C      ALGORITHM 705, COLLECTED ALGORITHMS FROM ACM.
C      THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C      VOL. 18, NO. 2, PP. 232-238.
C      Remark: VOL. 28, NO. 3. PP. 372-375
#! /bin/sh
# This is a shell archive, meaning:
# 1. Remove everything above the #! /bin/sh line.
# 2. Save the resulting text in a file.
# 3. Execute the file with /bin/sh (not csh) to create the files:
#	Doc/
#	Doc/Makefile
#	Doc/Makefile.Dp
#	Doc/PackingList
#	Doc/doc
#	Fortran77/
#	Fortran77/Dp/
#	Fortran77/Dp/Drivers/
#	Fortran77/Dp/Drivers/data4
#	Fortran77/Dp/Drivers/data5
#	Fortran77/Dp/Drivers/data6
#	Fortran77/Dp/Drivers/dr_subs.f
#	Fortran77/Dp/Drivers/driver1.f
#	Fortran77/Dp/Drivers/driver2.f
#	Fortran77/Dp/Drivers/driver3.f
#	Fortran77/Dp/Drivers/driver4.f
#	Fortran77/Dp/Drivers/driver5.f
#	Fortran77/Dp/Drivers/driver6.f
#	Fortran77/Dp/Drivers/driver7.f
#	Fortran77/Dp/Drivers/driver8.f
#	Fortran77/Dp/Drivers/driver9.f
#	Fortran77/Dp/Drivers/portrand.f
#	Fortran77/Dp/Drivers/res1
#	Fortran77/Dp/Drivers/res2
#	Fortran77/Dp/Drivers/res3
#	Fortran77/Dp/Drivers/res4
#	Fortran77/Dp/Drivers/res5
#	Fortran77/Dp/Drivers/res6
#	Fortran77/Dp/Drivers/res7
#	Fortran77/Dp/Drivers/res8
#	Fortran77/Dp/Drivers/res9
#	Fortran77/Dp/Src/
#	Fortran77/Dp/Src/blas1.f
#	Fortran77/Dp/Src/linpack.f
#	Fortran77/Dp/Src/port.f
#	Fortran77/Dp/Src/src.f
# This archive created: Wed Oct 16 14:43:51 2002
export PATH; PATH=/bin:$PATH
if test ! -d 'Doc'
then
	mkdir 'Doc'
fi
cd 'Doc'
if test -f 'Makefile'
then
	echo shar: will not over-write existing file "'Makefile'"
else
cat << "SHAR_EOF" > 'Makefile'

# Fortran compiler and linker
F77         = epcf90
F77OPTS     = -sloppy -C -d5 -g -temp=/tmp -u
F77LINK     = $(F77)
F77LINKOPTS = $(F77OPTS)

.f.o:
	$(F77) $(F77OPTS) -c $*.f

all: res1 res2 res3 res4 res5 res6 res7 res8 res9

Objs1= driver1.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

src.o:  ../Src/src.f
	$(F77) $(F77OPTS) -c $?
port.o: ../Src/port.f
	$(F77) $(F77OPTS) -c $?
blas1.o: ../Src/blas1.f
	$(F77) $(F77OPTS) -c $?
linpack.o: ../Src/linpack.f
	$(F77) $(F77OPTS) -c $?

driver1: $(Objs1)
	$(F77LINK) $(F77LINKOPTS) -o driver1 $(Objs1) $(SRCLIBS) $(Libs1)
res1: driver1  
	driver1  >temp 
	diff temp res1


Libs2= $(RANDOM)
Objs2= driver2.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver2: $(Objs2)
	$(F77LINK) $(F77LINKOPTS) -o driver2 $(Objs2) $(SRCLIBS) $(Libs2)
res2: driver2  
	driver2  >temp 
	diff temp res2


Libs3= $(RANDOM)
Objs3= driver3.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver3: $(Objs3)
	$(F77LINK) $(F77LINKOPTS) -o driver3 $(Objs3) $(SRCLIBS) $(Libs3)
res3: driver3  
	driver3  >temp 
	diff temp res3


Libs4= $(RANDOM)
Objs4= driver4.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver4: $(Objs4)
	$(F77LINK) $(F77LINKOPTS) -o driver4 $(Objs4) $(SRCLIBS) $(Libs4)
res4: driver4 data4 
	driver4 <data4 >temp 
	diff temp res4


Libs5= $(RANDOM)
Objs5= driver5.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver5: $(Objs5)
	$(F77LINK) $(F77LINKOPTS) -o driver5 $(Objs5) $(SRCLIBS) $(Libs5)
res5: driver5 data5 
	driver5 <data5 >temp 
	diff temp res5


Libs6= $(RANDOM)
Objs6= driver6.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver6: $(Objs6)
	$(F77LINK) $(F77LINKOPTS) -o driver6 $(Objs6) $(SRCLIBS) $(Libs6)
res6: driver6 data6 
	driver6 <data6 >temp 
	diff temp res6


Libs7= $(RANDOM)
Objs7= driver7.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver7: $(Objs7)
	$(F77LINK) $(F77LINKOPTS) -o driver7 $(Objs7) $(SRCLIBS) $(Libs7)
res7: driver7  
	driver7  >temp 
	diff temp res7


Libs8= $(RANDOM)
Objs8= driver8.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver8: $(Objs8)
	$(F77LINK) $(F77LINKOPTS) -o driver8 $(Objs8) $(SRCLIBS) $(Libs8)
res8: driver8  
	driver8  >temp 
	diff temp res8


Libs9= $(RANDOM)
Objs9= driver9.o dr_subs.o src.o port.o portrand.o linpack.o blas1.o

driver9: $(Objs9)
	$(F77LINK) $(F77LINKOPTS) -o driver9 $(Objs9) $(SRCLIBS) $(Libs9)
res9: driver9  
	driver9  >temp 
	diff temp res9

clean:
	rm *.o driver? temp

SHAR_EOF
fi # end of overwriting check
if test -f 'Makefile.Dp'
then
	echo shar: will not over-write existing file "'Makefile.Dp'"
else
cat << "SHAR_EOF" > 'Makefile.Dp'
include makefile.inc
all: res1 res2 res3 res4 res5 res6 res7 res8 res9
SRCLIBS= $(LINPACK) $(BLAS) $(PORT)
Libs1= $(RANDOM)
Objs1= driver1.o dr_subs.o src.o

driver1: $(Objs1)
	$(F77LINK) $(F77LINKOPTS) -o driver1 $(Objs1) $(SRCLIBS) $(Libs1)
res1: driver1  
	driver1  >res1


Libs2= $(RANDOM)
Objs2= driver2.o dr_subs.o src.o

driver2: $(Objs2)
	$(F77LINK) $(F77LINKOPTS) -o driver2 $(Objs2) $(SRCLIBS) $(Libs2)
res2: driver2  
	driver2  >res2


Libs3= $(RANDOM)
Objs3= driver3.o dr_subs.o src.o

driver3: $(Objs3)
	$(F77LINK) $(F77LINKOPTS) -o driver3 $(Objs3) $(SRCLIBS) $(Libs3)
res3: driver3  
	driver3  >res3


Libs4= $(RANDOM)
Objs4= driver4.o dr_subs.o src.o

driver4: $(Objs4)
	$(F77LINK) $(F77LINKOPTS) -o driver4 $(Objs4) $(SRCLIBS) $(Libs4)
res4: driver4 data4 
	driver4 <data4 >res4


Libs5= $(RANDOM)
Objs5= driver5.o dr_subs.o src.o

driver5: $(Objs5)
	$(F77LINK) $(F77LINKOPTS) -o driver5 $(Objs5) $(SRCLIBS) $(Libs5)
res5: driver5 data5 
	driver5 <data5 >res5


Libs6= $(RANDOM)
Objs6= driver6.o dr_subs.o src.o

driver6: $(Objs6)
	$(F77LINK) $(F77LINKOPTS) -o driver6 $(Objs6) $(SRCLIBS) $(Libs6)
res6: driver6 data6 
	driver6 <data6 >res6


Libs7= $(RANDOM)
Objs7= driver7.o dr_subs.o src.o

driver7: $(Objs7)
	$(F77LINK) $(F77LINKOPTS) -o driver7 $(Objs7) $(SRCLIBS) $(Libs7)
res7: driver7  
	driver7  >res7


Libs8= $(RANDOM)
Objs8= driver8.o dr_subs.o src.o

driver8: $(Objs8)
	$(F77LINK) $(F77LINKOPTS) -o driver8 $(Objs8) $(SRCLIBS) $(Libs8)
res8: driver8  
	driver8  >res8


Libs9= $(RANDOM)
Objs9= driver9.o dr_subs.o src.o

driver9: $(Objs9)
	$(F77LINK) $(F77LINKOPTS) -o driver9 $(Objs9) $(SRCLIBS) $(Libs9)
res9: driver9  
	driver9  >res9

clean:
	 rm *.o driver? temp
SHAR_EOF
fi # end of overwriting check
if test -f 'PackingList'
then
	echo shar: will not over-write existing file "'PackingList'"
else
cat << "SHAR_EOF" > 'PackingList'
Algorithm:705
Language:Fortran77
Precision:Dp
Src:src.f
SrcLibs:linpack blas port
Driver_0:driver1.f dr_subs.f @Src
DriverLib_0:random
Res_0:stdout=res1
Driver_1:driver2.f dr_subs.f @Src
DriverLib_1:random
Res_1:stdout=res2
Driver_2:driver3.f dr_subs.f @Src
DriverLib_2:random
Res_2:stdout=res3
Driver_3:driver4.f dr_subs.f @Src
DriverLib_3:random
Data_3:stdin=data4
Res_3:stdout=res4
Driver_4:driver5.f dr_subs.f @Src
DriverLib_4:random
Data_4:stdin=data5
Res_4:stdout=res5
Driver_5:driver6.f dr_subs.f @Src
DriverLib_5:random
Data_5:stdin=data6
Res_5:stdout=res6
Driver_6:driver7.f dr_subs.f @Src
DriverLib_6:random
Res_6:stdout=res7
Driver_7:driver8.f dr_subs.f @Src
DriverLib_7:random
Res_7:stdout=res8
Driver_8:driver9.f dr_subs.f @Src
DriverLib_8:random
Res_8:stdout=res9
SHAR_EOF
fi # end of overwriting check
if test -f 'doc'
then
	echo shar: will not over-write existing file "'doc'"
else
cat << "SHAR_EOF" > 'doc'
C      ALGORITHM 705, COLLECTED ALGORITHMS FROM ACM.
C      THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C      VOL. 18, NO. 2, PP. 232-238.
README - software for solving Sylvester equations - double precision version
 
    sylg    solves   A*X*B' + C*X*D' = E
    sylgc   solves   A*X*E' + E*X*A' + Q = 0
    sylgd   solves   A*X*A' - E*X*E' + Q = 0
 
For the sylgx routines, we got (NRM RESID)/(NRM Q) to be about 1.0d-14 in
double precision (acc. = about 17 digits).  On a UNIX(tm) system one can
testa routine by "make"ing  the test routines (e.g. "make tsylgc").
 
Installation:  The programs driver1.f, driver2.f, driver3.f are
recommended as simple installation tests.  They are set up to run a
small number of example problems. 

Further testing:  The programs driver1.f, driver2.f, driver3.f will run
a larger set of tests if two lines are commented out and two others
uncommented, as noted in the code.  Programs driver4.f .. driver9.f are
also provided for those who wish to do more extensive testing. 

17Apr90  J. Gardiner, OSU CIS, Columbus, OH 43210  (614)881-4135
13Dec90  J. Gardiner, OSU CIS, Columbus, OH 43210  (614)881-4135
12Jan01  Tim Hopkins

------------------------------------------------------------------------

driver1.f         test the subroutine sylg using predefined problems
		Calls: sylg msave d1nrm msub mulc trnata; (linpack)
		dsvdc

driver2.f        test the subroutine sylgc using predefined problems
		Calls: sylgc madd mulc trnata d1nrm msave; (linpack)
		dsvdc

driver3.f        test the subroutine sylgd using predefined problems
		Calls: sylgd madd mulc trnata d1nrm msave; (linpack)
		dsvdc

driver4.f        test the subroutine sylg using matrices from a file
(data4)		Calls: sylg msave d1nrm msub mulc trnata; (linpack)
		dsvdc

driver5.f       test the subroutine sylgc using matrices from a file
(data5)		Calls: sylgc madd mulc trnata d1nrm msave; (linpack)
		dsvdc

driver6.f       test the subroutine sylgd using matrices from a file
(data6)		Calls: sylgd madd mulc trnata d1nrm msave; (linpack)
		dsvdc

driver7.f       test the subroutine sylg using randomly generated problems
		Calls: sylg msave d1nrm msub mulc trnata; (linpack)
		dsvdc

driver8.f       test the subroutine sylgc using randomly generated problems
		Calls: sylgc madd mulc trnata d1nrm msave; (linpack)
		dsvdc

driver9.f       test the subroutine sylgd using randomly generated problems
		Calls: sylgd madd mulc trnata d1nrm msave; (linpack)
		dsvdc

res1..res9	Sample output from each of the above drivers.
 

