$SPAD/src/input ndftip.input

Timothy Daly December 3, 2016

Abstract

Contents

2

1 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

———-

— * —

)set break resume
)spool ndftip.output
)set message test on
)set message auto off
)clear all

———-

Note that the conversions of results from DoubleFloat to Float will become unnecessary if outputGeneral is extended to apply to DoubleFloat quantities. Those results not converted will, of course, then be displayed to 6 s.f.

— * —

--S 1 of 45
outputGeneral 6
--R
--R                                                                   Type: Void
--E 1
--S 2 of 45
seqA := [0.34907,0.54890,0.74776,0.94459,1.1385,1.3285,1.5137];
--R
--R
--R                                                            Type: List(Float)
--E 2
--S 3 of 45
seqB := [0.34907 - 0.37168*%i,  _
         0.54890 - 0.35669*%i,  _
         0.74776 - 0.31175*%i,  _
         0.94459 - 0.23702*%i,  _
         1.13850 - 0.13274*%i,  _
         1.32850 + 0.00074*%i,  _
         1.51370 + 0.16298*%i];
--R
--R
--R                                                   Type: List(Complex(Float))
--E 3
--S 4 of 45

hseqC : PackedHermitianSequence DoubleFloat
--R
--R
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is
--R      not available.
--E 4 of 45
--S 5 of 45
hseqC := packHS [0.34907,        _
                 0.54890 + %i*1.51370,  _
                 0.74776 + %i*1.32850,  _
                 0.94459 + %i*1.13850,  _
                 0.94459 - %i*1.13850,  _
                 0.74776 - %i*1.32850,  _
                 0.54890 - %i*1.51370];
--R
--R
--R                                                                 Type: Symbol
--E 5
--S 6 of 45
seqsD : List Vector DoubleFloat;
--R
--R                                                                   Type: Void
--E 6
--S 7 of 45
seqsD := [vector [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _
          vector [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
          vector [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
--R
--R
--R                                              Type: List(Vector(DoubleFloat))
--E 7
--S 8 of 45
seqsE : List PackedHermitianSequence DoubleFloat;
--R
--R
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is
--R      not available.
--E 8
--S 9 of 45
seqsE := [pHS [0.3854, 0.6772, 0.1138, 0.6751, 0.6362, 0.1424], _
          pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
          pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
--R

--R
--R                                                           Type: List(Symbol)
--E 9
--S 10 of 45
seqsF : List Vector Complex DoubleFloat
--R
--R                                                                   Type: Void
--E 10
--S 11 of 45
seqsF := [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i,   _
                  0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i,   _
                  0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i],  _
          vector [0.9172 + 0.9089*%i, 0.0644 + 0.3118*%i,   _
                  0.6037 + 0.3465*%i, 0.6430 + 0.6198*%i,   _
                  0.0428 + 0.2668*%i, 0.4815 + 0.1614*%i],  _
          vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i,   _
                  0.2060 + 0.7060*%i, 0.8630 + 0.8652*%i,   _
                  0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]];
--R
--R
--R                                     Type: List(Vector(Complex(DoubleFloat)))
--E 11
--S 12 of 45
dftA := nagDFT seqA;
--R
--R   There are no library operations named nagDFT
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagDFT with argument type(s)
--R                                 List(Float)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 12
--S 13 of 45 used to work?
dftA :: Vector Complex Float :: Matrix Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(dftA) to Vector(Complex(Float))
--R      for value

--R   dftA
--R
--E 13
                             -- Matrix to force display as a column,
                             -- Float to allow outputGeneral to work.
--       +         2.48361         +
--       |                         |
--       |- 0.265985 + 0.530898 %i |
--       |                         |
--       |- 0.257682 + 0.202979 %i |
--       |                         |
--       |- 0.256363 + 0.0580623 %i|
--       |                         |
--       |- 0.256363 - 0.0580623 %i|
--       |                         |
--       |- 0.257682 - 0.202979 %i |
--       |                         |
--       +- 0.265985 - 0.530898 %i +
-- test  2
--S 14 of 45 used to work?
nagInverseDFT dftA :: Vector Float
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                               Variable(dftA)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 14
--       [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137]
-- test  3
--S 15 of 45
dftB := nagDFT seqB;
--R
--R   There are no library operations named nagDFT
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its
--R      name.

