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|
< a accesskey = "H" href = "index.html" > HOME < / a >
< / div > < div id = "content" >
< 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 = "#orgf24c27b" > 1. Squared distance< / a >
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< ul >
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< li > < a href = "#org461e1e0" > 1.1. < code > qmckl_distance_sq< / code > < / a >
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< ul >
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< li > < a href = "#orgedc24a4" > 1.1.1. Performance< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
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< li > < a href = "#orgc681e01" > 2. Distance< / a >
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< ul >
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< li > < a href = "#org085deae" > 2.1. < code > qmckl_distance< / code > < / a >
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< ul >
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< li > < a href = "#org3b8e990" > 2.1.1. Requirements< / a > < / li >
< li > < a href = "#orgaf8bb31" > 2.1.2. C header< / a > < / li >
< li > < a href = "#org07619a8" > 2.1.3. Source< / a > < / li >
< li > < a href = "#org5c5d94c" > 2.1.4. Performance< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
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< li > < a href = "#orga17f9cf" > 3. Rescaled Distance< / a >
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< ul >
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< li > < a href = "#org535ebf2" > 3.1. < code > qmckl_distance_rescaled< / code > < / a >
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< ul >
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< li > < a href = "#org33b32bd" > 3.1.1. Requirements< / a > < / li >
< li > < a href = "#orge0285fb" > 3.1.2. C header< / a > < / li >
< li > < a href = "#org61f6138" > 3.1.3. Source< / a > < / li >
< li > < a href = "#org9ad623d" > 3.1.4. Performance< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
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< li > < a href = "#org672c272" > 4. Rescaled Distance Derivatives< / a >
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< ul >
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< li > < a href = "#orgfecb018" > 4.1. < code > qmckl_distance_rescaled_gl< / code > < / a > < / li >
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< / ul >
< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-orgf24c27b" class = "outline-2" >
< h2 id = "orgf24c27b" > < span class = "section-number-2" > 1< / span > Squared distance< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< / div >
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< div id = "outline-container-org461e1e0" class = "outline-3" >
< h3 id = "org461e1e0" > < 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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< 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 >
< tbody >
< tr >
< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Global state< / td >
< / tr >
< tr >
< td class = "org-left" > < code > transa< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
< 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 >
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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 >
< td class = "org-left" > < code > m< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > n< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > A< / code > < / td >
< td class = "org-left" > < code > double[][lda]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(m \times 3\) matrix \(A\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > lda< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > A< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > B< / code > < / td >
< td class = "org-left" > < code > double[][ldb]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(n \times 3\) matrix \(B\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > ldb< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > C< / code > < / td >
< td class = "org-left" > < code > double[n][ldc]< / code > < / td >
< td class = "org-left" > out< / td >
< td class = "org-left" > Array containing the \(m \times n\) matrix \(C\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > C< / code > < / td >
< / tr >
< / tbody >
< / table >
< p >
Requirements:
< / p >
< 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" >
< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance_sq< / span > (
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
< 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 class = "org-src-container" >
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< pre class = "src src-f90" > < span style = "color: #a020f0;" > function< / span > < span style = "color: #0000ff;" > qmckl_distance_sq< / span > (context, transa, transb, m, n, < span style = "color: #a020f0;" > & < / span >
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A, LDA, B, LDB, C, LDC) < span style = "color: #a020f0;" > & < / span >
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< span style = "color: #a020f0;" > bind< / span > (C) < span style = "color: #a020f0;" > result< / span > (info)
< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl_constants< / span >
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< 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: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > context< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transa< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > m< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > n< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldc< / span >
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< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(ldc,n)< / span >
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< span style = "color: #228b22;" > integer< / span > (qmckl_exit_code) ::< span style = "color: #a0522d;" > info< / span >
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< 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 >
< 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 >
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
< 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 >
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< 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 >
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info = QMCKL_INVALID_ARG_7
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
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< 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 >
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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 >