Routine descriptions
====================

bkcon           solve  S*Y*T' + T*Y*S' + R = 0
                Calls: (linpack) dgeco dgesl
 
bkdis           solve  S*Y*S' - T*Y*T' + R = 0
                Calls: (linpack) dgeco dgesl
 
bkhs2           solve P*Y*R' + S*Y*T' = F where P=up-Hess, R=up-tri, S=up-tri,
                T=quasi-up-tri
                Calls: hsco hsfa hssl; (linpack) ddot
 
d1nrm           compute 1-norm of a matrix
                Calls: -
 
hsco            Hessenberg version of Linpack dgeco
                Calls: hsfa; (linpack) daxpy ddot dscal dasum
 
hsfa            Hessenberg version of Linpack dgefa
                Calls: (linpack) daxpy dscal idamax
 
hssl            Hessenberg version of Linpack dgesl
                Calls: (linpack) daxpy ddot
 
ktran           transform an upper-Hessenberg to a matrix orthogonally
                similar to its transpose which is also upper-Hessenberg
                Calls: -
 
madd            adds two matrices
                Calls: -
 
mqfwo           computes the symmetric product x'sx
                Calls: mula
 
msave           copies a matrix
                Calls: -
 
mscale          scales a matrix by a scalar
                Calls: -
 
msub            subtracts two matrices
                Calls: -
 
mula            multiplies two matrices, product overwrites first
                Calls: -
 
mulb            multiplies two matrices, product overwrites second
                Calls: -
 
mulc            multiplies two matrices
                Calls: -
 
qzhesg          transform A to upper-Hessenberg, B to upper-triangular
                Calls: -
 
qzitg           transform A to quasi-upper-triangular keeping B upper-triangular
                Calls: (eispack) epslon
 
qzvalg          order off-diagonal elements of A to correspond to conjugate
                generalized eigenvalues
                Calls: -
 
sepg            computes approximately inf(1-norm(P*Y*R'+S*Y*T')/1-norm(Y))
                Calls: bkhs2 mscale ktran d1nrm
 
sepgc           computes approximately inf(1-norm(S*Y*T'+T*Y*S')/1-norm(Y))
                Calls: bkcon mscale ktran d1nrm
 
sepgd           computes approximately inf(1-norm(S*Y*S'-T*Y*T')/1-norm(Y))
                Calls: bkdis mscale ktran d1nrm
 
sylg            solve  A*X*B' + C*X*D' = E where A,B,C,D are square
                Calls: qzhesg qzitg qzvalg sepg bkhs2 mula mulb trnata
 
sylgc           solve  A*X*E' + E*X*A' + Q = 0  where Q is symmetric
                Calls: qzhesg qzitg qzvalg sepgc bkcon mqfwo mulb
 
sylgd           solve  A*X*A' - E*X*E' + Q = 0  where Q is symmetric
                Calls: qzhesg qzitg qzvalg sepgd bkdis mqfwo mulb

--- last line of README ---
SHAR_EOF
fi # end of overwriting check
cd ..
if test ! -d 'Fortran77'
then
	mkdir 'Fortran77'
fi
cd 'Fortran77'
if test ! -d 'Dp'
then
	mkdir 'Dp'
fi
cd 'Dp'
if test ! -d 'Drivers'
then
	mkdir 'Drivers'
fi
cd 'Drivers'
if test -f 'data4'
then
	echo shar: will not over-write existing file "'data4'"
else
cat << "SHAR_EOF" > 'data4'
2 1
 
0. 1.
0. 2.
 
2.
 
3. 4.
0. 0.
 
1.
 
-9.
-4.
y

SHAR_EOF
fi # end of overwriting check
if test -f 'data5'
then
	echo shar: will not over-write existing file "'data5'"
else
cat << "SHAR_EOF" > 'data5'
3
 
1. 2. 3.
6. -5. 4.
7. 8. 9.
 
-10. 20. -30.
41. -42. 43.
19. 18. 17.
 
18. 9. 7.
9. 17. 8.
7. 8. 16.
y
SHAR_EOF
fi # end of overwriting check
if test -f 'data6'
then
	echo shar: will not over-write existing file "'data6'"
else
cat << "SHAR_EOF" > 'data6'
5 3
 
1. 2. 3. 4. 5.
6. 7. 8. 9. 10.
11. 12. 13. 14. 15.
16. 17. 18. 19. 20.
21. 22. 23. 24. 25.
 
26. -27. 28.
-29. 30. -31.
32. -33. 34.
 
1. 0. 0. 0. 0.
1. 2. 1. 1. 1.
1. 1. 2. 1. 1.
1. 1. 1. 2. 1.
1. 1. 1. 1. 2.
 
199. 98. 97.
41. 142. 43.
59. 55. 151.
 