--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagDFT with argument type(s)
--R                            List(Complex(Float))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 15
--S 16 of 45 used to work?
dftB :: Vector Complex Float :: Matrix Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(dftB) to Vector(Complex(Float))
--R      for value
--R   dftB
--R
--E 16
--       +  2.48361 - 0.471004 %i  +
--       |                         |
--       | - 0.5518 + 0.496841 %i  |
--       |                         |
--       |- 0.367113 + 0.0975621 %i|
--       |                         |
--       |- 0.287669 - 0.0586476 %i|
--       |                         |
--       |- 0.225057 - 0.174772 %i |
--       |                         |
--       |- 0.148251 - 0.308396 %i |
--       |                         |
--       + 0.0198297 - 0.564956 %i +
-- test  4
--S 17 of 45 used to work?
(nagInverseDFT dftB) :: Vector Complex Float :: Matrix Complex Float
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                               Variable(dftB)

--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 17
--       +0.34907 - 0.37168 %i+
--       |                    |
--       |0.5489 - 0.35669 %i |
--       |                    |
--       |0.74776 - 0.31175 %i|
--       |                    |
--       |0.94459 - 0.23702 %i|
--       |                    |
--       |1.1385 - 0.13274 %i |
--       |                    |
--       |1.3285 + 0.00074 %i |
--       |                    |
--       +1.5137 + 0.16298 %i +
-- test  5
--S 18 of 45
hdftA := nagHermitianDFT seqA;
--R
--R   There are no library operations named nagHermitianDFT
--R      Use HyperDoc Browse or issue
--R                          )what op nagHermitianDFT
--R      to learn if there is any operation containing " nagHermitianDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagHermitianDFT with argument type(s)
--R                                 List(Float)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 18
--S 19 of 45 used to work?
(expand hdftA) :: Vector Complex Float :: Matrix Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Polynomial(Integer) to Vector(Complex(Float
--R      )) for value
--R   hdftA
--R
--E 19
--       +         2.48361         +
--       |                         |

--       |- 0.265985 + 0.530898 %i |
--       |                         |
--       |- 0.257682 + 0.202979 %i |
--       |                         |
--       |- 0.256363 + 0.0580623 %i|
--       |                         |
--       |- 0.256363 - 0.0580623 %i|
--       |                         |
--       |- 0.257682 - 0.202979 %i |
--       |                         |
--       +- 0.265985 - 0.530898 %i +
-- test  6
--S 20 of 45 used to work?
(nagInverseDFT hdftA) :: Vector Float
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                               Variable(hdftA)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 20
--       [0.34907,0.5489,0.74776,0.94459,1.1385,1.3285,1.5137]
-- test  7
--S 21 of 45
dftC := nagDFT hseqC;
--R
--R   There are no library operations named nagDFT
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagDFT with argument type(s)
--R                                   Symbol
--R
--R      Perhaps you should use "@" to indicate the required return type,

--R      or "$" to specify which version of the function you need.
--E 21
--S 22 of 45 used to work?
dftC :: Vector Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(dftC) to Vector(Float) for value
--R   dftC
--R
--E 22
-- [1.82616,1.86862,- 0.017503,0.502001,- 0.598725,- 0.0314404,- 2.62557]
-- test  8
--S 23 of 45 used to work?
(nagInverseDFT dftC) :: Vector Complex Float
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                               Variable(dftC)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 23
-- [0.34907, 0.5489 + 1.5137 %i, 0.74776 + 1.3285 %i, 0.94459 + 1.1385 %i,
--  0.94459 - 1.1385 %i, 0.74776 - 1.3285 %i, 0.5489 - 1.5137 %i]
-- test  9
--S 24 of 45 used to work?
nagHermitianInverseDFT dftC
--R
--R   There are no library operations named nagHermitianInverseDFT
--R      Use HyperDoc Browse or issue
--R                       )what op nagHermitianInverseDFT
--R      to learn if there is any operation containing "
--R      nagHermitianInverseDFT " in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagHermitianInverseDFT with argument type(s)

--R                               Variable(dftC)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 24
-- [0.34907000000000005, 0.54889999999999983, 0.74775999999999987,
--  0.94459000000000004, 1.1385000000000003, 1.3284999999999998,
--  1.5136999999999998]
-- test 10:
--S 25 of 45
dftsD := nagDFT seqsD;
--R
--R   There are no library operations named nagDFT
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagDFT with argument type(s)
--R                          List(Vector(DoubleFloat))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 25
--S 26 of 45 used to work?
dftsD :: List Vector Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(dftsD) to List(Vector(Complex(
--R      Float))) for value
--R   dftsD
--R
--E 26
-- [
--   [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684,
--    0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i]
--   ,
--   [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072,
--    0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i]
--   ,
--   [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011,

--    0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i]
--   ]
-- test 11:
--S 27 of 45
invdftsD := nagInverseDFT dftsD ;
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                               Variable(dftsD)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 27
--S 28 of 45 used to work?
invdftsD :: List Vector Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(invdftsD) to List(Vector(Complex(
--R      Float))) for value
--R   invdftsD
--R
--E 28
-- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424],
--  [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723],
--  [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]]
-- test 12:
--S 29 of 45
dftsE := nagDFT seqsE;
--R
--R   There are no library operations named nagDFT
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagDFT with argument type(s)