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< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance_sq< / span >
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< / pre >
< / div >
< / div >
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< div id = "outline-container-orgedc24a4" class = "outline-4" >
< h4 id = "orgedc24a4" > < 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" >
< 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-orgc681e01" class = "outline-2" >
< h2 id = "orgc681e01" > < 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-org085deae" class = "outline-3" >
< h3 id = "org085deae" > < 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 >
< 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 = "org6dbdfc4" 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 >
< 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 >
< tbody >
< tr >
< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Global state< / td >
< / tr >
< tr >
< td class = "org-left" > < code > transa< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
< 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 >
< td class = "org-left" > < code > transb< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
< 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 >
< td class = "org-left" > < code > m< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > n< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > A< / code > < / td >
< td class = "org-left" > < code > double[][lda]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(m \times 3\) matrix \(A\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > lda< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > A< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > B< / code > < / td >
< td class = "org-left" > < code > double[][ldb]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(n \times 3\) matrix \(B\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > ldb< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > C< / code > < / td >
< td class = "org-left" > < code > double[n][ldc]< / code > < / td >
< td class = "org-left" > out< / td >
< td class = "org-left" > Array containing the \(m \times n\) matrix \(C\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< 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-org3b8e990" class = "outline-4" >
< h4 id = "org3b8e990" > < 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-orgaf8bb31" class = "outline-4" >
< h4 id = "orgaf8bb31" > < 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" >
< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance< / span > (
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
< 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-org07619a8" class = "outline-4" >
< h4 id = "org07619a8" > < 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" >
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< pre class = "src src-f90" > < span style = "color: #a020f0;" > function< / span > < span style = "color: #0000ff;" > qmckl_distance< / span > (context, transa, transb, m, n, < span style = "color: #a020f0;" > & < / span >
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A, LDA, B, LDB, C, LDC) < span style = "color: #a020f0;" > & < / span >
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< span style = "color: #a020f0;" > bind< / span > (C) < span style = "color: #a020f0;" > result< / span > (info)
< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl_constants< / span >
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< 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: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > context< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transa< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > m< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > n< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldc< / span >
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< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(ldc,n)< / span >
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< span style = "color: #228b22;" > integer< / span > (qmckl_exit_code) ::< span style = "color: #a0522d;" > info< / span >
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< 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 >
< 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 >
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
< span style = "color: #a020f0;" > return< / span >
< span style = "color: #a020f0;" > endif< / span >
! < span style = "color: #b22222;" > check for LDA< / 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: #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: #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)
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 >
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< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance< / span >
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org5c5d94c" class = "outline-4" >
< h4 id = "org5c5d94c" > < 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 >
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-orga17f9cf" class = "outline-2" >
< h2 id = "orga17f9cf" > < 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-org535ebf2" class = "outline-3" >
< h3 id = "org535ebf2" > < 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 >
\[
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C_{ij} = \frac{ 1 - e^{-\kappa r_{ij}}}{\kappa}
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\]
< / 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 = "org1061984" 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 >
< 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 >
< tbody >
< tr >
< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Global state< / td >
< / tr >
< tr >
< td class = "org-left" > < code > transa< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
< 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 >
< td class = "org-left" > < code > transb< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
< 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 >
< td class = "org-left" > < code > m< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > n< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > A< / code > < / td >
< td class = "org-left" > < code > double[][lda]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(m \times 3\) matrix \(A\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > lda< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > A< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > B< / code > < / td >
< td class = "org-left" > < code > double[][ldb]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(n \times 3\) matrix \(B\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > ldb< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > C< / code > < / td >