-80. 79. -78.
77. -76. 75.
-74. 73. -72.
71. -70. 69.
-68. 67. -66.
y
SHAR_EOF
fi # end of overwriting check
if test -f 'dr_subs.f'
then
	echo shar: will not over-write existing file "'dr_subs.f'"
else
cat << "SHAR_EOF" > 'dr_subs.f'
C--**--CH2894--705--A:1--28:10:1999
C--**--CH2879--705--P:R--28:10:1999
      DOUBLE PRECISION FUNCTION DGAUS(MEAN, STDDEV)
C
      DOUBLE PRECISION MEAN, STDDEV
C
C     THIS ROUTINE GENERATES NORMALLY DISTRIBUTED PSEUDORANDOM NUMBERS
C     WITH GIVEN MEAN AND STANDARD DEVIATION.
C     YOU MUST INITIALIZE DXRAND() WITH "X = DXRAND(I)" WHERE I>0.
C
C     WRITTEN -
C       14NOV86 M.WETTE, UCSB ECE, SANTA BARBARA, CA 93106 (805)961-3616
C     MODIFIED -
C       28NOV88 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
      EXTERNAL DXRAND
      DOUBLE PRECISION RBUF, V1, V2, S, DXRAND
      LOGICAL RBGOOD
      SAVE RBUF, RBGOOD
      DATA RBGOOD/.FALSE./
C
C     CHECK FOR RANDOM NUMBER LEFT OVER IN BUFFER
      IF (RBGOOD) THEN
         DGAUS = STDDEV*RBUF + MEAN
         RBGOOD = .FALSE.
         RETURN
      ENDIF
C
C     GET RANDOM VECTOR IN UNIT CIRCLE
   20 CONTINUE
         V1 = 2.0D0*DXRAND(0) - 1.0D0
         V2 = 2.0D0*DXRAND(0) - 1.0D0
         S = V1*V1 + V2*V2
      IF (S .GE. 1.0D0) GOTO 20
C
      S = SQRT(-2.0D0*LOG(S)/S)
      RBUF = V1*S
      RBGOOD = .TRUE.
      DGAUS = STDDEV*V2*S + MEAN
      RETURN
C --- LAST LINE OF DGAUS ---
      END
      SUBROUTINE MADD (NA,NB,NC,M,N,A,B,C)
C
C     *****PARAMETERS:
      INTEGER NA,NB,NC,M,N
      DOUBLE PRECISION A(NA,N),B(NB,N),C(NC,N)
C
C     *****LOCAL VARIABLES:
      INTEGER I,J
C
C     *****SUBROUTINES CALLED:
C     NONE
C
C     ------------------------------------------------------------------
C
C     *****PURPOSE:
C     THIS SUBROUTINE COMPUTES THE MATRIX SUM A+B AND STORES THE
C     RESULT IN THE ARRAY C.  ALL MATRICES ARE M X N.  THE SUM
C     MAY BE OVERWRITTEN INTO A (B) BY DESIGNATING THE ARRAY C
C     TO BE A (B).
C
C     *****PARAMETER DESCRIPTION:
C
C     ON INPUT:
C
C        NA,NB,NC         ROW DIMENSIONS OF THE ARRAYS CONTAINING A,B,
C                         AND C,RESPECTIVELY, AS DECLARED IN THE CALLING
C                         PROGRAM DIMENSION STATEMENT;
C
C        M                NUMBER OF ROWS OF THE MATRICES A, B, AND C;
C
C        N                NUMBER OF COLUMNS OF THE MATRICES A, B, AND C;
C
C        A                AN M X N MATRIX;
C
C        B                AN M X N MATRIX.
C
C     ON OUTPUT:
C
C        C                AN M X N ARRAY CONTAINING A+B.
C
C     *****HISTORY:
C     WRITTEN BY ALAN J. LAUB (ELEC. SYS. LAB., M.I.T., RM. 35-331,
C     CAMBRIDGE, MA 02139,  PH.: (617)-253-2125), SEPTEMBER 1977.
C     MOST RECENT VERSION: SEP. 21, 1977.
C
C     ------------------------------------------------------------------
C
      DO 20 J=1,N
         DO 10 I=1,M
            C(I,J)=A(I,J)+B(I,J)
10       CONTINUE
20    CONTINUE
      RETURN
C
C     LAST LINE OF MADD
C
      END
      SUBROUTINE MSAVE (NA,NAS,M,N,A,ASAVE)
C
C     *****PARAMETERS:
      INTEGER NA,NAS,M,N
      DOUBLE PRECISION A(NA,N),ASAVE(NAS,N)
C
C     *****LOCAL VARIABLES:
      INTEGER I,J
C
C     *****SUBROUTINES CALLED:
C     NONE
C
C     ------------------------------------------------------------------
C
C     *****PURPOSE:
C     THIS SUBROUTINE COPIES THE CONTENTS OF THE M X N ARRAY A INTO
C     THE M X N ARRAY ASAVE.
C
C     *****PARAMETER DESCRIPTION:
C
C     ON INPUT:
C
C        NA,NAS           ROW DIMENSIONS OF THE ARRAYS CONTAINING A AND
C                         AS, RESPECTIVELY, AS DECLARED IN THE CALLING
C                         PROGRAM DIMENSION STATEMENT;
C
C        M                NUMBER OF ROWS OF THE MATRICES A AND ASAVE;
C
C        N                NUMBER OF COLUMNS OF THE MATRICES A AND ASAVE;
C
C        A                AN M X N MATRIX.
C
C     ON OUTPUT:
C
C        ASAVE            AN M X N ARRAY CONTAINING THE ARRAY A.
C
C     *****HISTORY:
C     WRITTEN BY ALAN J. LAUB (ELEC. SYS. LAB., M.I.T., RM. 35-331,
C     CAMBRIDGE, MA 02139,  PH.: (617)-253-2125), SEPTEMBER 1977.
C     MOST RECENT VERSION: SEP. 21, 1977.
C
C     ------------------------------------------------------------------
C
      DO 20 J=1,N
         DO 10 I=1,M
            ASAVE(I,J)=A(I,J)
10       CONTINUE
20    CONTINUE
      RETURN
C
C     LAST LINE OF MSAVE
C
      END
      SUBROUTINE MSUB (NA,NB,NC,M,N,A,B,C)
C
C     *****PARAMETERS:
      INTEGER NA,NB,NC,M,N
      DOUBLE PRECISION A(NA,N),B(NB,N),C(NC,N)
C
C     *****LOCAL VARIABLES:
      INTEGER I,J
C
C     *****SUBROUTINES CALLED:
C     NONE
C
C     ------------------------------------------------------------------
C
C     *****PURPOSE:
C     THIS SUBROUTINE COMPUTES THE MATRIX DIFFERENCE A-B AND STORES
C     THE RESULT IN THE ARRAY C.  ALL MATRICES ARE M X N.  THE
C     DIFFERENCE MAY BE OVERWRITTEN INTO A BY DESIGNATING THE
C     ARRAY C TO BE A.
C
C     *****PARAMETER DESCRIPTION:
C
C     ON INPUT:
C
C        NA,NB,NC         ROW DIMENSIONS OF THE ARRAYS CONTAINING A,B,
C                         AND C, RESPECTIVELY, AS DECLARED IN THE
C                         CALLING PROGRAM DIMENSION STATEMENT;
C
C        M                NUMBER OF ROWS OF THE MATRICES A,B, AND C;
C
C        N                NUMBER OF COLUMNS OF THE MATRICES A,B, AND C;
C
C        A                AN M X N MATRIX;
C
C        B                AN M X N MATRIX.
C
C     ON OUTPUT:
C
C        C                AN M X N ARRAY CONTAINING A-B.
C
C     *****HISTORY:
C     WRITTEN BY ALAN J. LAUB (ELEC. SYS. LAB., M.I.T., RM. 35-331,
C     CAMBRIDGE, MA 02139,  PH.: (617)-253-2125), SEPTEMBER 1977.
C     MOST RECENT VERSION: SEP. 21, 1977.
C
C     ------------------------------------------------------------------
C
      DO 20 J=1,N
         DO 10 I=1,M
            C(I,J)=A(I,J)-B(I,J)
10       CONTINUE
20    CONTINUE
      RETURN
C
C     LAST LINE OF MSUB
C
      END
      SUBROUTINE MULC (NA,NB,NC,M,N,L,A,B,C)
C
C     *****PARAMETERS:
      INTEGER NA,NB,NC,L,M,N
      DOUBLE PRECISION A(NA,N),B(NB,L),C(NC,L)
C
C     *****LOCAL VARIABLES:
      INTEGER I,J,K
C
C     *****SUBROUTINES CALLED:
C     NONE
C
C     ------------------------------------------------------------------
C
C     *****PURPOSE:
C     THIS SUBROUTINE COMPUTES THE MATRIX PRODUCT A*B AND STORES THE
C        RESULT IN THE ARRAY C.  A IS M X N, B IS N X L, AND C IS
C        M X L.  THE ARRAY C MUST BE DISTINCT FROM BOTH A AND B.
C
C     *****PARAMETER DESCRIPTION:
C
C     ON INPUT:
C
C        NA    ROW DIMENSION OF THE ARRAY CONTAINING A AS DECLARED
C              IN THE CALLING PROGRAM DIMENSION STATEMENT;
C
C        NB    ROW DIMENSION OF THE ARRAY CONTAINING B AS DECLARED
C              IN THE CALLING PROGRAM DIMENSION STATEMENT;
C
C        NC    ROW DIMENSION OF THE ARRAY CONTAINING C AS DECLARED
C              IN THE CALLING PROGRAM DIMENSION STATEMENT;
C
C        L     NUMBER OF COLUMNS OF THE MATRICES B AND C;
C
C        M     NUMBER OF ROWS OF THE MATRICES A AND C;
C
C        N     NUMBER OF COLUMNS OF THE MATRIX A AND NUMBER OF ROWS
C              OF THE MATRIX B;
C
C        A     AN M X N MATRIX;
C
C        B     AN N X L MATRIX.
C
C     ON OUTPUT:
C
C        C     AN M X L ARRAY CONTAINING A*B.
C
C     *****HISTORY:
C     ORIGINAL BY ALAN J. LAUB
C     MODIFIED AND RENAMED BY JUDITH D. GARDINER
C
C     ------------------------------------------------------------------
C
      DO 40 J=1,L
         DO 10 I=1,M
            C(I,J)=0.0D0
10       CONTINUE
         DO 30 K=1,N
            DO 20 I=1,M
               C(I,J)=C(I,J)+A(I,K)*B(K,J)
20          CONTINUE
30       CONTINUE
40    CONTINUE
      RETURN
C
C     LAST CARD OF MULC
C
      END
      SUBROUTINE RANDM(A, LDA, M, N, DPAR, JOB)
C
      INTEGER LDA,N,M,JOB
      DOUBLE PRECISION A(LDA,N),DPAR(3)
C
C     THIS SUBROUTINE IS A GENERAL FACILITY FOR PRODUCING RANDOM MATRI-
C     CES.  SEE JOB PARAMETER FOR OPTIONS.  TO USE THIS ROUTINE DXRAND
C     -MUST- BE INITIALIZED BY THE USER.
C
C     ON ENTRY -
C       LDA     INTEGER
C               LEADING DECLARED DIMENSION OF  A.
C
C       M,N     INTEGER
C               ROW AND COLUMN DIMENSION OF  A , RESPECTIVELY.
C
C       DPAR    DOUBLE PRECISION (3)
C               AN ARRAY OF PARAMETERS (SEE JOB BELOW).
C
C       JOB     INTEGER
C               INTEGER IN DECIMAL FORM  ABCDE  INDICATING THE FOLLOWING
C                  A,B,C      (NOT USED, SHOULD BE SET TO ZERO)
C                  D .EQ. 0   MAKE RANDOM DENSE MATRICES
C                  D .EQ. 1   MAKE RANDOM SPARSE MATRICES WITH EACH
C                             ELEMENT HAVING PROBABILITY DPAR(3) OF
C                             BEING  ZERO.
C                  E .EQ. 0   USE UNIFORMLY DISTRIBUTED NUMBERS ON THE
C                             INTERVAL  [ DPAR(1), DPAR(2) ) .
C                  E .EQ. 1   USE GAUSSIAN RANDOMS WITH MEAN  DPAR(1),
C                             AND VARIANCE  DPAR(2).
C                  E .EQ. 2   USE EXPONENTIALLY DISTRIBUTED VARIABLES
C                             IN THE RANGE [ DPAR(1), DPAR(2) ).
C
C     ON RETURN -
C       A       DOUBLE PRECISION(LDA,N)
C               M BY N MATRIX OF RANDOMS
C
C     SUBROUTINES AND FUNCTIONS USED -
C       (MATU) DGAUS; (FORTRAN) MOD IDINT DXRAND;
C
C     WRITTEN -
C       18FEB87 M.WETTE, UCSB ECE, SANTA BARBARA, CA 93106 (805)961-4691
C
      INTEGER I,J,ITYPE
      DOUBLE PRECISION DIFF,DM,DS,DA,DB,THRESH
      LOGICAL SPARSE
C
      EXTERNAL DXRAND
      DOUBLE PRECISION DXRAND,DGAUS
C
      ITYPE = MOD(JOB,10)
      THRESH = 0.0D0
      SPARSE = (MOD(JOB/10,10) .NE. 0)
C
      IF (ITYPE .NE. 0) GOTO 60
C        --- UNIFORM RANDOM ---
         DIFF = DPAR(2) - DPAR(1)
         DA = DPAR(1)
         IF (SPARSE) GOTO 30
            DO 20 J = 1,N
               DO 10 I = 1,M
                  A(I,J) = DIFF*DXRAND(0) + DA
   10          CONTINUE
   20       CONTINUE
         RETURN
   30    CONTINUE
            DO 50 J = 1,N
               DO 40 I = 1,M
                  A(I,J) = 0.0D0
                  IF (DXRAND(0) .GT. DPAR(3))
     *                A(I,J) = DIFF*DXRAND(0) + DA
   40          CONTINUE
   50       CONTINUE
         RETURN
   60 CONTINUE
      IF (ITYPE .NE. 1) GOTO 120
C        --- GAUSSIAN RANDOMS ---
         DM = DPAR(1)
         DS = DPAR(2)
         IF (SPARSE) GOTO 90
            DO 80 J = 1,N
               DO 70 I = 1,M
                     A(I,J) = DGAUS(DM,DS)
   70          CONTINUE
   80       CONTINUE
            RETURN
   90    CONTINUE
            DO 110 J = 1,N
               DO 100 I = 1,M
                  IF (DXRAND(0) .GT. DPAR(3))
     *               A(I,J) = DGAUS(DM,DS)
  100          CONTINUE
  110       CONTINUE
            RETURN
  120 CONTINUE
      IF (ITYPE .NE. 2) GOTO 180
C        --- EXPONENTIAL ---
         DA = DPAR(1)
         DB = LOG(DPAR(2)/DA)
         IF (SPARSE) GOTO 150
            DO 140 J = 1,N
               DO 130 I = 1,M
                  A(I,J) = DA*EXP(DB)
  130          CONTINUE
  140       CONTINUE
            RETURN
  150    CONTINUE
            DO 170 J = 1,N
               DO 160 I = 1,M
                  IF (DXRAND(0) .GT. THRESH)
     *               A(I,J) = DA*EXP(DB)
  160          CONTINUE
  170       CONTINUE
            RETURN
  180 CONTINUE
      RETURN
C
C --- LAST LINE OF RANDM ---
      END
      DOUBLE PRECISION FUNCTION DXRAND(I)
      INTEGER I
      REAL RAND
      IF (I .GT. 0) THEN
        CALL SEED(I)
        DXRAND = 0.0D0
      ELSE
        DXRAND = DBLE(RAND())
      ENDIF
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver1.f'
then
	echo shar: will not over-write existing file "'driver1.f'"
else
cat << "SHAR_EOF" > 'driver1.f'
C--**--CH2907--705--P:LAP--28:10:1999
C--**--CH2876--705--B:MA--28:10:1999
C--**--CH2862--705--A:H--28:10:1999
C     -- PROGRAM TSYLG --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE GENERAL
C     SYLVESTER EQUATION
C
C        A * X * B' +  C * X * D' =  E    (' DENOTES TRANSPOSE)
C
C     USING A SET OF ILL-CONDITIONED EQUATIONS.  SEE "SOLUTION OF THE
C     SYLVESTER MATRIX EQUATION AXB'+CXD'=E" BY GARDINER, LAUB, AMATO,
C     AND MOLER FOR A DESCRIPTION OF THE TEST PROBLEMS.
C
C     THE SOLUTION IS CHECKED BY COMPUTING THE RESIDUAL AND ITS RELATIVE
C     1-NORM.  THE CONDITION ESTIMATE IS CHECKED FOR SMALL SYSTEMS ONLY
C     (M*N <= 40) BY FORMING THE KRONECKER PRODUCT MATRIX AND COMPUTING
C     ITS SINGULAR VALUE DECOMPOSITION.
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLG; (LINPACK) DSVDC;
C       (MATU) MSAVE, D1NRM, MSUB, MULC, TRNATA
C
C     WRITTEN -
C       28NOV88 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C     REVISED -
C       17DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM M IS 9, MAXIMUM N IS 8 --
      INTEGER NAC, NBD, NE, NW1, NW2, NW3, M, N, IERR
      INTEGER MMAX, NMAX, MNMAX, WRKLEN, MAXSVD
      PARAMETER (MMAX=9, NMAX=8, MNMAX=9, MAXSVD=40,
     +  WRKLEN = 2*MMAX*MMAX+NMAX*NMAX+NMAX*MMAX+7*MMAX+MNMAX*MNMAX)
      DOUBLE PRECISION A0(MMAX,MMAX), B0(NMAX,NMAX), C0(MMAX,MMAX),
     +                 D0(NMAX,NMAX), E0(MMAX,NMAX)
      DOUBLE PRECISION A1(MMAX,MMAX), B1(NMAX,NMAX), C1(MMAX,MMAX),
     +                 D1(NMAX,NMAX), E1(MMAX,NMAX)
