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< / ul >
< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-org41f5cd4" class = "outline-2" >
< h2 id = "org41f5cd4" > < span class = "section-number-2" > 1< / span > Squared distance< / h2 >
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< / div >
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< h3 id = "orga341d9b" > < span class = "section-number-3" > 1.1< / span > < code > qmckl_distance_sq< / code > < / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< p >
< code > qmckl_distance_sq< / code > computes the matrix of the squared distances
between all pairs of points in two sets, one point within each set:
< / p >
< p >
\[
C_{ij} = \sum_{k=1}^3 (A_{k,i}-B_{k,j})^2
\]
< / p >
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< tr >
< th scope = "col" class = "org-left" > Variable< / th >
< th scope = "col" class = "org-left" > Type< / th >
< th scope = "col" class = "org-left" > In/Out< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
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< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
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< / tr >
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< td class = "org-left" > < code > transb< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
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< td class = "org-left" > < code > n< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
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< td class = "org-left" > < code > B< / code > < / td >
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< td class = "org-left" > in< / td >
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< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > C< / code > < / td >
< td class = "org-left" > < code > double[n][ldc]< / code > < / td >
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< td class = "org-left" > out< / td >
< td class = "org-left" > Array containing the \(m \times n\) matrix \(C\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > C< / code > < / td >
< / tr >
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< p >
Requirements:
< / p >
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< ul class = "org-ul" >
< li > < code > context< / code > is not < code > QMCKL_NULL_CONTEXT< / code > < / li >
< li > < code > m > 0< / code > < / li >
< li > < code > n > 0< / code > < / li >
< li > < code > lda > = 3< / code > if < code > transa == 'N'< / code > < / li >
< li > < code > lda > = m< / code > if < code > transa == 'T'< / code > < / li >
< li > < code > ldb > = 3< / code > if < code > transb == 'N'< / code > < / li >
< li > < code > ldb > = n< / code > if < code > transb == 'T'< / code > < / li >
< li > < code > ldc > = m< / code > < / li >
< li > < code > A< / code > is allocated with at least \(3 \times m \times 8\) bytes< / li >
< li > < code > B< / code > is allocated with at least \(3 \times n \times 8\) bytes< / li >
< li > < code > C< / code > is allocated with at least \(m \times n \times 8\) bytes< / li >
< / ul >
< div class = "org-src-container" >
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< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance_sq< / span > (
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transa< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transb< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > m< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > n< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > A< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > lda< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > B< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldb< / span > ,
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< span style = "color: #228b22;" > double< / span > * < span style = "color: #a020f0;" > const< / span > < span style = "color: #a0522d;" > C< / span > ,
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldc< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-f90" > < span style = "color: #228b22;" > integer< / span > < span style = "color: #a0522d;" > function qmckl_distance_sq_f(context, transa, transb, m, n, < / span > < span style = "color: #a020f0;" > & < / span >
A, LDA, B, LDB, C, LDC) < span style = "color: #a020f0;" > & < / span >
< span style = "color: #a020f0;" > result< / span > (info)
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< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl< / span >
< span style = "color: #a020f0;" > implicit< / span > < span style = "color: #228b22;" > none< / span >
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< span style = "color: #228b22;" > integer< / span > (qmckl_context) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > context< / span >
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< span style = "color: #228b22;" > character< / span > , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > transa, transb< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > m, n< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldc< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(ldc,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 ::< span style = "color: #a0522d;" > i,j< / span >
< span style = "color: #228b22;" > real< / span > *8 ::< span style = "color: #a0522d;" > x, y, z< / span >
< span style = "color: #228b22;" > integer< / span > ::< span style = "color: #a0522d;" > transab< / span >
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info = QMCKL_SUCCESS
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< span style = "color: #a020f0;" > if< / span > (context == QMCKL_NULL_CONTEXT) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_CONTEXT
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (m < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_4
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (n < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_5
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transa == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 0
< span style = "color: #a020f0;" > else if< / span > (transa == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 1
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transb == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
< span style = "color: #a020f0;" > continue< / span >
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< span style = "color: #a020f0;" > else if< / span > (transb == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
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transab = transab + 2
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transab < 0) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_1
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< span style = "color: #a020f0;" > return< / span >
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< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 1 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 2 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > select case< / span > (transab)
< span style = "color: #a020f0;" > case< / span > (0)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (1)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (2)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (3)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end select< / span >
< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance_sq_f< / span >
< / pre >
< / div >
< / div >
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< div id = "outline-container-org8e3601b" class = "outline-4" >
< h4 id = "org8e3601b" > < span class = "section-number-4" > 1.1.1< / span > Performance< / h4 >
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< div class = "outline-text-4" id = "text-1-1-1" >
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< p >
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This function is more efficient when < code > A< / code > and < code > B< / code > are
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transposed.
< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org1dd726e" class = "outline-2" >
< h2 id = "org1dd726e" > < span class = "section-number-2" > 2< / span > Distance< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< / div >
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< div id = "outline-container-org50962f3" class = "outline-3" >
< h3 id = "org50962f3" > < span class = "section-number-3" > 2.1< / span > < code > qmckl_distance< / code > < / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
< p >
< code > qmckl_distance< / code > computes the matrix of the distances between all
pairs of points in two sets, one point within each set:
< / p >
< p >
\[
C_{ij} = \sqrt{\sum_{k=1}^3 (A_{k,i}-B_{k,j})^2}
\]
< / p >
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< p >
If the input array is normal (< code > 'N'< / code > ), the xyz coordinates are in
the leading dimension: < code > [n][3]< / code > in C and < code > (3,n)< / code > in Fortran.
< / p >
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< table id = "org1e092a9" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
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< thead >
< tr >
< th scope = "col" class = "org-left" > Variable< / th >
< th scope = "col" class = "org-left" > Type< / th >
< th scope = "col" class = "org-left" > In/Out< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
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< tbody >
< tr >
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< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Global state< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > transa< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array < code > A< / code > is < code > 'N'< / code > : Normal, < code > 'T'< / code > : Transposed< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > transb< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array < code > B< / code > is < code > 'N'< / code > : Normal, < code > 'T'< / code > : Transposed< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > m< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > n< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > A< / code > < / td >
< td class = "org-left" > < code > double[][lda]< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(m \times 3\) matrix \(A\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > lda< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > A< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > B< / code > < / td >
< td class = "org-left" > < code > double[][ldb]< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(n \times 3\) matrix \(B\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > ldb< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > C< / code > < / td >
< td class = "org-left" > < code > double[n][ldc]< / code > < / td >
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< td class = "org-left" > out< / td >
< td class = "org-left" > Array containing the \(m \times n\) matrix \(C\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > C< / code > < / td >
< / tr >
< / tbody >
< / table >
< / div >
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< div id = "outline-container-org5c62cbe" class = "outline-4" >
< h4 id = "org5c62cbe" > < span class = "section-number-4" > 2.1.1< / span > Requirements< / h4 >
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< div class = "outline-text-4" id = "text-2-1-1" >
< ul class = "org-ul" >
< li > < code > context< / code > is not < code > QMCKL_NULL_CONTEXT< / code > < / li >
< li > < code > m > 0< / code > < / li >
< li > < code > n > 0< / code > < / li >
< li > < code > lda > = 3< / code > if < code > transa == 'N'< / code > < / li >
< li > < code > lda > = m< / code > if < code > transa == 'T'< / code > < / li >
< li > < code > ldb > = 3< / code > if < code > transb == 'N'< / code > < / li >
< li > < code > ldb > = n< / code > if < code > transb == 'T'< / code > < / li >
< li > < code > ldc > = m< / code > < / li >
< li > < code > A< / code > is allocated with at least \(3 \times m \times 8\) bytes< / li >
< li > < code > B< / code > is allocated with at least \(3 \times n \times 8\) bytes< / li >
< li > < code > C< / code > is allocated with at least \(m \times n \times 8\) bytes< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-orgb166008" class = "outline-4" >
< h4 id = "orgb166008" > < span class = "section-number-4" > 2.1.2< / span > C header< / h4 >
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< div class = "outline-text-4" id = "text-2-1-2" >
< div class = "org-src-container" >
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< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance< / span > (
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transa< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transb< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > m< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > n< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > A< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > lda< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > B< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldb< / span > ,
< span style = "color: #228b22;" > double< / span > * < span style = "color: #a020f0;" > const< / span > < span style = "color: #a0522d;" > C< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldc< / span > );
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org341b437" class = "outline-4" >
< h4 id = "org341b437" > < span class = "section-number-4" > 2.1.3< / span > Source< / h4 >
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< div class = "outline-text-4" id = "text-2-1-3" >
< div class = "org-src-container" >
< pre class = "src src-f90" > < span style = "color: #228b22;" > integer< / span > < span style = "color: #a0522d;" > function qmckl_distance_f(context, transa, transb, m, n, < / span > < span style = "color: #a020f0;" > & < / span >