--R                                List(Symbol)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 29
--S 30 of 45 used to work?
dftsE :: List Vector Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(dftsE) to List(Vector(Float)) for
--R      value
--R   dftsE
--R
--E 30
-- [[1.0788,0.662291,- 0.239146,- 0.578284,0.459192,- 0.438816],
--  [0.857321,1.22614,0.353348,- 0.222169,0.341327,- 1.22908],
--  [1.18245,0.262509,0.674406,0.552278,0.0539906,- 0.478963]]
-- test 13:
--S 31 of 45
invdftsE := nagInverseDFT dftsE;
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                               Variable(dftsE)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 31
--S 32 of 45 used to work?
invdftsE :: List Vector Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(invdftsE) to List(Vector(Complex(
--R      Float))) for value
--R   invdftsE
--R
--E 32
-- [

--   [0.3854, 0.6772 + 0.1424 %i, 0.1138 + 0.6362 %i, 0.6751,
--    0.1138 - 0.6362 %i, 0.6772 - 0.1424 %i]
--   ,
--   [0.5417, 0.2983 + 0.8723 %i, 0.1181 + 0.8638 %i, 0.7255,
--    0.1181 - 0.8638 %i, 0.2983 - 0.8723 %i]
--   ,
--   [0.9172, 0.0644 + 0.4815 %i, 0.6037 + 0.0428 %i, 0.643,
--    0.6037 - 0.0428 %i, 0.0644 - 0.4815 %i]
--   ]
-- test 14:
--S 33 of 45
hdftsD := nagHermitianDFT seqsD;
--R
--R   There are no library operations named nagHermitianDFT
--R      Use HyperDoc Browse or issue
--R                          )what op nagHermitianDFT
--R      to learn if there is any operation containing " nagHermitianDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagHermitianDFT with argument type(s)
--R                          List(Vector(DoubleFloat))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 33
--S 34 of 45 used to work?
map(expand,hdftsD) :: List Vector Complex Float
--R
--R   There are 74 exposed and 8 unexposed library operations named map
--R      having 2 argument(s) but none was determined to be applicable.
--R      Use HyperDoc Browse, or issue
--R                               )display op map
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named map
--R      with argument type(s)
--R                              Variable(expand)
--R                              Variable(hdftsD)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.

--E 34
-- [
--   [1.07373, - 0.104062 - 0.00438406 %i, 0.112554 - 0.373777 %i, - 0.146684,
--    0.112554 + 0.373777 %i, - 0.104062 + 0.00438406 %i]
--   ,
--   [1.39609, - 0.0365178 + 0.466584 %i, 0.077955 - 0.0607051 %i, - 0.152072,
--    0.077955 + 0.0607051 %i, - 0.0365178 - 0.466584 %i]
--   ,
--   [1.12374, 0.0914068 - 0.050841 %i, 0.393551 + 0.345775 %i, 0.153011,
--    0.393551 - 0.345775 %i, 0.0914068 + 0.050841 %i]
--   ]
-- test 15:
--S 35 of 45 used to work?
(nagInverseDFT hdftsD) :: List Vector Float
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                              Variable(hdftsD)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 35
-- [[0.3854,0.6772,0.1138,0.6751,0.6362,0.1424],
--  [0.5417,0.2983,0.1181,0.7255,0.8638,0.8723],
--  [0.9172,0.0644,0.6037,0.643,0.0428,0.4815]]
-- test 16:
--S 36 of 45
dftsF := nagDFT seqsF;
--R
--R   There are no library operations named nagDFT
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagDFT with argument type(s)

--R                     List(Vector(Complex(DoubleFloat)))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 36
--S 37 of 45 used to work?
dftsF :: List Vector Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(dftsF) to List(Vector(Complex(
--R      Float))) for value
--R   dftsF
--R
--E 37
-- [
--   [1.07373 + 1.39609 %i, - 0.570647 - 0.0409019 %i, 0.173259 - 0.295822 %i,
--    - 0.146684 - 0.152072 %i, 0.0518489 + 0.451732 %i,
--    0.362522 - 0.0321337 %i]
--   ,
--   [1.12374 + 1.06765 %i, 0.172759 + 0.0385858 %i, 0.418548 + 0.748083 %i,
--    0.153011 + 0.17522 %i, 0.368555 + 0.0565331 %i, 0.0100542 + 0.140268 %i]
--   ,
--   [0.909985 + 1.76167 %i, - 0.305418 + 0.0624335 %i,
--    0.407884 - 0.0694786 %i, - 0.078547 + 0.0725049 %i,
--    - 0.119334 + 0.128511 %i, - 0.531409 - 0.433531 %i]
--   ]
-- test 17:
--S 38 of 45
invdftsF := nagInverseDFT dftsF ;
--R
--R   There are no library operations named nagInverseDFT
--R      Use HyperDoc Browse or issue
--R                           )what op nagInverseDFT
--R      to learn if there is any operation containing " nagInverseDFT "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagInverseDFT with argument type(s)
--R                               Variable(dftsF)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 38

