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Timestamp:
Oct 7, 2015 11:56:08 PM (6 years ago)
Author:
knoop
Message:

Code annotations made doxygen readable

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  • palm/trunk/SOURCE/singleton.f90

    r1321 r1682  
    1  MODULE singleton
    2 
     1!> @file singleton.f90
    32!-----------------------------------------------------------------------------
    43! Current revisions:
    54! -----------------
    6 !
     5! Code annotations made doxygen readable
    76!
    87! Former revisions:
     
    2120! Description:
    2221! ------------
    23 ! Multivariate Fast Fourier Transform
    24 !
    25 ! Fortran 90 Implementation of Singleton's mixed-radix algorithm,
    26 ! RC Singleton, Stanford Research Institute, Sept. 1968.
    27 !
    28 ! Adapted from fftn.c, translated from Fortran 66 to C by Mark Olesen and
    29 ! John Beale.
    30 !
    31 ! Fourier transforms can be computed either in place, using assumed size
    32 ! arguments, or by generic function, using assumed shape arguments.
    33 !
    34 !
    35 ! Public:
    36 !
    37 !   fftkind                              kind parameter of complex arguments
    38 !                                        and function results.
    39 !
    40 !   fft(array, dim, inv, stat)           generic transform function
    41 !    COMPLEX(fftkind), DIMENSION(:,...,:), INTENT(IN)           :: array
    42 !    INTEGER,          DIMENSION(:),       INTENT(IN),  OPTIONAL:: dim
    43 !    LOGICAL,                              INTENT(IN),  OPTIONAL:: inv
    44 !    INTEGER,                              INTENT(OUT), OPTIONAL:: stat
    45 !
    46 !   fftn(array, shape, dim, inv, stat)   in place transform subroutine
    47 !    COMPLEX(fftkind), DIMENSION(*), INTENT(INOUT)        :: array
    48 !    INTEGER,          DIMENSION(:), INTENT(IN)           :: shape
    49 !    INTEGER,          DIMENSION(:), INTENT(IN),  OPTIONAL:: dim
    50 !    LOGICAL,                        INTENT(IN),  OPTIONAL:: inv
    51 !    INTEGER,                        INTENT(OUT), OPTIONAL:: stat
    52 !
    53 !
    54 ! Formal Parameters:
    55 !
    56 !   array    The complex array to be transformed. array can be of arbitrary
    57 !            rank (i.e. up to seven).
    58 !
    59 !   shape    With subroutine fftn, the shape of the array to be transformed
    60 !            has to be passed separately, since fftradix - the internal trans-
    61 !            formation routine - will treat array always as one dimensional.
    62 !            The product of elements in shape must be the number of
    63 !            elements in array.
    64 !            Although passing array with assumed shape would have been nicer,
    65 !            I prefered assumed size in order to prevent the compiler from
    66 !            using a copy-in-copy-out mechanism. That would generally be
    67 !            necessary with fftn passing array to fftradix and with fftn
    68 !            being prepared for accepting non consecutive array sections.
    69 !            Using assumed size, it's up to the user to pass an array argu-
    70 !            ment, that can be addressed as continous one dimensional array
    71 !            without copying. Otherwise, transformation will not really be
    72 !            performed in place.
    73 !            On the other hand, since the rank of array and the size of
    74 !            shape needn't match, fftn is appropriate for handling more than
    75 !            seven dimensions.
    76 !            As far as function fft is concerned all this doesn't matter,
    77 !            because the argument will be copied anyway. Thus no extra
    78 !            shape argument is needed for fft.
    79 !
    80 ! Optional Parameters:
    81 !
    82 !   dim      One dimensional integer array, containing the dimensions to be
    83 !            transformed. Default is (/1,...,N/) with N being the rank of
    84 !            array, i.e. complete transform. dim can restrict transformation
    85 !            to a subset of available dimensions. Its size must not exceed the
    86 !            rank of array or the size of shape respectivly.
    87 !
    88 !   inv      If .true., inverse transformation will be performed. Default is
    89 !            .false., i.e. forward transformation.
    90 !
    91 !   stat     If present, a system dependent nonzero status value will be
    92 !            returned in stat, if allocation of temporary storage failed.
    93 !
    94 !
    95 ! Scaling:
    96 !
    97 !   Transformation results will always be scaled by the square root of the
    98 !   product of sizes of each dimension in dim. (See examples below)
    99 !
    100 !
    101 ! Examples:
    102 !
    103 !   Let A be a L*M*N three dimensional complex array. Then
