$SPAD/src/input nepip.input

Timothy Daly December 3, 2016

Abstract

Contents

1 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

———-

— * —

)set break resume
)spool nepip.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.

— * —

--S 1 of 27
outputGeneral 5
--R
--R                                                                   Type: Void
--E 1
--S 2 of 27
mA1 := matrix [[ 0.5 ,   1.5 ,   6.6 ,   4.8],  _
               [ 1.5 ,   6.5 ,  16.2 ,   8.6],  _
               [ 6.6 ,  16.2 ,  37.6 ,   9.8],  _
               [ 4.8 ,   8.6 ,   9.8 , -17.1]];
--R
--R
--R                                                          Type: Matrix(Float)
--E 2
--S 3 of 27
mB1 := matrix[[ 1 ,  3 ,   4 ,  1],  _
              [ 3 , 13 ,  16 , 11],  _
              [ 4 , 16 ,  24 , 18],  _
              [ 1 , 11 ,  18 , 27]];
--R
--R
--R                                                        Type: Matrix(Integer)
--E 3

--S 4 of 27
mA2 := matrix [[ 3.9 ,  12.5 , -34.5 ,  -0.5],  _
               [ 4.3 ,  21.5 , -47.5 ,   7.5],  _
               [ 4.3 ,  21.5 , -43.5 ,   3.5],  _
               [ 4.4 ,  26.0 , -46.0 ,   6.0]];
--R
--R
--R                                                          Type: Matrix(Float)
--E 4
--S 5 of 27
mB2 := matrix[[ 1 , 2 , -3 , 1],  _
              [ 1 , 3 , -5 , 4],  _
              [ 1 , 3 , -4 , 3],  _
              [ 1 , 3 , -4 , 4]];
--R
--R
--R                                                        Type: Matrix(Integer)
--E 5
--S 6 of 27 used to work?
nagEigenvalues(mA1,mB1) :: List Float
--R
--R   There are no library operations named nagEigenvalues
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagEigenvalues with argument type(s)
--R                                Matrix(Float)
--R                               Matrix(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 6
--       [- 3.0,- 1.0,2.0,4.0]
--S 7 of 27
vv1 := nagEigenvectors(mA1,mB1);
--R
--R   There are no library operations named nagEigenvectors
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R

--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagEigenvectors with argument type(s)
--R                                Matrix(Float)
--R                               Matrix(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 7
--S 8 of 27 used to work?
(vv1.eigenvalues) :: List Float
--R
--R   There are no library operations named vv1
--R      Use HyperDoc Browse or issue
--R                                )what op vv1
--R      to learn if there is any operation containing " vv1 " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv1
--R      with argument type(s)
--R                            Variable(eigenvalues)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 8
--       [- 3.0,- 1.0,2.0,4.0]
--S 9 of 27 used to work?
(vv1.eigenvectors) :: List Vector Complex Float
--R
--R   There are no library operations named vv1
--R      Use HyperDoc Browse or issue
--R                                )what op vv1
--R      to learn if there is any operation containing " vv1 " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv1
--R      with argument type(s)
--R                           Variable(eigenvectors)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 9
-- [[- 4.35,0.05,1.0,- 0.5], [- 2.05,0.15,0.5,- 0.5], [- 3.95,0.85,0.5,- 0.5],
--  [2.65,0.05,- 1.0,0.5]]
--S 10 of 27

nagEigenvalues(mA2,mB2)
--R
--R   There are no library operations named nagEigenvalues
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagEigenvalues with argument type(s)
--R                                Matrix(Float)
--R                               Matrix(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 10

———-

All components are O(1) or more so:

— * —

--S 11 of 27 used to work?
% :: List Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Matrix(Integer) to List(Complex(Float)) for
--R      value
--R   +1  2  - 3  1+
--R   |            |
--R   |1  3  - 5  4|
--R   |            |
--R   |1  3  - 4  3|
--R   |            |
--R   +1  3  - 4  4+
--R
--E 11
--       [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]
--S 12 of 27
vv2 := nagEigenvectors(mA2,mB2);
--R
--R   There are no library operations named nagEigenvectors
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R

--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagEigenvectors with argument type(s)
--R                                Matrix(Float)
--R                               Matrix(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 12
--S 13 of 27
vv2.eigenvalues
--R
--R   There are no library operations named vv2
--R      Use HyperDoc Browse or issue
--R                                )what op vv2
--R      to learn if there is any operation containing " vv2 " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2
--R      with argument type(s)
--R                            Variable(eigenvalues)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 13

———-

All components are O(1) or more so:

— * —

--S 14 of 27 used to work?
% :: List Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Matrix(Integer) to List(Complex(Float)) for
--R      value
--R   +1  2  - 3  1+
--R   |            |
--R   |1  3  - 5  4|
--R   |            |
--R   |1  3  - 4  3|
--R   |            |
--R   +1  3  - 4  4+
--R
--E 14