A, LDA, B, LDB, C, LDC) < span style = "color: #a020f0;" > & < / span >
< span style = "color: #a020f0;" > result< / span > (info)
< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl< / span >
< span style = "color: #a020f0;" > implicit< / span > < span style = "color: #228b22;" > none< / span >
< span style = "color: #228b22;" > integer< / span > (qmckl_context) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > context< / span >
< span style = "color: #228b22;" > character< / span > , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > transa, transb< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > m, n< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldc< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(ldc,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 ::< span style = "color: #a0522d;" > i,j< / span >
< span style = "color: #228b22;" > real< / span > *8 ::< span style = "color: #a0522d;" > x, y, z< / span >
< span style = "color: #228b22;" > integer< / span > ::< span style = "color: #a0522d;" > transab< / span >
info = QMCKL_SUCCESS
< span style = "color: #a020f0;" > if< / span > (context == QMCKL_NULL_CONTEXT) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_CONTEXT
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (m < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_4
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (n < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_5
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transa == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 0
< span style = "color: #a020f0;" > else if< / span > (transa == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 1
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transb == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
< span style = "color: #a020f0;" > continue< / span >
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< span style = "color: #a020f0;" > else if< / span > (transb == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
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transab = transab + 2
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transab < 0) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_1
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< span style = "color: #a020f0;" > return< / span >
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< span style = "color: #a020f0;" > endif< / span >
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! < span style = "color: #b22222;" > check for LDA< / span >
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< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 1 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 2 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
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! < span style = "color: #b22222;" > check for LDB< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 0 < span style = "color: #a020f0;" > .and.< / span > LDB < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 1 < span style = "color: #a020f0;" > .and.< / span > LDB < n) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 0 < span style = "color: #a020f0;" > .and.< / span > LDB < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 2 < span style = "color: #a020f0;" > .and.< / span > LDB < n) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDC< / span >
< span style = "color: #a020f0;" > if< / span > (LDC < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_11
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
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< span style = "color: #a020f0;" > select case< / span > (transab)
< span style = "color: #a020f0;" > case< / span > (0)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
C(:,j) = dsqrt(C(:,j))
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (1)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
C(:,j) = dsqrt(C(:,j))
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (2)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
C(:,j) = dsqrt(C(:,j))
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (3)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
C(:,j) = dsqrt(C(:,j))
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end select< / span >
< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance_f< / span >
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgaee353c" class = "outline-4" >
< h4 id = "orgaee353c" > < span class = "section-number-4" > 2.1.4< / span > Performance< / h4 >
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< div class = "outline-text-4" id = "text-2-1-4" >
< p >
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This function is more efficient when < code > A< / code > and < code > B< / code > are transposed.
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< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org508d7b6" class = "outline-2" >
< h2 id = "org508d7b6" > < span class = "section-number-2" > 3< / span > Rescaled Distance< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< / div >
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< div id = "outline-container-org41c1072" class = "outline-3" >
< h3 id = "org41c1072" > < span class = "section-number-3" > 3.1< / span > < code > qmckl_distance_rescaled< / code > < / h3 >
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< div class = "outline-text-3" id = "text-3-1" >
< p >
< code > qmckl_distance_rescaled< / code > computes the matrix of the rescaled distances between all
pairs of points in two sets, one point within each set:
< / p >
< p >
\[
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C_{ij} = \left( 1 - \exp \left(-\kappa C_{ij} \right) \right)/\kappa
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\]
< / p >
< p >
If the input array is normal (< code > 'N'< / code > ), the xyz coordinates are in
the leading dimension: < code > [n][3]< / code > in C and < code > (3,n)< / code > in Fortran.