    104 !
    105 !     result = fft(A)
    106 !
    107 !   will produce a three dimensional transform, scaled by sqrt(L*M*N), while
    108 !
    109 !     call fftn(A, SHAPE(A))
    110 !
    111 !   will do the same in place.
    112 !
    113 !     result = fft(A, dim=(/1,3/))
    114 !
    115 !   will transform with respect to the first and the third dimension, scaled
    116 !   by sqrt(L*N).
    117 !
    118 !     result = fft(fft(A), inv=.true.)
    119 !
    120 !   should (approximately) reproduce A.
    121 !   With B having the same shape as A
    122 !
    123 !     result = fft(fft(A) * CONJG(fft(B)), inv=.true.)
    124 !
    125 !   will correlate A and B.
    126 !
    127 !
    128 ! Remarks:
    129 !
    130 !   Following changes have been introduced with respect to fftn.c:
    131 !   - complex arguments and results are of type complex, rather than
    132 !     real an imaginary part separately.
    133 !   - increment parameter (magnitude of isign) has been dropped,
    134 !     inc is always one, direction of transform is given by inv.     
    135 !   - maxf and maxp have been dropped. The amount of temporary storage
    136 !     needed is determined by the fftradix routine. Both fftn and fft
    137 !     can handle any size of array. (Maybe they take a lot of time and
    138 !     memory, but they will do it)
    139 !
    140 !   Redesigning fftradix in a way, that it handles assumed shape arrays
    141 !   would have been desirable. However, I found it rather hard to do this
    142 !   in an efficient way. Problems were:
    143 !   - to prevent stride multiplications when indexing arrays. At least our
    144 !     compiler was not clever enough to discover that in fact additions
    145 !     would do the job as well. On the other hand, I haven't been clever
    146 !     enough to find an implementation using array operations.
    147 !   - fftradix is rather large and different versions would be necessaray
    148 !     for each possible rank of array.
    149 !   Consequently, in place transformation still needs the argument stored
    150 !   in a consecutive bunch of memory and can't be performed on array
    151 !   sections like A(100:199:-3, 50:1020). Calling fftn with such sections
    152 !   will most probably imply copy-in-copy-out. However, the function fft
    153 !   works with everything it gets and should be convenient to use.
    154 !
    155 ! Michael Steffens, 09.12.96, <Michael.Steffens@mbox.muk.uni-hannover.de>
    156 ! Restructured fftradix for better optimization. M. Steffens, 4 June 1997
     22!> Multivariate Fast Fourier Transform
     23!>
     24!> Fortran 90 Implementation of Singleton's mixed-radix algorithm,
     25!> RC Singleton, Stanford Research Institute, Sept. 1968.
     26!>
     27!> Adapted from fftn.c, translated from Fortran 66 to C by Mark Olesen and
     28!> John Beale.
     29!>
     30!> Fourier transforms can be computed either in place, using assumed size
     31!> arguments, or by generic function, using assumed shape arguments.
     32!>
     33!>
     34!> Public:
     35!>
     36!>   fftkind                              kind parameter of complex arguments
     37!>                                        and function results.
     38!>
     39!>   fft(array, dim, inv, stat)           generic transform function
     40!>    COMPLEX(fftkind), DIMENSION(:,...,:), INTENT(IN)           :: array
     41!>    INTEGER,          DIMENSION(:),       INTENT(IN),  OPTIONAL:: dim
     42!>    LOGICAL,                              INTENT(IN),  OPTIONAL:: inv
     43!>    INTEGER,                              INTENT(OUT), OPTIONAL:: stat
     44!>
     45!>   fftn(array, shape, dim, inv, stat)   in place transform subroutine
     46!>    COMPLEX(fftkind), DIMENSION(*), INTENT(INOUT)        :: array
     47!>    INTEGER,          DIMENSION(:), INTENT(IN)           :: shape
     48!>    INTEGER,          DIMENSION(:), INTENT(IN),  OPTIONAL:: dim
     49!>    LOGICAL,                        INTENT(IN),  OPTIONAL:: inv
     50!>    INTEGER,                        INTENT(OUT), OPTIONAL:: stat
     51!>
     52!>
     53!> Formal Parameters:
     54!>
     55!>   array    The complex array to be transformed. array can be of arbitrary
     56!>            rank (i.e. up to seven).
     57!>
     58!>   shape    With subroutine fftn, the shape of the array to be transformed
     59!>            has to be passed separately, since fftradix - the internal trans-
     60!>            formation routine - will treat array always as one dimensional.
     61!>            The product of elements in shape must be the number of
     62!>            elements in array.
     63!>            Although passing array with assumed shape would have been nicer,
     64!>            I prefered assumed size in order to prevent the compiler from