      DOUBLE PRECISION WKM1(MMAX,NMAX), WKM2(MMAX,NMAX), 
     +                 WKM3(MAXSVD,MAXSVD), WKV(WRKLEN)
      INTEGER IWKV(2*MMAX)
C
      INTEGER I, J, II, JJ, INDX, JNDX, MXN
      INTEGER IDMY, KT
      DOUBLE PRECISION TMP, NRMR, NRME, WORST, RCOND, RCDSVD
      DOUBLE PRECISION DUMY(1), WORSTL, WORSTH, RATIO, S
      DOUBLE PRECISION D1NRM
C     --- OUTPUT UNIT FOR WRITE ---
      NAC = MMAX
      NBD = NMAX
      NE = MMAX
      NW1 = MMAX
      NW2 = MMAX
      NW3 = MAXSVD
C
C     -- INITIALIZE --
      WORST = 0.0D0
      WORSTL = 1.0D100
      WORSTH = 0.0D0
C
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
90001 FORMAT(" SOLVE  A*X*B  + C*X*D  = E  USING SYLG")
C
C     USE THESE TWO LINES TO RUN A COMPLETE TEST
C
       DO 320 M = 2,NAC
       DO 310 N = 2,NBD
C
C     USE THESE TWO LINES TO RUN A MINIMAL INSTALLATION TEST
C
C     DO 320 M = 3,3
C     DO 310 N = 2,2
C
      WRITE(*,90005) M, N
C
90005 FORMAT(/ " M =", I3, "   N =", I3)
      DO 230 KT = 0,40,10
         S = (2.0D0)**(-KT)
C
C GENERATE COEFFICIENT MATRICES  --  TRUE SOLUTION IS MATRIX OF ALL ONES
C
         DO 120 I=1,M
            DO 110 J=1,I
               A0(I,J) = 1.0D0
               A0(J,I) = 0.0D0
               C0(J,I) = S
               C0(I,J) = 0.0D0
  110       CONTINUE
            A0(I,I) = I
            C0(I,I) = 1.0D0
  120    CONTINUE
C
         DO 140 I=1,N
            DO 130 J=1,I
               B0(J,I) = S
               B0(I,J) = 0.0D0
               D0(I,J) = 1.0D0
               D0(J,I) = 0.0D0
  130       CONTINUE
            B0(I,I) = 1.0D0
            D0(I,I) = S - (N-I+1)
  140    CONTINUE
C
         DO 160 I=1,M
            WKV(I) = 0.0D0
            WKV(M+I) = 0.0D0
            DO 150 J=1,M
               WKV(I) = WKV(I) + A0(I,J)
               WKV(M+I) = WKV(M+I) + C0(I,J)
  150       CONTINUE
  160    CONTINUE
         DO 190 I=1,N
            TMP = 0.0D0
            DUMY(1) = 0.0D0
            DO 170 J=1,N
               TMP = TMP + B0(I,J)
               DUMY(1) = DUMY(1) + D0(I,J)
  170       CONTINUE
            DO 180 J=1,M
               E0(J,I) = TMP * WKV(J) + DUMY(1) * WKV(M+J)
  180       CONTINUE
  190    CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAC, NAC, M, M, A0, A1)
         CALL MSAVE(NAC, NAC, M, M, C0, C1)
         CALL MSAVE(NBD, NBD, N, N, B0, B1)
         CALL MSAVE(NBD, NBD, N, N, D0, D1)
         CALL MSAVE(NE, NE, M, N, E0, E1)
C
C        -- COMPUTE NORM OF E --
         NRME = D1NRM(NE, M, N, E0)
C
C        -- COMPUTE SOLUTION, ESTIMATE CONDITION IF SVD COMPUTABLE --
         MXN = M*N
         IF (MXN .LE. MAXSVD) THEN
            IERR = 1
         ELSE
            IERR = 0
         ENDIF
         CALL SYLG(NAC, NBD, NE, M, N, A0, B0, C0, D0, E0, WKV, IWKV,
     *             IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) KT, IERR
90003       FORMAT(" AT ITERATION", I2, " ERROR IN SYLG, IERR=", I2)
         ENDIF
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAC, NE, NW1, M, M, N, A1, E0, WKM1)
         CALL TRNATA(NBD, N, B1)
         CALL MULC(NW1, NBD, NW2, M, N, N, WKM1, B1, WKM2)
         CALL TRNATA(NBD, N, B1)
         CALL MSUB(NE, NW2, NE, M, N, E1, WKM2, E1)
         CALL MULC(NAC, NE, NW1, M, M, N, C1, E0, WKM1)
         CALL TRNATA(NBD, N, D1)
         CALL MULC(NW1, NBD, NW2, M, N, N, WKM1, D1, WKM2)
         CALL TRNATA(NBD, N, D1)
         CALL MSUB(NE, NW2, NE, M, N, E1, WKM2, E1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NE, M, N, E1)
         TMP = NRMR/NRME
         IF (TMP .GT. WORST) WORST = TMP
C
C        -- COMPUTE REAL CONDITION NUMBER --
         IF (MXN .LE. MAXSVD) THEN
            DO 40 J = 1,N
               DO 30 JJ = 1,M
                  DO 20 I = 1,N
                     DO 10 II = 1,M
                        INDX = M*(I-1) + II
                        JNDX = M*(J-1) + JJ
                        WKM3(INDX,JNDX) = A1(II,JJ)*B1(I,J)
     &                                    + C1(II,JJ)*D1(I,J)
   10                CONTINUE
   20             CONTINUE
   30          CONTINUE
   40       CONTINUE
            IDMY = 1
            CALL DSVDC(WKM3, NW3, MXN, MXN, WKV, WKV(MXN+1), DUMY, IDMY,
     *                 DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006) KT
90006          FORMAT(" ITERATION", I2, " SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(MXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
            IF (RATIO .LT. WORSTL) WORSTL = RATIO
            IF (RATIO .GT. WORSTH) WORSTH = RATIO
         ENDIF
C
C        -- PRINT RESULTS --
         IF (MXN .LE. MAXSVD) THEN
            WRITE(*,90002) KT, TMP, RCOND, RATIO
         ELSE
            WRITE(*,90007) KT, TMP
         ENDIF
90002    FORMAT(1X, I2, '  (NRM RESID)/(NRM E)=', E10.3,          '  RCO
     +ND(EST)=', E10.3, ' EST/TRUE=', E10.3)
C
90007    FORMAT(1X, I2, '  (NRM RESID)/(NRM E)=', E10.3)
  230 CONTINUE
C
  310 CONTINUE
  320 CONTINUE
C
      WRITE(*,90004) WORST
90004 FORMAT(/ " WORST CASE RESIDUAL IS", E10.3)
      WRITE(*,90008) WORSTL, WORSTH
C
90008 FORMAT(' WORST CASE RCOND RATIOS (EST/TRUE) ARE', E10.3,       ' (
     +LOW) AND', E10.3, ' (HIGH)')
      WRITE(*,90010)
90010 FORMAT(// ' THE RESIDUAL SHOULD BE ON THE ORDER OF 1E-14',        
     +  ' OR SMALLER ON MOST MACHINES.')
      WRITE(*,90011)
C
90011 FORMAT(' THE RCOND RATIOS SHOULD BE ON THE ORDER OF 1,',       ' I
     +.E., BETWEEN .1 AND 10.')
      STOP
C --- LAST LINE OF TSYLG ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver2.f'
then
	echo shar: will not over-write existing file "'driver2.f'"
else
cat << "SHAR_EOF" > 'driver2.f'
C--**--CH2908--705--P:LAP--28:10:1999
C--**--CH2885--705--C:SU--28:10:1999
C--**--CH2881--705--B:MA--28:10:1999
C--**--CH2863--705--A:H--28:10:1999
C     -- PROGRAM TSYLGC --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE SYMMETRIC
C     SYLVESTER EQUATION
C
C        A*X*E' + E*X*A' + Q = 0    (' DENOTES TRANSPOSE)
C
C     USING A SET OF ILL-CONDITIONED EQUATIONS.  SEE "SOLUTION OF THE
C     SYLVESTER MATRIX EQUATION AXB'+CXD'=E" BY GARDINER, LAUB, AMATO,
C     AND MOLER FOR A DESCRIPTION OF THE TEST PROBLEMS.
C
C     THE SOLUTION IS CHECKED BY COMPUTING THE RESIDUAL AND ITS RELATIVE
C     1-NORM.  THE CONDITION ESTIMATE IS CHECKED FOR SMALL SYSTEMS ONLY
C     (N*N <= 40) BY FORMING THE KRONECKER PRODUCT MATRIX AND COMPUTING
C     ITS SINGULAR VALUE DECOMPOSITION.
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLGC; (LINPACK) DSVDC; (MATU) MADD MULC TRNATA D1NRM MSAVE
C
C     WRITTEN -
C       27JAN89 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C     REVISED -
C       12DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM N IS 8 --
      INTEGER NAE, NQ, NW, N, IERR, NWX, IDMY, KT
      INTEGER NMAX, WRKLEN, MAXSVD
      PARAMETER (NMAX=8, WRKLEN=2*NMAX*NMAX+3*NMAX,
     +           MAXSVD=40)
      DOUBLE PRECISION A(NMAX,NMAX), E(NMAX,NMAX), Q(NMAX,NMAX)
      DOUBLE PRECISION WKM1(NMAX,NMAX), WKM2(NMAX,NMAX),
     +                 WKV(WRKLEN)
C
      INTEGER I, J, NXN, II, JJ, INDX, JNDX
      DOUBLE PRECISION A1(NMAX,NMAX), E1(NMAX,NMAX), Q1(NMAX,NMAX), 
     +                 WKMX(MAXSVD,MAXSVD)
      DOUBLE PRECISION TMP, NRMR, NRMQ, WORST, RCOND, RCDSVD
      DOUBLE PRECISION WORSTL, WORSTH, RATIO, DUMY(1), ST
      DOUBLE PRECISION D1NRM
C     --- OUTPUT UNIT FOR WRITE ---
      NAE = NMAX
      NQ = NMAX
      NW = NMAX
      NWX = MAXSVD
C
C     -- INITIALIZE --
      WORST = 0.0D0
      WORSTL = 1.0D100
      WORSTH = 0.0D0
C
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
90001 FORMAT(" SOLVE  A*X*E  + E*X*A  + Q = 0  USING SYLGC")
C
C     USE THIS LINE TO RUN A COMPLETE TEST
C
       DO 300 N = 1,NMAX
C
C     USE THIS LINE TO RUN A MINIMAL INSTALLATION TEST
C
C     DO 300 N = 5,5
C
      WRITE(*,90005) N
C
90005 FORMAT(/ " N =", I3)
      DO 230 KT = 0,40,10
         ST = (2.0D0)**(-KT)
C
C GENERATE COEFFICIENT MATRICES  --  TRUE SOLUTION IS MATRIX OF ALL ONES
C
         DO 80 I=1,N
            DO 70 J=1,I
               A(I,J) = 1.0D0
               A(J,I) = 0.0D0
               E(J,I) = ST
               E(I,J) = 0.0D0
   70       CONTINUE
            A(I,I) = ST + (I-1)
            E(I,I) = 1.0D0
   80    CONTINUE
C
         DO 160 I=1,N
            WKV(I) = 0.0D0
            DO 150 J=1,N
               WKV(I) = WKV(I) + A(I,J)
  150       CONTINUE
  160    CONTINUE
         DO 190 I=1,N
            TMP = 0.0D0
            DO 170 J=1,N
               TMP = TMP + E(I,J)
  170       CONTINUE
            DO 180 J=1,N
               Q(J,I) = TMP * WKV(J)
  180       CONTINUE
  190    CONTINUE
         DO 210 I=1,N
            DO 200 J=1,I
               Q(I,J) = -(Q(I,J) + Q(J,I))
               Q(J,I) = Q(I,J)
  200       CONTINUE
  210    CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAE, NAE, N, N, A, A1)
         CALL MSAVE(NAE, NAE, N, N, E, E1)
         CALL MSAVE(NQ, NQ, N, N, Q, Q1)
C
C        -- COMPUTE NORM OF Q --
         NRMQ = D1NRM(NQ, N, N, Q)
C
C        -- COMPUTE SOLUTION, ESTIMATE CONDITION IF SVD COMPUTABLE --
         NXN = N*N
         IF (NXN .LE. MAXSVD) THEN
            IERR = 1
         ELSE
            IERR = 0
         ENDIF
         CALL SYLGC(NAE, NQ, N, A, E, Q, WKV, IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) KT, IERR
90003       FORMAT(" AT ITERATION", I2, " ERROR IN SYLGC, IERR=", I2)
         ENDIF
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAE, NQ, NW, N, N, N, A1, Q, WKM1)
         CALL TRNATA(NAE, N, E1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, E1, WKM2)
         CALL TRNATA(NAE, N, E1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
         CALL MULC(NAE, NQ, NW, N, N, N, E1, Q, WKM1)
         CALL TRNATA(NAE, N, A1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, A1, WKM2)
         CALL TRNATA(NAE, N, A1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NQ, N, N, Q1)
         TMP = NRMR/NRMQ
         IF (TMP .GT. WORST) WORST = TMP
C
C        -- COMPUTE REAL CONDITION NUMBER
         IF (NXN .LE. MAXSVD) THEN
            DO 140 J = 1,N
               DO 130 JJ = 1,N
                  DO 120 I = 1,N
                     DO 110 II = 1,N
                        INDX = N*(I-1) + II
                        JNDX = N*(J-1) + JJ
                        WKMX(INDX,JNDX) = A1(II,JJ)*E1(I,J)
     *                                    + E1(II,JJ)*A1(I,J)
  110                CONTINUE
  120             CONTINUE
  130          CONTINUE
  140       CONTINUE
            IDMY = 1
            CALL DSVDC(WKMX, NWX, NXN, NXN, WKV, WKV(NXN+1), DUMY, IDMY,
     *                 DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006) KT
90006          FORMAT(" ITERATION", I2, " SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(NXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
            IF (RATIO .LT. WORSTL) WORSTL = RATIO
            IF (RATIO .GT. WORSTH) WORSTH = RATIO
         ENDIF
C
C        -- PRINT RESULTS --
         IF (NXN .LE. MAXSVD) THEN
            WRITE(*,90002) KT, TMP, RCOND, RATIO
         ELSE
            WRITE(*,90007) KT, TMP
         ENDIF
90002    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3,          '  RCO
     +ND(EST)=', E10.3, ' EST/TRUE=', E10.3)
C
C
90007    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3)
  230 CONTINUE
  300 CONTINUE
C
      WRITE(*,90004) WORST
90004 FORMAT(/ " WORST CASE RESIDUAL IS", E10.3)
      WRITE(*,90008) WORSTL, WORSTH
C
90008 FORMAT(' WORST CASE RCOND RATIOS (EST/TRUE) ARE', E10.3,       ' (
     +LOW) AND', E10.3, ' (HIGH)')
      WRITE(*,90010)
90010 FORMAT(// ' THE RESIDUAL SHOULD BE ON THE ORDER OF 1E-14',        
     +  ' OR SMALLER ON MOST MACHINES.')
      WRITE(*,90011)
C
90011 FORMAT(' THE RCOND RATIOS SHOULD BE ON THE ORDER OF 1,',       ' I
     +.E., BETWEEN .1 AND 10.')
      STOP
C --- LAST LINE OF TSYLGC ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver3.f'
then
	echo shar: will not over-write existing file "'driver3.f'"
else
cat << "SHAR_EOF" > 'driver3.f'
C--**--CH3665--705--C:SU--8:6:2000
C--**--CH2912--705--P:FIX--28:10:1999
C--**--CH2909--705--P:LAP--28:10:1999
C--**--CH2903--705--P:RW--28:10:1999
C--**--CH2895--705--B:FIX--28:10:1999
C--**--CH2886--705--B:MA--28:10:1999
C--**--CH2864--705--A:H--28:10:1999
C     -- PROGRAM TSYLGD --
C
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE SYMMETRIC
C     SYLVESTER EQUATION
C
C        A*X*A' - E*X*E' + Q = 0    (' DENOTES TRANSPOSE)
C
C     USING A SET OF ILL-CONDITIONED EQUATIONS.  SEE "SOLUTION OF THE
C     SYLVESTER MATRIX EQUATION AXB'+CXD'=E" BY GARDINER, LAUB, AMATO,
C     AND MOLER FOR A DESCRIPTION OF THE TEST PROBLEMS.
C
C     THE SOLUTION IS CHECKED BY COMPUTING THE RESIDUAL AND ITS RELATIVE
C     1-NORM.  THE CONDITION ESTIMATE IS CHECKED FOR SMALL SYSTEMS ONLY
C     (N*N <= 40) BY FORMING THE KRONECKER PRODUCT MATRIX AND COMPUTING
C     ITS SINGULAR VALUE DECOMPOSITION.
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLGD; (LINPACK) DSVDC; (MATU) MADD MULC TRNATA D1NRM MSAVE MSUB
C
C     WRITTEN -
C       27JAN89 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C     REVISED -
C       14DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM N IS 8 --