< / p >
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< table id = "org4f24625" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
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< thead >
< tr >
< th scope = "col" class = "org-left" > Variable< / th >
< th scope = "col" class = "org-left" > Type< / th >
< th scope = "col" class = "org-left" > In/Out< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
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< tbody >
< tr >
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< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Global state< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > transa< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array < code > A< / code > is < code > 'N'< / code > : Normal, < code > 'T'< / code > : Transposed< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > transb< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array < code > B< / code > is < code > 'N'< / code > : Normal, < code > 'T'< / code > : Transposed< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > m< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > n< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > A< / code > < / td >
< td class = "org-left" > < code > double[][lda]< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(m \times 3\) matrix \(A\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > lda< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > A< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > B< / code > < / td >
< td class = "org-left" > < code > double[][ldb]< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(n \times 3\) matrix \(B\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > ldb< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > C< / code > < / td >
< td class = "org-left" > < code > double[n][ldc]< / code > < / td >
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< td class = "org-left" > out< / td >
< td class = "org-left" > Array containing the \(m \times n\) matrix \(C\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > C< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > rescale_factor_kappa< / code > < / td >
< td class = "org-left" > < code > double< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Factor for calculating rescaled distances< / td >
< / tr >
< / tbody >
< / table >
< / div >
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< div id = "outline-container-org1a3fcea" class = "outline-4" >
< h4 id = "org1a3fcea" > < span class = "section-number-4" > 3.1.1< / span > Requirements< / h4 >
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< div class = "outline-text-4" id = "text-3-1-1" >
< ul class = "org-ul" >
< li > < code > context< / code > is not < code > QMCKL_NULL_CONTEXT< / code > < / li >
< li > < code > m > 0< / code > < / li >
< li > < code > n > 0< / code > < / li >
< li > < code > lda > = 3< / code > if < code > transa == 'N'< / code > < / li >
< li > < code > lda > = m< / code > if < code > transa == 'T'< / code > < / li >
< li > < code > ldb > = 3< / code > if < code > transb == 'N'< / code > < / li >
< li > < code > ldb > = n< / code > if < code > transb == 'T'< / code > < / li >
< li > < code > ldc > = m< / code > < / li >
< li > < code > A< / code > is allocated with at least \(3 \times m \times 8\) bytes< / li >
< li > < code > B< / code > is allocated with at least \(3 \times n \times 8\) bytes< / li >
< li > < code > C< / code > is allocated with at least \(m \times n \times 8\) bytes< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-org41fbb84" class = "outline-4" >
< h4 id = "org41fbb84" > < span class = "section-number-4" > 3.1.2< / span > C header< / h4 >
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< div class = "outline-text-4" id = "text-3-1-2" >
< div class = "org-src-container" >
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< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled< / span > (
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transa< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transb< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > m< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > n< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > A< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > lda< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > B< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldb< / span > ,
< span style = "color: #228b22;" > double< / span > * < span style = "color: #a020f0;" > const< / span > < span style = "color: #a0522d;" > C< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldc< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > < span style = "color: #a0522d;" > rescale_factor_kappa< / span > );
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org98b3fc8" class = "outline-4" >
< h4 id = "org98b3fc8" > < span class = "section-number-4" > 3.1.3< / span > Source< / h4 >
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< div class = "outline-text-4" id = "text-3-1-3" >
< div class = "org-src-container" >
< pre class = "src src-f90" > < span style = "color: #228b22;" > integer< / span > < span style = "color: #a0522d;" > function qmckl_distance_rescaled_f(context, transa, transb, m, n, < / span > < span style = "color: #a020f0;" > & < / span >
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) < span style = "color: #a020f0;" > & < / span >
< span style = "color: #a020f0;" > result< / span > (info)
< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl< / span >
< span style = "color: #a020f0;" > implicit< / span > < span style = "color: #228b22;" > none< / span >
< span style = "color: #228b22;" > integer< / span > (qmckl_context) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > context< / span >