     65!>            using a copy-in-copy-out mechanism. That would generally be
     66!>            necessary with fftn passing array to fftradix and with fftn
     67!>            being prepared for accepting non consecutive array sections.
     68!>            Using assumed size, it's up to the user to pass an array argu-
     69!>            ment, that can be addressed as continous one dimensional array
     70!>            without copying. Otherwise, transformation will not really be
     71!>            performed in place.
     72!>            On the other hand, since the rank of array and the size of
     73!>            shape needn't match, fftn is appropriate for handling more than
     74!>            seven dimensions.
     75!>            As far as function fft is concerned all this doesn't matter,
     76!>            because the argument will be copied anyway. Thus no extra
     77!>            shape argument is needed for fft.
     78!>
     79!> Optional Parameters:
     80!>
     81!>   dim      One dimensional integer array, containing the dimensions to be
     82!>            transformed. Default is (/1,...,N/) with N being the rank of
     83!>            array, i.e. complete transform. dim can restrict transformation
     84!>            to a subset of available dimensions. Its size must not exceed the
     85!>            rank of array or the size of shape respectivly.
     86!>
     87!>   inv      If .true., inverse transformation will be performed. Default is
     88!>            .false., i.e. forward transformation.
     89!>
     90!>   stat     If present, a system dependent nonzero status value will be
     91!>            returned in stat, if allocation of temporary storage failed.
     92!>
     93!>
     94!> Scaling:
     95!>
     96!>   Transformation results will always be scaled by the square root of the
     97!>   product of sizes of each dimension in dim. (See examples below)
     98!>
     99!>
     100!> Examples:
     101!>
     102!>   Let A be a L*M*N three dimensional complex array. Then
     103!>
     104!>     result = fft(A)
     105!>
     106!>   will produce a three dimensional transform, scaled by sqrt(L*M*N), while
     107!>
     108!>     call fftn(A, SHAPE(A))
     109!>
     110!>   will do the same in place.
     111!>
     112!>     result = fft(A, dim=(/1,3/))
     113!>
     114!>   will transform with respect to the first and the third dimension, scaled
     115!>   by sqrt(L*N).
     116!>
     117!>     result = fft(fft(A), inv=.true.)
     118!>
     119!>   should (approximately) reproduce A.
     120!>   With B having the same shape as A
     121!>
     122!>     result = fft(fft(A) * CONJG(fft(B)), inv=.true.)
     123!>
     124!>   will correlate A and B.
     125!>
     126!>
     127!> Remarks:
     128!>
     129!>   Following changes have been introduced with respect to fftn.c:
     130!>   - complex arguments and results are of type complex, rather than
     131!>     real an imaginary part separately.
     132!>   - increment parameter (magnitude of isign) has been dropped,
     133!>     inc is always one, direction of transform is given by inv.     
     134!>   - maxf and maxp have been dropped. The amount of temporary storage
     135!>     needed is determined by the fftradix routine. Both fftn and fft
     136!>     can handle any size of array. (Maybe they take a lot of time and
     137!>     memory, but they will do it)
     138!>
     139!>   Redesigning fftradix in a way, that it handles assumed shape arrays
     140!>   would have been desirable. However, I found it rather hard to do this
     141!>   in an efficient way. Problems were:
     142!>   - to prevent stride multiplications when indexing arrays. At least our
     143!>     compiler was not clever enough to discover that in fact additions
     144!>     would do the job as well. On the other hand, I haven't been clever
     145!>     enough to find an implementation using array operations.
     146!>   - fftradix is rather large and different versions would be necessaray
     147!>     for each possible rank of array.
     148!>   Consequently, in place transformation still needs the argument stored
     149!>   in a consecutive bunch of memory and can't be performed on array
     150!>   sections like A(100:199:-3, 50:1020). Calling fftn with such sections
     151!>   will most probably imply copy-in-copy-out. However, the function fft
     152!>   works with everything it gets and should be convenient to use.
     153!>
     154!> Michael Steffens, 09.12.96, <Michael.Steffens@mbox.muk.uni-hannover.de>
     155!> Restructured fftradix for better optimization. M. Steffens, 4 June 1997
    157156!-----------------------------------------------------------------------------
     157 MODULE singleton
     158 
    158159
    159160    USE kinds
     