      INTEGER NAE, NQ, NW, N, IERR, NWX, IDMY, KT
C     INTEGER MAXN
      INTEGER NMAX, WRKLEN, MAXSVD
      PARAMETER (NMAX=8, WRKLEN=2*NMAX*NMAX+3*NMAX,MAXSVD=40)
      DOUBLE PRECISION A(NMAX,NMAX), E(NMAX,NMAX), Q(NMAX,NMAX)
      DOUBLE PRECISION WKM1(NMAX,NMAX), WKM2(NMAX,NMAX),
     +                 WKV(WRKLEN)
C
      INTEGER I, J, NXN, II, JJ, INDX, JNDX
      DOUBLE PRECISION A1(NMAX,NMAX), E1(NMAX,NMAX), Q1(NMAX,NMAX), 
     +                 WKMX(MAXSVD,MAXSVD)
      DOUBLE PRECISION TMP, NRMR, NRMQ, WORST, RCOND, RCDSVD
      DOUBLE PRECISION WORSTL, WORSTH, RATIO, DUMY(1), ST
      DOUBLE PRECISION D1NRM
      NAE = NMAX
      NQ = NMAX
      NW = NMAX
      NWX = MAXSVD
C
C     -- INITIALIZE --
      WORST = 0.0D0
      WORSTL = 1.0D100
      WORSTH = 0.0D0
C     NTEST = 5
C
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
90001 FORMAT(" SOLVE  A*X*A  - E*X*E  + Q = 0  USING SYLGD")
C
C     USE THIS LINE TO RUN A COMPLETE TEST
C
       DO 300 N = 2,NMAX
C
C     USE THIS LINE TO RUN A MINIMAL INSTALLATION TEST
C
C     DO 300 N = 5,5
C
      WRITE(*,90005) N
C
90005 FORMAT(/ " N =", I3)
      DO 230 KT = 0,40,10
         ST = (2.0D0)**(-KT)
C
C GENERATE COEFFICIENT MATRICES  --  TRUE SOLUTION IS MATRIX OF ALL ONES
C
         DO 80 I=1,N
            DO 70 J=1,I
               A(I,J) = 1.0D0
               A(J,I) = 0.0D0
               E(J,I) = ST
               E(I,J) = 0.0D0
   70       CONTINUE
            A(I,I) = ST + I
            E(I,I) = 1.0D0
   80    CONTINUE
C
         DO 160 I=1,N
            WKV(I) = 0.0D0
            WKV(I+N) = 0.0D0
            DO 150 J=1,N
               WKV(I) = WKV(I) + A(I,J)
               WKV(I+N) = WKV(I+N) + E(I,J)
  150       CONTINUE
  160    CONTINUE
         DO 190 I=1,N
            TMP = 0.0D0
            DUMY(1) = 0.0D0
            DO 170 J=1,N
               TMP = TMP + A(I,J)
               DUMY(1) = DUMY(1) + E(I,J)
  170       CONTINUE
            DO 180 J=1,N
               Q(J,I) = -( TMP * WKV(J) - DUMY(1) * WKV(J+N) )
  180       CONTINUE
  190    CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAE, NAE, N, N, A, A1)
         CALL MSAVE(NAE, NAE, N, N, E, E1)
         CALL MSAVE(NQ, NQ, N, N, Q, Q1)
C
C        -- COMPUTE NORM OF Q --
         NRMQ = D1NRM(NQ, N, N, Q)
C
C        -- COMPUTE SOLUTION, ESTIMATE CONDITION IF SVD COMPUTABLE --
         NXN = N*N
         IF (NXN .LE. MAXSVD) THEN
            IERR = 1
         ELSE
            IERR = 0
         ENDIF
         CALL SYLGD(NAE, NQ, N, A, E, Q, WKV, IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) KT, IERR
90003       FORMAT(" AT ITERATION", I2, " ERROR IN SYLGD, IERR=", I2)
         ENDIF
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAE, NQ, NW, N, N, N, A1, Q, WKM1)
         CALL TRNATA(NAE, N, A1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, A1, WKM2)
         CALL TRNATA(NAE, N, A1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
         CALL MULC(NAE, NQ, NW, N, N, N, E1, Q, WKM1)
         CALL TRNATA(NAE, N, E1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, E1, WKM2)
         CALL TRNATA(NAE, N, E1)
         CALL MSUB(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NQ, N, N, Q1)
         TMP = NRMR/NRMQ
         IF (TMP .GT. WORST) WORST = TMP
C
C        -- COMPUTE REAL CONDITION NUMBER
         IF (NXN .LE. MAXSVD) THEN
            DO 140 J = 1,N
               DO 130 JJ = 1,N
                  DO 120 I = 1,N
                     DO 110 II = 1,N
                        INDX = N*(I-1) + II
                        JNDX = N*(J-1) + JJ
                        WKMX(INDX,JNDX) = A1(II,JJ)*A1(I,J)
     *                                    - E1(II,JJ)*E1(I,J)
  110                CONTINUE
  120             CONTINUE
  130          CONTINUE
  140       CONTINUE
            IDMY = 1
            CALL DSVDC(WKMX, NWX, NXN, NXN, WKV, WKV(NXN+1), DUMY, IDMY,
     *                 DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006) KT
90006          FORMAT(" ITERATION", I2, " SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(NXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
            IF (RATIO .LT. WORSTL) WORSTL = RATIO
            IF (RATIO .GT. WORSTH) WORSTH = RATIO
         ENDIF
C
C        -- PRINT RESULTS --
         IF (NXN .LE. MAXSVD) THEN
            WRITE(*,90002) KT, TMP, RCOND, RATIO
         ELSE
            WRITE(*,90007) KT, TMP
         ENDIF
90002    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3,          '  RCO
     +ND(EST)=', E10.3, ' EST/TRUE=', E10.3)
C
C
90007    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3)
  230 CONTINUE
  300 CONTINUE
C
      WRITE(*,90004) WORST
90004 FORMAT(/ " WORST CASE RESIDUAL IS", E10.3)
      WRITE(*,90008) WORSTL, WORSTH
C
90008 FORMAT(' WORST CASE RCOND RATIOS (EST/TRUE) ARE', E10.3,       ' (
     +LOW) AND', E10.3, ' (HIGH)')
      WRITE(*,90010)
90010 FORMAT(// ' THE RESIDUAL SHOULD BE ON THE ORDER OF 1E-14',        
     +  ' OR SMALLER ON MOST MACHINES.')
      WRITE(*,90011)
C
90011 FORMAT(' THE RCOND RATIOS SHOULD BE ON THE ORDER OF 1,',       ' I
     +.E., BETWEEN .1 AND 10.')
      STOP
C --- LAST LINE OF TSYLGD ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver4.f'
then
	echo shar: will not over-write existing file "'driver4.f'"
else
cat << "SHAR_EOF" > 'driver4.f'
C--**--CH2919--705--P:FIX--28:10:1999
C--**--CH2910--705--P:LAP--28:10:1999
C--**--CH2896--705--B:FIX--28:10:1999
C--**--CH2887--705--B:MA--28:10:1999
C--**--CH2865--705--A:H--28:10:1999
C--**--CH2859--705--P:RW--28:10:1999
C     -- PROGRAM TSYLGF --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE GENERAL
C     SYLVESTER EQUATION
C
C        A * X * B' +  C * X * D' =  E    (' DENOTES TRANSPOSE)
C
C     READING THE COEFFICIENT MATRICES FROM A FILE.
C
C     THE SOLUTION IS CHECKED BY COMPUTING THE RESIDUAL AND ITS RELATIVE
C     1-NORM.  THE CONDITION ESTIMATE IS CHECKED FOR SMALL SYSTEMS ONLY
C     (M*N <= 40) BY FORMING THE KRONECKER PRODUCT MATRIX AND COMPUTING
C     ITS SINGULAR VALUE DECOMPOSITION.
C
C     INPUT FILE FORMAT (SEE EXAMPLE FILE TEST1.IN):
C       INPUT IS FREE FORMAT; MATRICES ARE READ BY ROWS.
C       DIMENSIONS M AND N (INTEGER)
C       A; EACH ROW MUST BEGIN ON A NEW LINE AND MAY TAKE AS MANY LINES
C       AS NECESSARY.
C       B; C; D; E; SAME COMMENT.
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLG; (LINPACK) DSVDC;
C       (MATU) MSAVE, D1NRM, MSUB, MULC, TRNATA
C
C     WRITTEN -
C       12DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM M IS 9, MAXIMUM N IS 8 --
      INTEGER NAC, NBD, NE, NW, M, N, IERR
      INTEGER MMAX, NMAX, MNMAX, WRKLEN, MAXSVD
      PARAMETER (MMAX=9, NMAX=8, MNMAX=9, MAXSVD=40,
     +  WRKLEN = 2*MMAX*MMAX+NMAX*NMAX+NMAX*MMAX+7*MMAX+MNMAX*MNMAX)
      DOUBLE PRECISION A0(MMAX,MMAX), B0(NMAX,NMAX), C0(MMAX,MMAX),
     +                 D0(NMAX,NMAX), E0(MMAX,NMAX)
      DOUBLE PRECISION A1(MMAX,MMAX), B1(NMAX,NMAX), C1(MMAX,MMAX),
     +                 D1(NMAX,NMAX), E1(MMAX,NMAX)
      DOUBLE PRECISION WKM1(MMAX,MMAX), WKM2(NMAX,NMAX), 
     +                 WRKSVD(MAXSVD,MAXSVD), WKV(WRKLEN)
      INTEGER IWKV(2*MMAX)
C
      INTEGER I, J, II, JJ, INDX, JNDX, MXN
      INTEGER IDMY
      DOUBLE PRECISION NRMR, NRME, RCOND, RCDSVD
      DOUBLE PRECISION DUMY(1), RATIO
      DOUBLE PRECISION D1NRM
C     CHARACTER*20 INNAME, OUTNAM
      CHARACTER YESNO
C
      NAC = MMAX
      NBD = NMAX
      NE = MMAX
      NW = NMAX
C
C     -- INITIALIZE --
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
C
C      WRITE(*,91002)
C91002 FORMAT(/' ENTER NAME OF FILE CONTAINING COEFFICIENT MATRICES ')
C      READ(5,91003) INNAME
C91003 FORMAT(A)
C      OPEN(2,FILE=INNAME)
C      WRITE(*,91004)
C91004 FORMAT(/' ENTER NAME OF FILE FOR OUTPUT OF SOLUTION MATRIX')
C      READ(5,91003) OUTNAM
C      OPEN(3,FILE=OUTNAM)
C
C     -- READ COEFFICIENT MATRICES --
90001 FORMAT(" SOLVE  A*X*B  + C*X*D  = E  USING SYLG")
      READ(*,*) M, N
      IF (M .GT. NAC  .OR.  N .GT. NBD) THEN
         WRITE(*,91005) M, N, NAC, NBD
91005    FORMAT(/' DIMENSION OF PROBLEM IS TOO LARGE:  M =',I2,', N =', 
     +         I2 / ' MAXIMUM:  M =',I2,', N =',I2)
         STOP
      ENDIF
      WRITE(*,91008) M, N
C
91008 FORMAT(/' M =',I2,', N =',I2)
      DO 201 I=1,M
         READ(*,*)(A0(I,J),J=1,M)
 201  CONTINUE
      DO 202 I=1,N
         READ(*,*)(B0(I,J),J=1,N)
 202  CONTINUE
      DO 203 I=1,M
         READ(*,*)(C0(I,J),J=1,M)
 203  CONTINUE
      DO 204 I=1,N
         READ(*,*)(D0(I,J),J=1,N)
 204  CONTINUE
      DO 205 I=1,M
         READ(*,*)(E0(I,J),J=1,N)
 205  CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAC, NAC, M, M, A0, A1)
         CALL MSAVE(NAC, NAC, M, M, C0, C1)
         CALL MSAVE(NBD, NBD, N, N, B0, B1)
         CALL MSAVE(NBD, NBD, N, N, D0, D1)
         CALL MSAVE(NE, NE, M, N, E0, E1)
C
C        -- COMPUTE NORM OF E --
         NRME = D1NRM(NE, M, N, E0)
C
C        -- COMPUTE SOLUTION AND ESTIMATE CONDITION
         IERR = 1
         CALL SYLG(NAC, NBD, NE, M, N, A0, B0, C0, D0, E0, WKV, IWKV,
     *             IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) IERR
90003       FORMAT(" ERROR FROM SYLG, IERR=", I2)
         ENDIF
C
C        -- SAVE SOLUTION --
         DO 301 I=1,M
            WRITE(*,92001) (E0(I,J),J=1,N)
92001       FORMAT(1X,6E12.4)
 301     CONTINUE
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAC, NE, NW, M, M, N, A1, E0, WKM1)
         CALL TRNATA(NBD, N, B1)
         CALL MULC(NW, NBD, NW, M, N, N, WKM1, B1, WKM2)
         CALL TRNATA(NBD, N, B1)
         CALL MSUB(NE, NW, NE, M, N, E1, WKM2, E1)
         CALL MULC(NAC, NE, NW, M, M, N, C1, E0, WKM1)
         CALL TRNATA(NBD, N, D1)
         CALL MULC(NW, NBD, NW, M, N, N, WKM1, D1, WKM2)
         CALL TRNATA(NBD, N, D1)
         CALL MSUB(NE, NW, NE, M, N, E1, WKM2, E1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NE, M, N, E1) / NRME
C
C        -- PRINT RESULTS --
         WRITE(*,90002) NRMR, RCOND
C
C     -- COMPUTE REAL CONDITION NUMBER IF REQUESTED --
90002    FORMAT(1X, '  (NRM RESID)/(NRM E)=', E10.3,          '  RCOND(E
     +ST)=', E10.3)
      MXN = M*N
      IF (MXN .LE. MAXSVD) THEN
         WRITE(*,91006)
91006    FORMAT(/' DO YOU WISH TO HAVE THE ACTUAL CONDITION NUMBER',    
     +      ' COMPUTED? (Y OR N) ')
         READ(5,*)YESNO
         IF (YESNO .EQ. 'y'  .OR.  YESNO .EQ. 'Y') THEN
            DO 40 J = 1,N
               DO 30 JJ = 1,M
                  DO 20 I = 1,N
                     DO 10 II = 1,M
                        INDX = M*(I-1) + II
                        JNDX = M*(J-1) + JJ
                        WRKSVD(INDX,JNDX) = A1(II,JJ)*B1(I,J)
     *                                    + C1(II,JJ)*D1(I,J)
   10                CONTINUE
   20             CONTINUE
   30          CONTINUE
   40       CONTINUE
            IDMY = 1
            CALL DSVDC(WRKSVD, MAXSVD, MXN, MXN, WKV, WKV(MXN+1), DUMY,
     *                 IDMY, DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006)
90006          FORMAT(" SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(MXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
C
            WRITE(*,90007) RCDSVD, RATIO
90007       FORMAT(1X, '  RCOND(TRUE)=', E10.3, ' EST/TRUE=', E10.3)
         ENDIF
      ENDIF
C
      CLOSE(2)
      CLOSE(3)
      STOP
C --- LAST LINE OF TSYLGF ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver5.f'
then
	echo shar: will not over-write existing file "'driver5.f'"
else
cat << "SHAR_EOF" > 'driver5.f'
C--**--CH2913--705--P:LAP--28:10:1999
C--**--CH2897--705--C:SU--28:10:1999
C--**--CH2888--705--B:MA--28:10:1999
C--**--CH2866--705--A:H--28:10:1999
C--**--CH2860--705--P:RW--28:10:1999
C     -- PROGRAM TSYLGCF --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE SYMMETRIC
C     SYLVESTER EQUATION
C
C        A*X*E' + E*X*A' + Q = 0    (' DENOTES TRANSPOSE)
C
C     READING THE COEFFICIENT MATRICES FROM A FILE.
C
C     THE SOLUTION IS CHECKED BY COMPUTING THE RESIDUAL AND ITS RELATIVE
C     1-NORM.  THE CONDITION ESTIMATE IS CHECKED FOR SMALL SYSTEMS ONLY
C     (N*N <= 40) BY FORMING THE KRONECKER PRODUCT MATRIX AND COMPUTING
C     ITS SINGULAR VALUE DECOMPOSITION.
C
C     INPUT FILE FORMAT (SEE EXAMPLE FILE TESTCD.IN):
C       INPUT IS FREE FORMAT; MATRICES ARE READ BY ROWS.
C       DIMENSION N (INTEGER)
C       A; EACH ROW MUST BEGIN ON A NEW LINE AND MAY TAKE AS MANY LINES
C       AS NECESSARY.
C       E; Q; SAME COMMENT.
C
C     SOLUTION MATRIX X IS WRITTEN TO AN OUTPUT FILE (SEE EXAMPLE FILE
C       TESTC.OUT).
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLGC; (LINPACK) DSVDC; (MATU) MADD MULC TRNATA D1NRM MSAVE
C
C     WRITTEN -
C       14DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM N IS 8 --
      INTEGER NAE, NQ, NW, N, IERR, NWX, IDMY
      INTEGER NMAX, WRKLEN, MAXSVD
      PARAMETER (NMAX=8, WRKLEN=2*NMAX*NMAX+3*NMAX,
     +           MAXSVD=40)
      DOUBLE PRECISION A(NMAX,NMAX), E(NMAX,NMAX), Q(NMAX,NMAX)
      DOUBLE PRECISION WKM1(NMAX,NMAX), WKM2(NMAX,NMAX),
     +                 WKV(WRKLEN)
C
      INTEGER I, J, NXN, II, JJ, INDX, JNDX
      DOUBLE PRECISION A1(NMAX,NMAX), E1(NMAX,NMAX), Q1(NMAX,NMAX), 
     +                 WKMX(MAXSVD,MAXSVD)