< span style = "color: #228b22;" > character< / span > , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > transa, transb< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > m, n< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldc< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(ldc,*)< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > rescale_factor_kappa< / span >
< span style = "color: #228b22;" > integer< / span > *8 ::< span style = "color: #a0522d;" > i,j< / span >
< span style = "color: #228b22;" > real< / span > *8 ::< span style = "color: #a0522d;" > x, y, z, dist, rescale_factor_kappa_inv< / span >
< span style = "color: #228b22;" > integer< / span > ::< span style = "color: #a0522d;" > transab< / span >
rescale_factor_kappa_inv = 1.0d0/rescale_factor_kappa;
info = QMCKL_SUCCESS
< span style = "color: #a020f0;" > if< / span > (context == QMCKL_NULL_CONTEXT) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_CONTEXT
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (m < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_4
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (n < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_5
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transa == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 0
< span style = "color: #a020f0;" > else if< / span > (transa == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 1
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transb == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
< span style = "color: #a020f0;" > continue< / span >
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< span style = "color: #a020f0;" > else if< / span > (transb == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
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transab = transab + 2
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDA< / span >
< span style = "color: #a020f0;" > if< / span > (transab < 0) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_1
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 1 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 2 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDB< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 0 < span style = "color: #a020f0;" > .and.< / span > LDB < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 1 < span style = "color: #a020f0;" > .and.< / span > LDB < n) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 0 < span style = "color: #a020f0;" > .and.< / span > LDB < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 2 < span style = "color: #a020f0;" > .and.< / span > LDB < n) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDC< / span >
< span style = "color: #a020f0;" > if< / span > (LDC < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_11
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > select case< / span > (transab)
< span style = "color: #a020f0;" > case< / span > (0)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (1)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (2)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (3)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end select< / span >
< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled_f< / span >
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org6a8051b" class = "outline-4" >
< h4 id = "org6a8051b" > < span class = "section-number-4" > 3.1.4< / span > Performance< / h4 >
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< div class = "outline-text-4" id = "text-3-1-4" >
< p >
This function is more efficient when < code > A< / code > and < code > B< / code > are transposed.
< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org0aa544a" class = "outline-2" >
< h2 id = "org0aa544a" > < span class = "section-number-2" > 4< / span > Rescaled Distance Derivatives< / h2 >
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< div class = "outline-text-2" id = "text-4" >
< / div >
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< div id = "outline-container-orgbeb1322" class = "outline-3" >
< h3 id = "orgbeb1322" > < span class = "section-number-3" > 4.1< / span > < code > qmckl_distance_rescaled_deriv_e< / code > < / h3 >
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< div class = "outline-text-3" id = "text-4-1" >
< p >
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< code > qmckl_distance_rescaled_deriv_e< / code > 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.
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.
< / p >
< p >
\[
C_{ij} = \left( 1 - \exp{-\kappa C_{ij}}\right)/\kappa
\]
< / p >
< p >
Here the gradient is defined as follows:
< / p >
< p >
\[
\nabla (C_{ij}(\mathbf{r}_{ee})) = \left(\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta x},\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta y},\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta z} \right)
\]
and the laplacian is defined as follows:
< / p >
< p >
\[
\triangle (C_{ij}(r_{ee})) = \frac{\delta^2}{\delta x^2} + \frac{\delta^2}{\delta y^2} + \frac{\delta^2}{\delta z^2}
\]
< / p >
< p >
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Using the above three formulae, the expression for the gradient and laplacian is
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as follows:
< / p >
< p >
\[
\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta x} = \frac{|(x_i - x_j)|}{r_{ij}} (1 - \kappa R_{ij})
\]
< / p >
< p >
\[
\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta y} = \frac{|(y_i - y_j)|}{r_{ij}} (1 - \kappa R_{ij})
\]
< / p >
< p >
\[
\frac{\delta C_{ij}(\mathbf{r}_{ee})}{\delta z} = \frac{|(z_i - z_j)|}{r_{ij}} (1 - \kappa R_{ij})
\]
< / p >
< p >
\[
\Delta(C_{ij}(r_{ee}) = \left[ \frac{2}{r_{ij}} - \kappa \right] (1-\kappa R_{ij})
\]
< / p >
< p >
If the input array is normal (< code > 'N'< / code > ), the xyz coordinates are in
the leading dimension: < code > [n][3]< / code > in C and < code > (3,n)< / code > in Fortran.