< td class = "org-left" > < code > double[n][ldc]< / code > < / td >
< td class = "org-left" > out< / td >
< td class = "org-left" > Array containing the \(m \times n\) matrix \(C\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > C< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > rescale_factor_kappa< / code > < / td >
< td class = "org-left" > < code > double< / code > < / td >
< 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-org33b32bd" class = "outline-4" >
< h4 id = "org33b32bd" > < 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-orge0285fb" class = "outline-4" >
< h4 id = "orge0285fb" > < 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" >
< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled< / span > (
< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
< 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-org61f6138" class = "outline-4" >
< h4 id = "org61f6138" > < 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" >
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< pre class = "src src-f90" > < span style = "color: #a020f0;" > function< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled< / span > (context, transa, transb, m, n, < span style = "color: #a020f0;" > & < / span >
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A, LDA, B, LDB, C, LDC, rescale_factor_kappa) < span style = "color: #a020f0;" > & < / span >
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< span style = "color: #a020f0;" > bind< / span > (C) < span style = "color: #a020f0;" > result< / span > (info)
< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl_constants< / span >
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< 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: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > context< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transa< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > m< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > n< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldc< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > rescale_factor_kappa< / span >
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< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(ldc,n)< / span >
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< span style = "color: #228b22;" > integer< / span > (qmckl_exit_code) ::< span style = "color: #a0522d;" > info< / span >
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< 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 >
< 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 >
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: #b22222;" > check for LDB< / 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 >
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< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled< / span >
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org9ad623d" class = "outline-4" >
< h4 id = "org9ad623d" > < 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-org672c272" class = "outline-2" >
< h2 id = "org672c272" > < 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-orgfecb018" class = "outline-3" >
< h3 id = "orgfecb018" > < span class = "section-number-3" > 4.1< / span > < code > qmckl_distance_rescaled_gl< / code > < / h3 >
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< div class = "outline-text-3" id = "text-4-1" >
< p >
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< code > qmckl_distance_rescaled_gl< / 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
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contains the gradient vector and the last index is the Laplacian.
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< / p >
< p >
\[
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C(r_{ij}) = \left( 1 - \exp(-\kappa\, r_{ij})\right)/\kappa
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\]
< / p >
< p >
Here the gradient is defined as follows:
< / p >
< p >
\[
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\nabla_i C(r_{ij}) = \left(\frac{\partial C(r_{ij})}{\partial x_i},\frac{\partial C(r_{ij})}{\partial y_i},\frac{\partial C(r_{ij})}{\partial z_i} \right)
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\]
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and the Laplacian is defined as follows:
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< / p >
< p >
\[
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\Delta_i C(r_{ij}) = \frac{\partial^2}{\partial x_i^2} + \frac{\partial^2}{\partial y_i^2} + \frac{\partial^2}{\partial z_i^2}
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\]
< / p >
< p >
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Using the above three formulas, the expression for the gradient and Laplacian is:
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< / p >
< p >
\[
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\frac{\partial C(r_{ij})}{\partial x_i} = \frac{|(x_i -
x_j)|}{r_{ij}} \exp (- \kappa \, r_{ij})
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\]
< / p >
< p >
\[
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\Delta C_{ij}(r_{ij}) = \left[ \frac{2}{r_{ij}} - \kappa \right] \exp (- \kappa \, r_{ij})
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\]
< / 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 = "orgab8ff46" 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 >
< 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 >
< tbody >
< tr >
< td class = "org-left" > < code > context< / code > < / td >
< td class = "org-left" > < code > qmckl_context< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Global state< / td >
< / tr >
< tr >
< td class = "org-left" > < code > transa< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
< 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 >
< td class = "org-left" > < code > transb< / code > < / td >
< td class = "org-left" > < code > char< / code > < / td >
< 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 >
< td class = "org-left" > < code > m< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the first set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > n< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Number of points in the second set< / td >
< / tr >
< tr >
< td class = "org-left" > < code > A< / code > < / td >
< td class = "org-left" > < code > double[][lda]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(m \times 3\) matrix \(A\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > lda< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > A< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > B< / code > < / td >