      DOUBLE PRECISION NRMR, NRMQ, RCOND, RCDSVD
      DOUBLE PRECISION RATIO, DUMY(1)
      DOUBLE PRECISION D1NRM
C     CHARACTER*20 INNAME, OUTNAM
      CHARACTER YESNO
C
      NAE = NMAX
      NQ = NMAX
      NW = NMAX
      NWX = MAXSVD
C
C     -- INITIALIZE --
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
C
C
C      WRITE(*,91002)
C91002 FORMAT(/' ENTER NAME OF FILE CONTAINING COEFFICIENT MATRICES ')
C      READ(5,91003) INNAME
C91003 FORMAT(A)
C      OPEN(2,FILE=INNAME)
C      WRITE(*,91004)
C91004 FORMAT(/' ENTER NAME OF FILE FOR OUTPUT OF SOLUTION MATRIX')
C      READ(5,91003) OUTNAM
C      OPEN(3,FILE=OUTNAM)
C
C     -- READ COEFFICIENT MATRICES --
90001 FORMAT(" SOLVE  A*X*E  + E*X*A  + Q = 0  USING SYLGC")
      READ(*,*) N
      IF (N .GT. NAE) THEN
         WRITE(*,91005) N, NAE
91005    FORMAT(/' DIMENSION OF PROBLEM IS TOO LARGE:  N =',I2,         
     + '  MAXIMUM IS ',I2)
         STOP
      ENDIF
      WRITE(*,91008) N
C
91008 FORMAT(/' N =',I2)
      DO 201 I=1,N
         READ(*,*)(A(I,J),J=1,N)
 201  CONTINUE
      DO 202 I=1,N
         READ(*,*)(E(I,J),J=1,N)
 202  CONTINUE
      DO 203 I=1,N
         READ(*,*)(Q(I,J),J=1,N)
 203  CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAE, NAE, N, N, A, A1)
         CALL MSAVE(NAE, NAE, N, N, E, E1)
         CALL MSAVE(NQ, NQ, N, N, Q, Q1)
C
C        -- COMPUTE NORM OF Q --
         NRMQ = D1NRM(NQ, N, N, Q)
C
C        -- COMPUTE SOLUTION AND ESTIMATE CONDITION --
         IERR = 1
         CALL SYLGC(NAE, NQ, N, A, E, Q, WKV, IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) IERR
90003       FORMAT(" ERROR FROM SYLGC, IERR=", I2)
         ENDIF
C
C        -- SAVE SOLUTION --
         DO 301 I=1,N
            WRITE(*,92001) (Q(I,J),J=1,N)
92001       FORMAT(1X,6E12.4)
 301     CONTINUE
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAE, NQ, NW, N, N, N, A1, Q, WKM1)
         CALL TRNATA(NAE, N, E1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, E1, WKM2)
         CALL TRNATA(NAE, N, E1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
         CALL MULC(NAE, NQ, NW, N, N, N, E1, Q, WKM1)
         CALL TRNATA(NAE, N, A1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, A1, WKM2)
         CALL TRNATA(NAE, N, A1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NQ, N, N, Q1) / NRMQ
C
C        -- PRINT RESULTS --
         WRITE(*,90002) NRMR, RCOND
C
C     -- COMPUTE REAL CONDITION NUMBER IF REQUESTED --
90002    FORMAT(1X, '  (NRM RESID)/(NRM Q)=', E10.3,          '  RCOND(E
     +ST)=', E10.3)
      NXN = N*N
      IF (NXN .LE. MAXSVD) THEN
         WRITE(*,91006)
91006    FORMAT(/' DO YOU WISH TO HAVE THE ACTUAL CONDITION NUMBER',    
     +      ' COMPUTED? (Y OR N) ')
         READ(5,*)YESNO
         IF (YESNO .EQ. 'y'  .OR.  YESNO .EQ. 'Y') THEN
            DO 140 J = 1,N
               DO 130 JJ = 1,N
                  DO 120 I = 1,N
                     DO 110 II = 1,N
                        INDX = N*(I-1) + II
                        JNDX = N*(J-1) + JJ
                        WKMX(INDX,JNDX) = A1(II,JJ)*E1(I,J)
     *                                    + E1(II,JJ)*A1(I,J)
  110                CONTINUE
  120             CONTINUE
  130          CONTINUE
  140       CONTINUE
            IDMY = 1
            CALL DSVDC(WKMX, NWX, NXN, NXN, WKV, WKV(NXN+1), DUMY, IDMY,
     *                 DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006)
90006          FORMAT(" SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(NXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
C
            WRITE(*,90007) RCDSVD, RATIO
90007       FORMAT(1X, '  RCOND(TRUE)=', E10.3, ' EST/TRUE=', E10.3)
         ENDIF
      ENDIF
C
      CLOSE(2)
      CLOSE(3)
      STOP
C --- LAST LINE OF TSYLGCF ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver6.f'
then
	echo shar: will not over-write existing file "'driver6.f'"
else
cat << "SHAR_EOF" > 'driver6.f'
C--**--CH2914--705--P:LAP--28:10:1999
C--**--CH2898--705--C:SU--28:10:1999
C--**--CH2889--705--B:MA--28:10:1999
C--**--CH2867--705--A:H--28:10:1999
C--**--CH2861--705--P:RW--28:10:1999
C     -- PROGRAM TSYLGDF --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE SYMMETRIC
C     SYLVESTER EQUATION
C
C        A*X*A' - E*X*E' + Q = 0    (' DENOTES TRANSPOSE)
C
C     READING THE COEFFICIENT MATRICES FROM A FILE.
C
C     THE SOLUTION IS CHECKED BY COMPUTING THE RESIDUAL AND ITS RELATIVE
C     1-NORM.  THE CONDITION ESTIMATE IS CHECKED FOR SMALL SYSTEMS ONLY
C     (N*N <= 40) BY FORMING THE KRONECKER PRODUCT MATRIX AND COMPUTING
C     ITS SINGULAR VALUE DECOMPOSITION.
C
C     INPUT FILE FORMAT (SEE EXAMPLE FILE TESTCD.IN):
C       INPUT IS FREE FORMAT; MATRICES ARE READ BY ROWS.
C       DIMENSION N (INTEGER)
C       A; EACH ROW MUST BEGIN ON A NEW LINE AND MAY TAKE AS MANY LINES
C       AS NECESSARY.
C       E; Q; SAME COMMENT.
C
C     SOLUTION MATRIX X IS WRITTEN TO AN OUTPUT FILE (SEE EXAMPLE FILE
C       TESTD.OUT).
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLGD; (LINPACK) DSVDC; (MATU) MADD MULC TRNATA D1NRM MSAVE MSUB
C
C     WRITTEN -
C       14DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM N IS 8 --
      INTEGER NAE, NQ, NW, N, IERR, NWX, IDMY
      INTEGER NMAX, WRKLEN, MAXSVD
      PARAMETER (NMAX=8, WRKLEN=2*NMAX*NMAX+3*NMAX,MAXSVD=40)
      DOUBLE PRECISION A(NMAX,NMAX), E(NMAX,NMAX), Q(NMAX,NMAX)
      DOUBLE PRECISION WKM1(NMAX,NMAX), WKM2(NMAX,NMAX),
     +                 WKV(WRKLEN)
C
      INTEGER I, J, NXN, II, JJ, INDX, JNDX
      DOUBLE PRECISION A1(NMAX,NMAX), E1(NMAX,NMAX), Q1(NMAX,NMAX), 
     +                 WKMX(MAXSVD,MAXSVD)
      DOUBLE PRECISION NRMR, NRMQ, RCOND, RCDSVD
      DOUBLE PRECISION RATIO, DUMY(1)
      DOUBLE PRECISION D1NRM
C     CHARACTER*20 INNAME, OUTNAM
      CHARACTER YESNO
C
C
C     -- INITIALIZE --
      NAE = NMAX
      NQ = NMAX
      NW = NMAX
      NWX = MAXSVD