    183184
    184185
     186!------------------------------------------------------------------------------!
     187! Description:
     188! ------------
     189!> @todo Missing function description.
     190!------------------------------------------------------------------------------!
    185191 FUNCTION fft1d(array, dim, inv, stat) RESULT(ft)
    186192!
     
    207213
    208214
     215!------------------------------------------------------------------------------!
     216! Description:
     217! ------------
     218!> @todo Missing function description.
     219!------------------------------------------------------------------------------!
    209220 FUNCTION fft2d(array, dim, inv, stat) RESULT(ft)
    210221!
     
    230241
    231242
     243!------------------------------------------------------------------------------!
     244! Description:
     245! ------------
     246!> @todo Missing function description.
     247!------------------------------------------------------------------------------!
    232248 FUNCTION fft3d(array, dim, inv, stat) RESULT(ft)
    233249!
     
    255271
    256272
     273!------------------------------------------------------------------------------!
     274! Description:
     275! ------------
     276!> @todo Missing function description.
     277!------------------------------------------------------------------------------!
    257278 FUNCTION fft4d(array, dim, inv, stat) RESULT(ft)
    258279!
     
    279300
    280301
     302!------------------------------------------------------------------------------!
     303! Description:
     304! ------------
     305!> @todo Missing function description.
     306!------------------------------------------------------------------------------!
    281307 FUNCTION fft5d(array, dim, inv, stat) RESULT(ft)
    282308!
     
    305331
    306332
     333!------------------------------------------------------------------------------!
     334! Description:
     335! ------------
     336!> @todo Missing function description.
     337!------------------------------------------------------------------------------!
    307338 FUNCTION fft6d(array, dim, inv, stat) RESULT(ft)
    308339!
     
    331362
    332363
     364!------------------------------------------------------------------------------!
     365! Description:
     366! ------------
     367!> @todo Missing function description.
     368!------------------------------------------------------------------------------!
    333369 FUNCTION fft7d(array, dim, inv, stat) RESULT(ft)
    334370!
     
    357393
    358394
     395!------------------------------------------------------------------------------!
     396! Description:
     397! ------------
     398!> @todo Missing subroutine description.
     399!------------------------------------------------------------------------------!
    359400 SUBROUTINE fftn(array, shape, dim, inv, stat)
    360401!
     
    410451
    411452
     453!------------------------------------------------------------------------------!
     454! Description:
     455! ------------
     456!> @todo Missing subroutine description.
     457!------------------------------------------------------------------------------!
    412458 SUBROUTINE fftradix(array, ntotal, npass, nspan, inv, stat)
    413459!
     
    472518
    473519
     520!------------------------------------------------------------------------------!
     521! Description:
     522! ------------
     523!> @todo Missing subroutine description.
     524!------------------------------------------------------------------------------!
    474525    SUBROUTINE factorize(npass, factor, nfactor, nsquare)
    475526!
     
    536587
    537588
     589!------------------------------------------------------------------------------!
     590! Description:
     591! ------------
     592!> @todo Missing subroutine description.
     593!------------------------------------------------------------------------------!
    538594    SUBROUTINE transform(array, ntotal, npass, nspan, &
    539595         factor, nfactor, ctmp, sine, cosine, inv) !-- compute fourier transform
     
    886942
    887943
     944!------------------------------------------------------------------------------!
     945! Description:
     946! ------------
     947!> @todo Missing subroutine description.
     948!------------------------------------------------------------------------------!
    888949    SUBROUTINE permute(array, ntotal, npass, nspan, &
    889950         factor, nfactor, nsquare, maxfactor, &
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