< td class = "org-left" > < code > double[][ldb]< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Array containing the \(n \times 3\) matrix \(B\)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > ldb< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > B< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > C< / code > < / td >
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< td class = "org-left" > < code > double[n][ldc][4]< / 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 >
< td class = "org-left" > < code > ldc< / code > < / td >
< td class = "org-left" > < code > int64_t< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Leading dimension of array < code > C< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < code > rescale_factor_kappa< / code > < / td >
< td class = "org-left" > < code > double< / code > < / td >
< td class = "org-left" > in< / td >
< td class = "org-left" > Factor for calculating rescaled distances derivatives< / td >
< / tr >
< / tbody >
< / table >
< p >
Requirements:
< / p >
< 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" >
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< pre class = "src src-c" > < span style = "color: #228b22;" > qmckl_exit_code< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled_gl< / span > (
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< span style = "color: #a020f0;" > const< / span > < span style = "color: #228b22;" > qmckl_context< / span > < span style = "color: #a0522d;" > context< / span > ,
< 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" >
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< pre class = "src src-f90" > < span style = "color: #a020f0;" > function< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled_gl< / span > (context, transa, transb, m, n, < span style = "color: #a020f0;" > & < / span >
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A, LDA, B, LDB, C, LDC, rescale_factor_kappa) < span style = "color: #a020f0;" > & < / span >
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< span style = "color: #a020f0;" > bind< / span > (C) < span style = "color: #a020f0;" > result< / span > (info)
< span style = "color: #a020f0;" > use< / span > < span style = "color: #0000ff;" > qmckl_constants< / span >
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< span style = "color: #a020f0;" > implicit< / span > < span style = "color: #228b22;" > none< / span >
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< span style = "color: #228b22;" > integer< / span > (qmckl_exit_code) ::< span style = "color: #a0522d;" > info< / span >
< span style = "color: #228b22;" > integer< / span > (qmckl_context), < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > context< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transa< / span >
< span style = "color: #228b22;" > character< / span > (< span style = "color: #008b8b;" > c_char< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > transb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > m< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > n< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > lda< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldb< / span >
< span style = "color: #228b22;" > integer< / span > (< span style = "color: #008b8b;" > c_int64_t< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > ldc< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) , < span style = "color: #a020f0;" > value< / span > ::< span style = "color: #a0522d;" > rescale_factor_kappa< / span >
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< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > A(lda,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (in) ::< span style = "color: #a0522d;" > B(ldb,*)< / span >
< span style = "color: #228b22;" > real< / span > (< span style = "color: #008b8b;" > c_double< / span > ) , < span style = "color: #a020f0;" > intent< / span > (out) ::< span style = "color: #a0522d;" > C(4,ldc,n)< / span >
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< 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 >
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< span style = "color: #228b22;" > real< / span > *8 ::< span style = "color: #a0522d;" > rij< / span >
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< 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 >
< 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 >
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: #b22222;" > check for LDB< / 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)
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dist = < span style = "color: #a020f0;" > max< / span > (1.d-20, dsqrt(x*x + y*y + z*z))
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dist_inv = 1.0d0/dist
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rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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< 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)
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dist = < span style = "color: #a020f0;" > max< / span > (1.d-20, dsqrt(x*x + y*y + z*z))
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dist_inv = 1.0d0/dist
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rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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< 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)
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dist = < span style = "color: #a020f0;" > max< / span > (1.d-20, dsqrt(x*x + y*y + z*z))
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dist_inv = 1.0d0/dist
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rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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< 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)
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dist = < span style = "color: #a020f0;" > max< / span > (1.d-20, dsqrt(x*x + y*y + z*z))
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dist_inv = 1.0d0/dist
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rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
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< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end do< / span >
< span style = "color: #a020f0;" > end select< / span >
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< span style = "color: #a020f0;" > end function< / span > < span style = "color: #0000ff;" > qmckl_distance_rescaled_gl< / span >
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< / pre >
< / div >
< p >
This function is more efficient when < code > A< / code > and < code > B< / code > are transposed.
< / p >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: TREX CoE< / p >
2024-02-24 00:20:11 +01:00
< p class = "date" > Created: 2024-02-23 Fri 23:19< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