      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
C
C
C      WRITE(*,91002)
C91002 FORMAT(/' ENTER NAME OF FILE CONTAINING COEFFICIENT MATRICES ')
C      READ(5,91003) INNAME
C91003 FORMAT(A)
C      OPEN(2,FILE=INNAME)
C      WRITE(*,91004)
C91004 FORMAT(/' ENTER NAME OF FILE FOR OUTPUT OF SOLUTION MATRIX')
C      READ(5,91003) OUTNAM
C      OPEN(3,FILE=OUTNAM)
C
C     -- READ COEFFICIENT MATRICES --
90001 FORMAT(" SOLVE  A*X*A  - E*X*E  + Q = 0  USING SYLGD")
      READ(*,*) N
      IF (N .GT. NAE) THEN
         WRITE(*,91005) N, NAE
91005    FORMAT(/' DIMENSION OF PROBLEM IS TOO LARGE:  N =',I2,         
     + '  MAXIMUM IS ',I2)
         STOP
      ENDIF
      WRITE(*,91008) N
C
91008 FORMAT(/' N =',I2)
      DO 201 I=1,N
         READ(*,*)(A(I,J),J=1,N)
 201  CONTINUE
      DO 202 I=1,N
         READ(*,*)(E(I,J),J=1,N)
 202  CONTINUE
      DO 203 I=1,N
         READ(*,*)(Q(I,J),J=1,N)
 203  CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAE, NAE, N, N, A, A1)
         CALL MSAVE(NAE, NAE, N, N, E, E1)
         CALL MSAVE(NQ, NQ, N, N, Q, Q1)
C
C        -- COMPUTE NORM OF Q --
         NRMQ = D1NRM(NQ, N, N, Q)
C
C        -- COMPUTE SOLUTION AND ESTIMATE CONDITION --
         IERR = 1
         CALL SYLGD(NAE, NQ, N, A, E, Q, WKV, IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) IERR
90003       FORMAT(" ERROR FROM SYLGD, IERR=", I2)
         ENDIF
C
C        -- SAVE SOLUTION --
         DO 301 I=1,N
            WRITE(*,92001) (Q(I,J),J=1,N)
92001       FORMAT(1X,6E12.4)
 301     CONTINUE
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAE, NQ, NW, N, N, N, A1, Q, WKM1)
         CALL TRNATA(NAE, N, A1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, A1, WKM2)
         CALL TRNATA(NAE, N, A1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
         CALL MULC(NAE, NQ, NW, N, N, N, E1, Q, WKM1)
         CALL TRNATA(NAE, N, E1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, E1, WKM2)
         CALL TRNATA(NAE, N, E1)
         CALL MSUB(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NQ, N, N, Q1) / NRMQ
C
C        -- PRINT RESULTS --
         WRITE(*,90002) NRMR, RCOND
C
C     -- COMPUTE REAL CONDITION NUMBER IF REQUESTED --
90002    FORMAT(1X, '  (NRM RESID)/(NRM Q)=', E10.3,          '  RCOND(E
     +ST)=', E10.3)
      NXN = N*N
      IF (NXN .LE. MAXSVD) THEN
         WRITE(*,91006)
91006    FORMAT(/' DO YOU WISH TO HAVE THE ACTUAL CONDITION NUMBER',    
     +      ' COMPUTED? (Y OR N) ')
         READ(5,*)YESNO
         IF (YESNO .EQ. 'y'  .OR.  YESNO .EQ. 'Y') THEN
            DO 140 J = 1,N
               DO 130 JJ = 1,N
                  DO 120 I = 1,N
                     DO 110 II = 1,N
                        INDX = N*(I-1) + II
                        JNDX = N*(J-1) + JJ
                        WKMX(INDX,JNDX) = A1(II,JJ)*A1(I,J)
     *                                    - E1(II,JJ)*E1(I,J)
  110                CONTINUE
  120             CONTINUE
  130          CONTINUE
  140       CONTINUE
            IDMY = 1
            CALL DSVDC(WKMX, NWX, NXN, NXN, WKV, WKV(NXN+1), DUMY, IDMY,
     *                 DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006)
90006          FORMAT(" SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(NXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
C
            WRITE(*,90007) RCDSVD, RATIO
90007       FORMAT(1X, '  RCOND(TRUE)=', E10.3, ' EST/TRUE=', E10.3)
         ENDIF
      ENDIF
C
      CLOSE(2)
      CLOSE(3)
      STOP
C --- LAST LINE OF TSYLGDF ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver7.f'
then
	echo shar: will not over-write existing file "'driver7.f'"
else
cat << "SHAR_EOF" > 'driver7.f'
C--**--CH3666--705--C:GEN--8:6:2000
C--**--CH2915--705--P:LAP--28:10:1999
C--**--CH2904--705--P:RW--28:10:1999
C--**--CH2899--705--P:R--28:10:1999
C--**--CH2890--705--B:MA--28:10:1999
C--**--CH2868--705--A:H--28:10:1999
C     -- PROGRAM TSYLGR --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE GENERAL
C     SYLVESTER EQUATION
C
C        A * X * B' +  C * X * D' =  E    (' DENOTES TRANSPOSE)
C
C     USING RANDOMLY GENERATED COEFFICIENT MATRICES.  MATRIX ELEMENTS
C     HAVE A GAUSSIAN DISTRIBUTION WITH MEAN 0 AND STANDARD DEVIATION 1.
C
C     TSYLGR MAY NOT BE PORTABLE. THE FUNCTION DXRAND MUST BE PROVIDED B
C     THE USER ON SYSTEMS OTHER THAN UNIX.  DXRAND IS A DOUBLE PRECISION
C     PSEUDORANDOM NUMBER GENERATOR WHICH GIVES A UNIFORM DISTRIBUTION I
C     THE INTERVAL [0,1].  DXRAND IS INITIALIZED WITH T=DXRAND(K), K AN
C     INTEGER, K>0.  SUBSEQUENT CALLS ARE T=DXRAND(0).
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLG; (LINPACK) DSVDC;
C       RANDM; (MATU) MSAVE, D1NRM, MSUB, MULC, TRNATA; DXRAND
C
C     WRITTEN -
C       18FEB87 M.WETTE, UCSB ECE, SANTA BARBARA, CA 93106 (805)961-4691
C     MODIFIED -
C       28NOV88 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C       12DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM M IS 9, MAXIMUM N IS 8 --
      INTEGER NAC, NBD, NE, NW, M, N, IERR
      INTEGER MMAX, NMAX, MNMAX, WRKLEN, MAXSVD
      PARAMETER (MMAX=9, NMAX=8, MNMAX=9, MAXSVD=40,
     +  WRKLEN = 2*MMAX*MMAX+NMAX*NMAX+NMAX*MMAX+7*MMAX+MNMAX*MNMAX)
      DOUBLE PRECISION A0(MMAX,MMAX), B0(NMAX,NMAX), C0(MMAX,MMAX),
     +                 D0(NMAX,NMAX), E0(MMAX,NMAX)
      DOUBLE PRECISION A1(MMAX,MMAX), B1(NMAX,NMAX), C1(MMAX,MMAX),
     +                 D1(NMAX,NMAX), E1(MMAX,NMAX)
      DOUBLE PRECISION WKM1(MMAX,NMAX), WKM2(MMAX,NMAX), 
     +                 WRKSVD(MAXSVD,MAXSVD), WKV(WRKLEN)
      INTEGER IWKV(2*MMAX)
C
      INTEGER I, J, LL, II, JJ, INDX, JNDX, MXN, NTEST
      INTEGER IDMY
      DOUBLE PRECISION TMP, NRMR, NRME, DPAR(3), WORST, RCOND, RCDSVD
      DOUBLE PRECISION DUMY(1), WORSTL, WORSTH, RATIO
      DOUBLE PRECISION DXRAND, D1NRM
C
C     -- INITIALIZE --
      NAC = MMAX
      NBD = NMAX
      NE = MMAX
      NW=MMAX
      WORST = 0.0D0
      WORSTL = 1.0D100
      WORSTH = 0.0D0
      NTEST = 5
      TMP = DXRAND(13)
      DPAR(1) = 0.0D0
      DPAR(2) = 1.0D2
C
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
C
90001 FORMAT(" SOLVE  A*X*B  + C*X*D  = E  USING SYLG")
      DO 320 M = 1,NAC
      DO 310 N = 1,NBD
C
      WRITE(*,90005) M, N
C
90005 FORMAT(/ " M =", I3, "   N =", I3)
      DO 230 LL = 1,NTEST
C
C        -- GENERATE NORMALLY DIST. RANDOM DATA --
         CALL RANDM(A0, NAC, M, M, DPAR, 01)
         CALL RANDM(B0, NBD, N, N, DPAR, 01)
         CALL RANDM(C0, NAC, M, M, DPAR, 01)
         CALL RANDM(D0, NBD, N, N, DPAR, 01)
         CALL RANDM(E0, NE, M, N, DPAR, 01)
C
C        -- SAVE A COPY --
         CALL MSAVE(NAC, NAC, M, M, A0, A1)
         CALL MSAVE(NAC, NAC, M, M, C0, C1)
         CALL MSAVE(NBD, NBD, N, N, B0, B1)
         CALL MSAVE(NBD, NBD, N, N, D0, D1)
         CALL MSAVE(NE, NE, M, N, E0, E1)
C
C        -- COMPUTE NORM OF E --
         NRME = D1NRM(NE, M, N, E0)
C
C        -- COMPUTE SOLUTION, ESTIMATE CONDITION IF SVD COMPUTABLE --
         MXN = M*N
         IF (MXN .LE. MAXSVD) THEN
            IERR = 1
         ELSE
            IERR = 0
         ENDIF
         CALL SYLG(NAC, NBD, NE, M, N, A0, B0, C0, D0, E0, WKV, IWKV,
     *             IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) LL, IERR
90003       FORMAT(" AT ITERATION", I2, " ERROR IN SYLG, IERR=", I2)
         ENDIF
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAC, NE, NW, M, M, N, A1, E0, WKM1)
         CALL TRNATA(NBD, N, B1)
         CALL MULC(NW, NBD, NE, M, N, N, WKM1, B1, WKM2)
         CALL TRNATA(NBD, N, B1)
         CALL MSUB(NE, NE, NE, M, N, E1, WKM2, E1)
         CALL MULC(NAC, NE, NW, M, M, N, C1, E0, WKM1)
         CALL TRNATA(NBD, N, D1)
         CALL MULC(NW, NBD, NE, M, N, N, WKM1, D1, WKM2)
         CALL TRNATA(NBD, N, D1)
         CALL MSUB(NE, NE, NE, M, N, E1, WKM2, E1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NE, M, N, E1)
         TMP = NRMR/NRME
         IF (TMP .GT. WORST) WORST = TMP
C
C        -- COMPUTE REAL CONDITION NUMBER --
         IF (MXN .LE. MAXSVD) THEN
            DO 40 J = 1,N
               DO 30 JJ = 1,M
                  DO 20 I = 1,N
                     DO 10 II = 1,M
                        INDX = M*(I-1) + II
                        JNDX = M*(J-1) + JJ
                        WRKSVD(INDX,JNDX) = A1(II,JJ)*B1(I,J)
     &                                    + C1(II,JJ)*D1(I,J)
   10                CONTINUE
   20             CONTINUE
   30          CONTINUE
   40       CONTINUE
            IDMY = 1
            CALL DSVDC(WRKSVD, MAXSVD, MXN, MXN, WKV, WKV(MXN+1), DUMY,
     *                 IDMY, DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006) LL
90006          FORMAT(" ITERATION", I2, " SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(MXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
            IF (RATIO .LT. WORSTL) WORSTL = RATIO
            IF (RATIO .GT. WORSTH) WORSTH = RATIO
         ENDIF
C
C        -- PRINT RESULTS --
         IF (MXN .LE. MAXSVD) THEN
            WRITE(*,90002) LL, TMP, RCOND, RATIO
         ELSE
            WRITE(*,90007) LL, TMP
         ENDIF
90002    FORMAT(1X, I2, '  (NRM RESID)/(NRM E)=', E10.3,          '  RCO
     +ND(EST)=', E10.3, ' EST/TRUE=', E10.3)
C
90007    FORMAT(1X, I2, '  (NRM RESID)/(NRM E)=', E10.3)
  230 CONTINUE
C
  310 CONTINUE
  320 CONTINUE
C
      WRITE(*,90004) WORST
90004 FORMAT(/ " WORST CASE RESIDUAL IS", E10.3)
      WRITE(*,90008) WORSTL, WORSTH
C
90008 FORMAT(' WORST CASE RCOND RATIOS (EST/TRUE) ARE', E10.3,       ' (
     +LOW) AND', E10.3, ' (HIGH)')
      STOP
C --- LAST LINE OF TSYLGR ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver8.f'
then
	echo shar: will not over-write existing file "'driver8.f'"
else
cat << "SHAR_EOF" > 'driver8.f'
C--**--CH2916--705--P:LAP--28:10:1999
C--**--CH2905--705--P:RW--28:10:1999
C--**--CH2900--705--P:R--28:10:1999
C--**--CH2891--705--B:MA--28:10:1999
C--**--CH2869--705--A:H--28:10:1999
C     -- PROGRAM TSYLGCR --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE SYMMETRIC
C     SYLVESTER EQUATION
C
C        A*X*E' + E*X*A' + Q = 0    (' DENOTES TRANSPOSE)
C
C     USING RANDOMLY GENERATED COEFFICIENT MATRICES.  MATRIX ELEMENTS
C     HAVE A GAUSSIAN DISTRIBUTION WITH MEAN 0 AND STANDARD DEVIATION 1.
C     Q IS TAKEN TO BE THE SYMMETRIC PART OF A RANDOM MATRIX.
C
C     TSYLGCR MAY NOT BE PORTABLE.  THE FUNCTION DXRAND MUST BE PROVIDED
C     THE USER ON SYSTEMS OTHER THAN UNIX.  DXRAND IS A DOUBLE PRECISION
C     PSEUDORANDOM NUMBER GENERATOR WHICH GIVES A UNIFORM DISTRIBUTION I
C     THE INTERVAL [0,1].  DXRAND IS INITIALIZED WITH T=DXRAND(K), K AN
C     INTEGER, K>0.  SUBSEQUENT CALLS ARE T=DXRAND(0).
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLGC; (LINPACK) DSVDC;
C       RANDM; (MATU) MADD MSUB MULC MSAVE D1NRM; DXRAND
C
C     WRITTEN -
C       26FEB87 M.WETTE, UCSB ECE, SANTA BARBARA, CA 93106 (805)961-4691
C     REVISED -
C       27JAN89 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C       14DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM N IS 8 --
      INTEGER NAE, NQ, NW, N, IERR, MAXN, NWX, IDMY
      INTEGER NMAX, WRKLEN, MAXSVD
      PARAMETER (NMAX=8, WRKLEN=2*NMAX*NMAX+3*NMAX,
     +           MAXSVD=40)
      DOUBLE PRECISION A(NMAX,NMAX), E(NMAX,NMAX), Q(NMAX,NMAX)
      DOUBLE PRECISION WKM1(NMAX,NMAX), WKM2(NMAX,NMAX),
     +                 WKV(WRKLEN)
C
      INTEGER I, J, LL, NTEST, NXN, II, JJ, INDX, JNDX
      DOUBLE PRECISION A1(NMAX,NMAX), E1(NMAX,NMAX), Q1(NMAX,NMAX), 
     +                 WKMX(MAXSVD,MAXSVD)
      DOUBLE PRECISION TMP, NRMR, NRMQ, DPAR(3), WORST, RCOND, RCDSVD
      DOUBLE PRECISION WORSTL, WORSTH, RATIO, DUMY(1)
      DOUBLE PRECISION DXRAND, D1NRM
C
C     -- INITIALIZE --
      MAXN = NMAX
      NAE = NMAX
      NQ = NMAX
      NW = NMAX
      NWX = MAXSVD
      WORST = 0.0D0
      WORSTL = 1.0D100
      WORSTH = 0.0D0
      NTEST = 5
      TMP = DXRAND(13)
      DPAR(1) = 0.0D0
      DPAR(2) = 1.0D2
C
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
C
90001 FORMAT(" SOLVE  A*X*E  + E*X*A  + Q = 0  USING SYLGC")
      DO 300 N = 1,MAXN
C
      WRITE(*,90005) N
C
90005 FORMAT(/ " N =", I3)
      DO 230 LL = 1,NTEST
C
C        -- GENERATE NORMALLY DIST. RANDOM DATA --
         CALL RANDM(A, NAE, N, N, DPAR, 01)
         CALL RANDM(E, NAE, N, N, DPAR, 01)
         CALL RANDM(Q, NQ, N, N, DPAR, 01)
         DO 20 J = 1,N
            DO 10 I = J,N
               Q(I,J) = (Q(I,J) + Q(J,I)) / 2.0D0
               Q(J,I) = Q(I,J)
   10       CONTINUE
   20    CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAE, NAE, N, N, A, A1)
         CALL MSAVE(NAE, NAE, N, N, E, E1)
         CALL MSAVE(NQ, NQ, N, N, Q, Q1)
C
C        -- COMPUTE NORM OF Q --
         NRMQ = D1NRM(NQ, N, N, Q)
C
C        -- COMPUTE SOLUTION, ESTIMATE CONDITION IF SVD COMPUTABLE --
         NXN = N*N
         IF (NXN .LE. MAXSVD) THEN
            IERR = 1
         ELSE
            IERR = 0
         ENDIF
         CALL SYLGC(NAE, NQ, N, A, E, Q, WKV, IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) LL, IERR
90003       FORMAT(" AT ITERATION", I2, " ERROR IN SYLGC, IERR=", I2)
         ENDIF
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAE, NQ, NW, N, N, N, A1, Q, WKM1)
         CALL TRNATA(NAE, N, E1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, E1, WKM2)
         CALL TRNATA(NAE, N, E1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
         CALL MULC(NAE, NQ, NW, N, N, N, E1, Q, WKM1)
         CALL TRNATA(NAE, N, A1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, A1, WKM2)
         CALL TRNATA(NAE, N, A1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NQ, N, N, Q1)
         TMP = NRMR/NRMQ
         IF (TMP .GT. WORST) WORST = TMP
C
C        -- COMPUTE REAL CONDITION NUMBER
         IF (NXN .LE. MAXSVD) THEN
            DO 140 J = 1,N
               DO 130 JJ = 1,N
                  DO 120 I = 1,N
                     DO 110 II = 1,N
                        INDX = N*(I-1) + II
                        JNDX = N*(J-1) + JJ
                        WKMX(INDX,JNDX) = A1(II,JJ)*E1(I,J)
     *                                    + E1(II,JJ)*A1(I,J)
  110                CONTINUE
  120             CONTINUE
  130          CONTINUE
  140       CONTINUE
            IDMY = 1
            CALL DSVDC(WKMX, NWX, NXN, NXN, WKV, WKV(NXN+1), DUMY, IDMY,
     *                 DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006) LL
90006          FORMAT(" ITERATION", I2, " SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(NXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
            IF (RATIO .LT. WORSTL) WORSTL = RATIO
            IF (RATIO .GT. WORSTH) WORSTH = RATIO
         ENDIF
C
C        -- PRINT RESULTS --
         IF (NXN .LE. MAXSVD) THEN
            WRITE(*,90002) LL, TMP, RCOND, RATIO
         ELSE
            WRITE(*,90007) LL, TMP
         ENDIF
90002    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3,          '  RCO
     +ND(EST)=', E10.3, ' EST/TRUE=', E10.3)
C
C
90007    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3)
  230 CONTINUE
  300 CONTINUE
C
      WRITE(*,90004) WORST
90004 FORMAT(/ " WORST CASE RESIDUAL IS", E10.3)
      WRITE(*,90008) WORSTL, WORSTH
C
90008 FORMAT(' WORST CASE RCOND RATIOS (EST/TRUE) ARE', E10.3,       ' (
     +LOW) AND', E10.3, ' (HIGH)')
      STOP
C --- LAST LINE OF TSYLGCR ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver9.f'
then
	echo shar: will not over-write existing file "'driver9.f'"
else
cat << "SHAR_EOF" > 'driver9.f'
C--**--CH2917--705--P:LAP--28:10:1999
C--**--CH2906--705--P:RW--28:10:1999
C--**--CH2901--705--P:R--28:10:1999
C--**--CH2892--705--B:MA--28:10:1999
C--**--CH2870--705--A:H--28:10:1999
C     -- PROGRAM TSYLGDR --
C
C     THIS PROGRAM TESTS THE SOFTWARE FOR SOLVING THE SYMMETRIC
C     SYLVESTER EQUATION
C
C        A*X*A' - E*X*E' + Q = 0    (' DENOTES TRANSPOSE)
C
C     USING RANDOMLY GENERATED COEFFICIENT MATRICES.  MATRIX ELEMENTS
C     HAVE A GAUSSIAN DISTRIBUTION WITH MEAN 0 AND STANDARD DEVIATION 1.
C     Q IS TAKEN TO BE THE SYMMETRIC PART OF A RANDOM MATRIX.
C
C     TSYLGDR MAY NOT BE PORTABLE.  THE FUNCTION DXRAND MUST BE PROVIDED
C     THE USER ON SYSTEMS OTHER THAN UNIX.  DXRAND IS A DOUBLE PRECISION
C     PSEUDORANDOM NUMBER GENERATOR WHICH GIVES A UNIFORM DISTRIBUTION I
C     THE INTERVAL [0,1].  DXRAND IS INITIALIZED WITH T=DXRAND(K), K AN
C     INTEGER, K>0.  SUBSEQUENT CALLS ARE T=DXRAND(0).
C
C     SUBROUTINES AND FUNCTIONS CALLED -
C       SYLGD; (LINPACK) DSVDC;
C       RANDM; (MATU) MADD MSUB MULC MSAVE D1NRM; DXRAND
C
C     WRITTEN -
C       26FEB87 M.WETTE, UCSB ECE, SANTA BARBARA, CA 93106 (805)961-4691
C     REVISED -
C       27JAN89 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C       14DEC90 J. GARDINER, OSU CIS, COLUMBUS, OH  43210  (614)292-8658
C
C     -- MAXIMUM N IS 8 --
      INTEGER NAE, NQ, NW, N, IERR, MAXN, NWX, IDMY
      INTEGER NMAX, WRKLEN, MAXSVD
      PARAMETER (NMAX=8, WRKLEN=2*NMAX*NMAX+3*NMAX,MAXSVD=40)
      DOUBLE PRECISION A(NMAX,NMAX), E(NMAX,NMAX), Q(NMAX,NMAX)
      DOUBLE PRECISION WKM1(NMAX,NMAX), WKM2(NMAX,NMAX),
     +                 WKV(WRKLEN)
C
      INTEGER I, J, LL, NTEST, NXN, II, JJ, INDX, JNDX
      DOUBLE PRECISION A1(NMAX,NMAX), E1(NMAX,NMAX), Q1(NMAX,NMAX), 
     +                 WKMX(MAXSVD,MAXSVD)
      DOUBLE PRECISION TMP, NRMR, NRMQ, DPAR(3), WORST, RCOND, RCDSVD
      DOUBLE PRECISION WORSTL, WORSTH, RATIO, DUMY(1)
      DOUBLE PRECISION DXRAND, D1NRM
C
C     -- INITIALIZE --
      MAXN = NMAX
      NAE = NMAX
      NQ = NMAX
      NW = NMAX
      NWX = MAXSVD
      WORST = 0.0D0
      WORSTL = 1.0D100
      WORSTH = 0.0D0
      NTEST = 5
      TMP = DXRAND(13)
      DPAR(1) = 0.0D0
      DPAR(2) = 1.0D2
C
      WRITE(*,90000)
      WRITE(*,90001)
90000 FORMAT("             T        T")
C
90001 FORMAT(" SOLVE  A*X*E  + E*X*A  + Q = 0  USING SYLGD")
      DO 300 N = 1,MAXN
C
      WRITE(*,90005) N
C
90005 FORMAT(/ " N =", I3)
      DO 230 LL = 1,NTEST
C
C        -- GENERATE NORMALLY DIST. RANDOM DATA --
         CALL RANDM(A, NAE, N, N, DPAR, 01)
         CALL RANDM(E, NAE, N, N, DPAR, 01)
         CALL RANDM(Q, NQ, N, N, DPAR, 01)
         DO 20 J = 1,N
            DO 10 I = J,N
               Q(I,J) = (Q(I,J) + Q(J,I)) / 2.0D0
               Q(J,I) = Q(I,J)
   10       CONTINUE
   20    CONTINUE
C
C        -- SAVE A COPY --
         CALL MSAVE(NAE, NAE, N, N, A, A1)
         CALL MSAVE(NAE, NAE, N, N, E, E1)
         CALL MSAVE(NQ, NQ, N, N, Q, Q1)
C
C        -- COMPUTE NORM OF Q --
         NRMQ = D1NRM(NQ, N, N, Q)
C
C        -- COMPUTE SOLUTION, ESTIMATE CONDITION IF SVD COMPUTABLE --
         NXN = N*N
         IF (NXN .LE. MAXSVD) THEN
            IERR = 1
         ELSE
            IERR = 0
         ENDIF
         CALL SYLGD(NAE, NQ, N, A, E, Q, WKV, IERR, RCOND)
         IF (IERR .NE. 0) THEN
            WRITE(*,90003) LL, IERR
90003       FORMAT(" AT ITERATION", I2, " ERROR IN SYLGD, IERR=", I2)
         ENDIF
C
C        -- COMPUTE RESIDUAL --
         CALL MULC(NAE, NQ, NW, N, N, N, A1, Q, WKM1)
         CALL TRNATA(NAE, N, A1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, A1, WKM2)
         CALL TRNATA(NAE, N, A1)
         CALL MADD(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
         CALL MULC(NAE, NQ, NW, N, N, N, E1, Q, WKM1)
         CALL TRNATA(NAE, N, E1)
         CALL MULC(NW, NAE, NW, N, N, N, WKM1, E1, WKM2)
         CALL TRNATA(NAE, N, E1)
         CALL MSUB(NQ, NW, NQ, N, N, Q1, WKM2, Q1)
C
C        -- COMPUTE NORM OF RESIDUAL --
         NRMR = D1NRM(NQ, N, N, Q1)
         TMP = NRMR/NRMQ
         IF (TMP .GT. WORST) WORST = TMP
C
C        -- COMPUTE REAL CONDITION NUMBER
         IF (NXN .LE. MAXSVD) THEN
            DO 140 J = 1,N
               DO 130 JJ = 1,N
                  DO 120 I = 1,N
                     DO 110 II = 1,N
                        INDX = N*(I-1) + II
                        JNDX = N*(J-1) + JJ
                        WKMX(INDX,JNDX) = A1(II,JJ)*A1(I,J)
     *                                    - E1(II,JJ)*E1(I,J)
  110                CONTINUE
  120             CONTINUE
  130          CONTINUE
  140       CONTINUE
            IDMY = 1
            CALL DSVDC(WKMX, NWX, NXN, NXN, WKV, WKV(NXN+1), DUMY, IDMY,
     *                 DUMY, IDMY, WKM1, 00, IERR)
            IF (IERR .NE. 0) THEN
               WRITE(*,90006) LL
90006          FORMAT(" ITERATION", I2, " SVD FAILED")
               RCDSVD = 0.0D0
            ELSE
               RCDSVD = WKV(NXN) / WKV(1)
            ENDIF
            RATIO = RCOND / RCDSVD
            IF (RATIO .LT. WORSTL) WORSTL = RATIO
            IF (RATIO .GT. WORSTH) WORSTH = RATIO
         ENDIF
C
C        -- PRINT RESULTS --
         IF (NXN .LE. MAXSVD) THEN
            WRITE(*,90002) LL, TMP, RCOND, RATIO
         ELSE
            WRITE(*,90007) LL, TMP
         ENDIF
90002    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3,          '  RCO
     +ND(EST)=', E10.3, ' EST/TRUE=', E10.3)
C
C
90007    FORMAT(1X, I2, '  (NRM RESID)/(NRM Q)=', E10.3)
  230 CONTINUE
  300 CONTINUE
C
      WRITE(*,90004) WORST
90004 FORMAT(/ " WORST CASE RESIDUAL IS", E10.3)
      WRITE(*,90008) WORSTL, WORSTH
C
90008 FORMAT(' WORST CASE RCOND RATIOS (EST/TRUE) ARE', E10.3,       ' (
     +LOW) AND', E10.3, ' (HIGH)')
      STOP
C --- LAST LINE OF TSYLGDR ---
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'portrand.f'
then
	echo shar: will not over-write existing file "'portrand.f'"
else
cat << "SHAR_EOF" > 'portrand.f'
      REAL FUNCTION RAND()
C..PORTABLE RANDOM NUMBER GENERATOR
C..USING THE RECURSION -
C..
C..       IX=IX*A MOD P
      INTEGER A,P,IX,B15,B16,XHI,XALO,LEFTLO,FHI,K
C..7**5, 2**15,  2**16, 2**31-1
      PARAMETER (A=16807, B15=32768, B16=65536,
     +           P=2147483647)
      COMMON /RANCOM/ IX
      SAVE /RANCOM/
C
C..GET 15 HIGH ORDER BITS OF IX
      XHI=IX/B16
C..GET 16 LO BITS OF IX AND FORM LO PRODUCT
      XALO=(IX-XHI*B16)*A
C..GET 15 HI ORDER BITS OF LO PRODUCT
      LEFTLO=XALO/B16
C..FORM THE 31 HIGHEST BITS OF FULL PRODUCT
      FHI=XHI*A + LEFTLO
C..GET OVERFLOW PAST 31ST BIT OF FULL PRODUCT
      K=FHI/B15
C..ASSEMBLE ALL THE PARTS AND PRESUBTRACT P
C..THE PARENTHESES ARE ESSENTIAL
      IX=(((XALO-LEFTLO*B16)-P)+(FHI-K*B15)*B16)+K
C..ADD P BACK IN IF NECESSARY
      IF(IX.LT.0)IX=IX+P
C..MULTIPLY BY 1/(2**31-1)
      RAND=FLOAT(IX)*4.656612875E-10
      RETURN
      END