< / p >
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< table id = "orgf471b89" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
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< thead >
< tr >
< th scope = "col" class = "org-left" > Variable< / th >
< th scope = "col" class = "org-left" > Type< / th >
< th scope = "col" class = "org-left" > In/Out< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
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< tbody >
< tr >
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< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Global state< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > transa< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array < code > A< / code > is < code > 'N'< / code > : Normal, < code > 'T'< / code > : Transposed< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > transb< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array < code > B< / code > is < code > 'N'< / code > : Normal, < code > 'T'< / code > : Transposed< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > m< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > n< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > A< / code > < / td >
< td class = "org-left" > < code > double[][lda]< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(m \times 3\) matrix \(A\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > lda< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > A< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > B< / code > < / td >
< td class = "org-left" > < code > double[][ldb]< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(n \times 3\) matrix \(B\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > ldb< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > C< / code > < / td >
< td class = "org-left" > < code > double[4][n][ldc]< / code > < / td >
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< td class = "org-left" > out< / td >
< td class = "org-left" > Array containing the \(4 \times m \times n\) matrix \(C\)< / td >
< / tr >
< tr >
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< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > C< / code > < / td >
< / tr >
< tr >
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< td class = "org-left" > < code > rescale_factor_kappa< / code > < / td >
< td class = "org-left" > < code > double< / code > < / td >
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< td class = "org-left" > in< / td >
< td class = "org-left" > Factor for calculating rescaled distances derivatives< / td >
< / tr >
< / tbody >
< / table >
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< p >
Requirements:
< / p >
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< ul class = "org-ul" >
< li > < code > context< / code > is not < code > QMCKL_NULL_CONTEXT< / code > < / li >
< li > < code > m > 0< / code > < / li >
< li > < code > n > 0< / code > < / li >
< li > < code > lda > = 3< / code > if < code > transa == 'N'< / code > < / li >
< li > < code > lda > = m< / code > if < code > transa == 'T'< / code > < / li >
< li > < code > ldb > = 3< / code > if < code > transb == 'N'< / code > < / li >
< li > < code > ldb > = n< / code > if < code > transb == 'T'< / code > < / li >
< li > < code > ldc > = m< / code > < / li >
< li > < code > A< / code > is allocated with at least \(3 \times m \times 8\) bytes< / li >
< li > < code > B< / code > is allocated with at least \(3 \times n \times 8\) bytes< / li >
< li > < code > C< / code > is allocated with at least \(4 \times m \times n \times 8\) bytes< / li >
< / ul >
< div class = "org-src-container" >
< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled_deriv_e< / span > (
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transa< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > char< / span > < span style = "color: #a0522d;" > transb< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > m< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > n< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > A< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > lda< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > * < span style = "color: #a0522d;" > B< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldb< / span > ,
< span style = "color: #228b22;" > double< / span > * < span style = "color: #a020f0;" > const< / span > < span style = "color: #a0522d;" > C< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > int64_t< / span > < span style = "color: #a0522d;" > ldc< / span > ,
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > double< / span > < span style = "color: #a0522d;" > rescale_factor_kappa< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-f90" > < span style = "color: #228b22;" > integer< / span > < span style = "color: #a0522d;" > function qmckl_distance_rescaled_deriv_e_f(context, transa, transb, m, n, < / span > < span style = "color: #a020f0;" > & < / span >
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) < span style = "color: #a020f0;" > & < / span >
< span style = "color: #a020f0;" > result< / span > (info)
< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl< / span >
< span style = "color: #a020f0;" > implicit< / span > < span style = "color: #228b22;" > none< / span >
< span style = "color: #228b22;" > integer< / span > (qmckl_context) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > context< / span >