--S 39 of 45
invdftsF :: List Vector Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Variable(invdftsF) to List(Vector(Complex(
--R      Float))) for value
--R   invdftsF
--R
--E 39
-- [
--   [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
--    0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
--   ,
--   [0.9172 + 0.9089 %i, 0.0644 + 0.3118 %i, 0.6037 + 0.3465 %i,
--    0.643 + 0.6198 %i, 0.0428 + 0.2668 %i, 0.4815 + 0.1614 %i]
--   ,
--   [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.206 + 0.706 %i,
--    0.863 + 0.8652 %i, 0.6967 + 0.919 %i, 0.2792 + 0.3355 %i]
--   ]
-- test 18:
--S 40 of 45 used to work?
nagHermitianInverseDFT dftsE
--R
--R   There are no library operations named nagHermitianInverseDFT
--R      Use HyperDoc Browse or issue
--R                       )what op nagHermitianInverseDFT
--R      to learn if there is any operation containing "
--R      nagHermitianInverseDFT " in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagHermitianInverseDFT with argument type(s)
--R                               Variable(dftsE)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 40
-- [
--   [0.38540000000000013, 0.67720000000000025, 0.11380000000000001,
--    0.67510000000000014, 0.63620000000000021, 0.14240000000000003]
--   ,
--   [0.54170000000000018, 0.29830000000000012, 0.1181, 0.72550000000000014,
--    0.86380000000000023, 0.87230000000000019]
--   ,

--   [0.91720000000000035, 0.064399999999999999, 0.60370000000000024,
--    0.64300000000000013, 0.042799999999999991, 0.48150000000000015]
--   ]
-- error tests:
-- test 19:
--S 41 of 45
nagDFT [vector [0.3854 + 0.5417*%i, 0.6772 + 0.2983*%i,   _
                0.1138 + 0.1181*%i, 0.6751 + 0.7255*%i,   _
                0.6362 + 0.8638*%i, 0.1424 + 0.8723*%i],  _
        vector [0.1156 + 0.6214*%i, 0.0685 + 0.8681*%i,   _
                0.6967 + 0.9190*%i, 0.2792 + 0.3355*%i]]
--R
--R
--R   (10)
--R   SUB
--R      nagDFT
--R  ,
--R      [0.3854 + 0.5417 %i, 0.6772 + 0.2983 %i, 0.1138 + 0.1181 %i,
--R       0.6751 + 0.7255 %i, 0.6362 + 0.8638 %i, 0.1424 + 0.8723 %i]
--R  ,
--R      [0.1156 + 0.6214 %i, 0.0685 + 0.8681 %i, 0.6967 + 0.919 %i,
--R       0.2792 + 0.3355 %i]
--R                                                                 Type: Symbol
--E 41
-- test 20:
--S 42 of 45
nagHermitianDFT [vector [0.3854, 0.6751, 0.6362, 0.1424], _
                 vector [0.5417, 0.7255, 0.8638, 0.8723], _
                 vector [0.9172, 0.0428, 0.4815]]
--R
--R
--R   (11)
--R   SUB
--R      nagHermitianDFT
--R  ,
--R      [0.3854,0.6751,0.6362,0.1424]
--R  ,
--R      [0.5417,0.7255,0.8638,0.8723]
--R  ,
--R      [0.9172,0.0428,0.4815]
--R                                                                 Type: Symbol
--E 42
-- test 21:
--S 43 of 45 used to work?
badSeqs : List PackedHermitianSequence DoubleFloat
--R

--R
--RDaly Bug
--R   Category, domain or package constructor PackedHermitianSequence is
--R      not available.
--E 43
--badSeqs := [pHS [0.3854, 0.1138, 0.6751, 0.6362, 0.1424],         _
--            pHS [0.5417, 0.2983, 0.1181, 0.7255, 0.8638, 0.8723], _
--            pHS [0.9172, 0.0644, 0.6037, 0.6430, 0.0428, 0.4815]];
--
--
--R--                                                            Type: List Symbol
--S 44 of 45
nagDFT badSeqs
--R
--R   There are no library operations named nagDFT
--R      Use HyperDoc Browse or issue
--R                               )what op nagDFT
--R      to learn if there is any operation containing " nagDFT " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagDFT with argument type(s)
--R                              Variable(badSeqs)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 44
--S 45 of 45
outputGeneral()
--R
--R                                                                   Type: Void
--E 45
)spool
)lisp (bye)

———-

References^{[1] nothing}

20