--       [2.0,3.0 + 4.0 %i,3.0 - 4.0 %i,4.0]
--S 15 of 27 used to work?
vv2.eigenvectors :: List Vector Complex Float
--R
--R   There are no library operations named vv2
--R      Use HyperDoc Browse or issue
--R                                )what op vv2
--R      to learn if there is any operation containing " vv2 " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2
--R      with argument type(s)
--R                           Variable(eigenvectors)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 15
-- [[0.99606,0.0056917,0.062609,0.062609],
--
--   [0.94491, 0.18898 + 0.26077 E -14 %i, 0.11339 - 0.15119 %i,
--    0.11339 - 0.15119 %i]
--   ,
--
--   [0.94491, 0.18898 - 0.26077 E -14 %i, 0.11339 + 0.15119 %i,
--    0.11339 + 0.15119 %i]
--   ,
--  [0.98752,0.010972,- 0.032917,0.15361]]
-- The same call with eps=0.0001:
--S 16 of 27
vv2a := nagEigenvectors(mA2,mB2,0.0001);
--R
--R   There are no library operations named nagEigenvectors
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagEigenvectors with argument type(s)
--R                                Matrix(Float)
--R                               Matrix(Integer)
--R                                    Float
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.

--E 16
--S 17 of 27 used to work?
vv2a.eigenvalues :: List Complex Float
--R
--R   There are no library operations named vv2a
--R      Use HyperDoc Browse or issue
--R                                )what op vv2a
--R      to learn if there is any operation containing " vv2a " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2a
--R      with argument type(s)
--R                            Variable(eigenvalues)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 17
--       [1.9989,3.0003 + 3.9994 %i,3.0003 - 3.9994 %i,4.0]
--S 18 of 27
vv2a.eigenvectors :: List Vector Complex Float
--R
--R   There are no library operations named vv2a
--R      Use HyperDoc Browse or issue
--R                                )what op vv2a
--R      to learn if there is any operation containing " vv2a " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv2a
--R      with argument type(s)
--R                           Variable(eigenvectors)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 18
-- [[0.99605,0.0057355,0.062656,0.062656],
--
--   [0.94491, 0.18899 - 0.000048882 %i, 0.11336 - 0.15119 %i,
--    0.11336 - 0.15119 %i]
--   ,
--
--   [0.94491, 0.18899 + 0.000048882 %i, 0.11336 + 0.15119 %i,
--    0.11336 + 0.15119 %i]
--   ,
--  [0.98751,0.011031,- 0.032912,0.15367]]
--S 19 of 27

mB1(1,1) := -1;
--R
--R
--R                                                                Type: Integer
--E 19

———-

The next test should fail on F02ADF then call F02BJF:

— * —

--S 20 of 27
nagEigenvalues(mA1,mB1)
--R
--R   There are no library operations named nagEigenvalues
--R      Use HyperDoc Browse or issue
--R                           )what op nagEigenvalues
--R      to learn if there is any operation containing " nagEigenvalues "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagEigenvalues with argument type(s)
--R                                Matrix(Float)
--R                               Matrix(Integer)
--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

———-

All components are O(1) or more so:

— * —

--S 21 of 27 used to work?
% :: List Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Integer to List(Complex(Float)) for value
--R   - 1
--R
--E 21
--       [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]

———-

Similarly, this should fail on F02AEF then call F02BJF:

— * —

--S 22 of 27
vv3 := nagEigenvectors(mA1,mB1);
--R
--R   There are no library operations named nagEigenvectors
--R      Use HyperDoc Browse or issue
--R                          )what op nagEigenvectors
--R      to learn if there is any operation containing " nagEigenvectors "
--R      in its name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named
--R      nagEigenvectors with argument type(s)
--R                                Matrix(Float)
--R                               Matrix(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 22
--S 23 of 27
vv3.eigenvalues
--R
--R   There are no library operations named vv3
--R      Use HyperDoc Browse or issue
--R                                )what op vv3
--R      to learn if there is any operation containing " vv3 " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv3
--R      with argument type(s)
--R                            Variable(eigenvalues)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 23

———-

All components are O(1) or more so:

— * —

--S 24 of 27 used to work?
% :: List Complex Float
--R
--R
--RDaly Bug
--R   Cannot convert from type Integer to List(Complex(Float)) for value
--R   - 1

--R
--E 24
--       [3.5016,- 1.5471,0.041212 + 0.21738 %i,0.041212 - 0.21738 %i]
--S 25 of 27 used to work?
vv3.eigenvectors :: List Vector Complex Float
--R
--R   There are no library operations named vv3
--R      Use HyperDoc Browse or issue
--R                                )what op vv3
--R      to learn if there is any operation containing " vv3 " in its
--R      name.
--R
--RDaly Bug
--R   Cannot find a definition or applicable library operation named vv3
--R      with argument type(s)
--R                           Variable(eigenvectors)
--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
--  [[- 0.034577,0.63045,- 0.75202,0.1892],
--   [0.17876,- 0.73845,0.047413,0.64845],
--
--    [0.80838, - 0.00095133 + 0.47557 %i, - 0.20354 - 0.21737 %i,
--     0.15404 + 0.089179 %i]
--    ,
--
--    [0.80838, - 0.00095133 - 0.47557 %i, - 0.20354 + 0.21737 %i,
--     0.15404 - 0.089179 %i]
--   ]
--S 26 of 27
outputGeneral()
--R
--R                                                                   Type: Void
--E 26
--S 27 of 27
output "End of tests"
--R
--R   End of tests
--R                                                                   Type: Void
--E 27
)spool
)lisp (bye)

———-

References^{[1] nothing}

12