< span style = "color: #228b22;" > character< / span > , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > transa, transb< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > m, n< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > integer< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > ldc< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(4,ldc,*)< / span >
< span style = "color: #228b22;" > real< / span > *8 , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > rescale_factor_kappa< / span >
< span style = "color: #228b22;" > integer< / span > *8 ::< span style = "color: #a0522d;" > i,j< / span >
< span style = "color: #228b22;" > real< / span > *8 ::< span style = "color: #a0522d;" > x, y, z, dist, dist_inv< / span >
< span style = "color: #228b22;" > real< / span > *8 ::< span style = "color: #a0522d;" > rescale_factor_kappa_inv, rij< / span >
< span style = "color: #228b22;" > integer< / span > ::< span style = "color: #a0522d;" > transab< / span >
rescale_factor_kappa_inv = 1.0d0/rescale_factor_kappa;
info = QMCKL_SUCCESS
< span style = "color: #a020f0;" > if< / span > (context == QMCKL_NULL_CONTEXT) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_CONTEXT
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (m < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_4
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (n < = 0_8) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_5
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transa == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 0
< span style = "color: #a020f0;" > else if< / span > (transa == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transa == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
transab = 1
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (transb == < span style = "color: #8b2252;" > 'N'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 'n'< / span > ) < span style = "color: #a020f0;" > then< / span >
< span style = "color: #a020f0;" > continue< / span >
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< span style = "color: #a020f0;" > else if< / span > (transb == < span style = "color: #8b2252;" > 'T'< / span > < span style = "color: #a020f0;" > .or.< / span > transb == < span style = "color: #8b2252;" > 't'< / span > ) < span style = "color: #a020f0;" > then< / span >
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transab = transab + 2
< span style = "color: #a020f0;" > else< / span >
transab = -100
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDA< / span >
< span style = "color: #a020f0;" > if< / span > (transab < 0) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_1
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 1 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 0 < span style = "color: #a020f0;" > .and.< / span > LDA < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 2 < span style = "color: #a020f0;" > .and.< / span > LDA < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDB< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 0 < span style = "color: #a020f0;" > .and.< / span > LDB < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,1) == 1 < span style = "color: #a020f0;" > .and.< / span > LDB < n) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 0 < span style = "color: #a020f0;" > .and.< / span > LDB < 3) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > if< / span > (< span style = "color: #a020f0;" > iand< / span > (transab,2) == 2 < span style = "color: #a020f0;" > .and.< / span > LDB < n) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_9
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDC< / span >
< span style = "color: #a020f0;" > if< / span > (LDC < m) < span style = "color: #a020f0;" > then< / span >
info = QMCKL_INVALID_ARG_11
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
< span style = "color: #a020f0;" > select case< / span > (transab)
< span style = "color: #a020f0;" > case< / span > (0)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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)
dist_inv = 1.0d0/dist
rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (1)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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)
dist_inv = 1.0d0/dist
rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (2)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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)
dist_inv = 1.0d0/dist
rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > case< / span > (3)
< span style = "color: #a020f0;" > do< / span > j=1,n
< span style = "color: #a020f0;" > do< / span > 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)
dist_inv = 1.0d0/dist
rij = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
C(1,i,j) = x * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(2,i,j) = y * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(3,i,j) = z * dist_inv * ( 1.0d0 - rescale_factor_kappa_inv * rij)
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa_inv) * ( 1.0d0 - rescale_factor_kappa_inv * rij)
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end select< / span >
< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled_deriv_e_f< / span >
< / pre >
< / div >
< p >
This function is more efficient when < code > A< / code > and < code > B< / code > are transposed.
< / p >
< / div >
< / div >
< / div >
< / div >
2021-03-23 22:25:11 +01:00
< div id = "postamble" class = "status" >
2021-04-30 01:35:52 +02:00
< p class = "author" > Author: TREX CoE< / p >
2022-07-27 19:32:22 +02:00
< p class = "date" > Created: 2022-07-27 Wed 17:32< / p >
2021-03-23 22:25:11 +01:00
< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