      subroutine seed(iseed)
c
c seed the portable random number generator
c
      integer iseed, ix
      common /rancom/ ix
      SAVE /RANCOM/
      ix = iseed
      end
SHAR_EOF
fi # end of overwriting check
if test -f 'res1'
then
	echo shar: will not over-write existing file "'res1'"
else
cat << "SHAR_EOF" > 'res1'
             T        T
 SOLVE  A*X*B  + C*X*D  = E  USING SYLG

 M =  2   N =  2
  0  (NRM RESID)/(NRM E)= 0.508E-15  RCOND(EST)= 0.909E-01 EST/TRUE= 0.623E+00
 10  (NRM RESID)/(NRM E)= 0.610E-15  RCOND(EST)= 0.351E-03 EST/TRUE= 0.360E+00
 20  (NRM RESID)/(NRM E)= 0.722E-15  RCOND(EST)= 0.343E-06 EST/TRUE= 0.360E+00
 30  (NRM RESID)/(NRM E)= 0.611E-15  RCOND(EST)= 0.335E-09 EST/TRUE= 0.360E+00
 40  (NRM RESID)/(NRM E)= 0.389E-15  RCOND(EST)= 0.327E-12 EST/TRUE= 0.360E+00

 M =  2   N =  3
  0  (NRM RESID)/(NRM E)= 0.888E-16  RCOND(EST)= 0.410E-01 EST/TRUE= 0.430E+00
 10  (NRM RESID)/(NRM E)= 0.518E-15  RCOND(EST)= 0.138E-03 EST/TRUE= 0.317E+00
 20  (NRM RESID)/(NRM E)= 0.444E-15  RCOND(EST)= 0.135E-06 EST/TRUE= 0.317E+00
 30  (NRM RESID)/(NRM E)= 0.407E-15  RCOND(EST)= 0.132E-09 EST/TRUE= 0.317E+00
 40  (NRM RESID)/(NRM E)= 0.444E-15  RCOND(EST)= 0.129E-12 EST/TRUE= 0.317E+00

 M =  2   N =  4
  0  (NRM RESID)/(NRM E)= 0.256E-15  RCOND(EST)= 0.322E-01 EST/TRUE= 0.458E+00
 10  (NRM RESID)/(NRM E)= 0.105E-14  RCOND(EST)= 0.102E-03 EST/TRUE= 0.398E+00
 20  (NRM RESID)/(NRM E)= 0.833E-15  RCOND(EST)= 0.992E-07 EST/TRUE= 0.397E+00
 30  (NRM RESID)/(NRM E)= 0.611E-15  RCOND(EST)= 0.809E-10 EST/TRUE= 0.331E+00
 40  (NRM RESID)/(NRM E)= 0.611E-15  RCOND(EST)= 0.946E-13 EST/TRUE= 0.397E+00

 M =  2   N =  5
  0  (NRM RESID)/(NRM E)= 0.444E-15  RCOND(EST)= 0.273E-01 EST/TRUE= 0.495E+00
 10  (NRM RESID)/(NRM E)= 0.799E-15  RCOND(EST)= 0.107E-03 EST/TRUE= 0.621E+00
 20  (NRM RESID)/(NRM E)= 0.888E-15  RCOND(EST)= 0.104E-06 EST/TRUE= 0.618E+00
 30  (NRM RESID)/(NRM E)= 0.115E-14  RCOND(EST)= 0.101E-09 EST/TRUE= 0.618E+00
 40  (NRM RESID)/(NRM E)= 0.977E-15  RCOND(EST)= 0.990E-13 EST/TRUE= 0.617E+00

 M =  2   N =  6
  0  (NRM RESID)/(NRM E)= 0.608E-15  RCOND(EST)= 0.245E-01 EST/TRUE= 0.540E+00
 10  (NRM RESID)/(NRM E)= 0.925E-15  RCOND(EST)= 0.701E-04 EST/TRUE= 0.555E+00
 20  (NRM RESID)/(NRM E)= 0.163E-14  RCOND(EST)= 0.677E-07 EST/TRUE= 0.552E+00
 30  (NRM RESID)/(NRM E)= 0.592E-15  RCOND(EST)= 0.661E-10 EST/TRUE= 0.552E+00
 40  (NRM RESID)/(NRM E)= 0.814E-15  RCOND(EST)= 0.646E-13 EST/TRUE= 0.552E+00

 M =  2   N =  7
  0  (NRM RESID)/(NRM E)= 0.525E-15  RCOND(EST)= 0.213E-01 EST/TRUE= 0.555E+00
 10  (NRM RESID)/(NRM E)= 0.114E-14  RCOND(EST)= 0.713E-04 EST/TRUE= 0.733E+00
 20  (NRM RESID)/(NRM E)= 0.888E-15  RCOND(EST)= 0.688E-07 EST/TRUE= 0.729E+00
 30  (NRM RESID)/(NRM E)= 0.397E-15  RCOND(EST)= 0.672E-10 EST/TRUE= 0.729E+00
 40  (NRM RESID)/(NRM E)= 0.476E-15  RCOND(EST)= 0.656E-13 EST/TRUE= 0.729E+00

 M =  2   N =  8
  0  (NRM RESID)/(NRM E)= 0.135E-14  RCOND(EST)= 0.185E-01 EST/TRUE= 0.559E+00
 10  (NRM RESID)/(NRM E)= 0.153E-14  RCOND(EST)= 0.538E-04 EST/TRUE= 0.690E+00
 20  (NRM RESID)/(NRM E)= 0.500E-15  RCOND(EST)= 0.519E-07 EST/TRUE= 0.687E+00
 30  (NRM RESID)/(NRM E)= 0.999E-15  RCOND(EST)= 0.507E-10 EST/TRUE= 0.687E+00
 40  (NRM RESID)/(NRM E)= 0.122E-14  RCOND(EST)= 0.495E-13 EST/TRUE= 0.689E+00

 M =  3   N =  2
  0  (NRM RESID)/(NRM E)= 0.740E-15  RCOND(EST)= 0.146E-01 EST/TRUE= 0.468E+00
 10  (NRM RESID)/(NRM E)= 0.740E-15  RCOND(EST)= 0.456E-04 EST/TRUE= 0.395E+00
 20  (NRM RESID)/(NRM E)= 0.432E-15  RCOND(EST)= 0.441E-07 EST/TRUE= 0.394E+00
 30  (NRM RESID)/(NRM E)= 0.678E-15  RCOND(EST)= 0.430E-10 EST/TRUE= 0.394E+00
 40  (NRM RESID)/(NRM E)= 0.173E-15  RCOND(EST)= 0.421E-13 EST/TRUE= 0.394E+00

 M =  3   N =  3
  0  (NRM RESID)/(NRM E)= 0.285E-15  RCOND(EST)= 0.358E-02 EST/TRUE= 0.511E+00
 10  (NRM RESID)/(NRM E)= 0.490E-15  RCOND(EST)= 0.222E-04 EST/TRUE= 0.288E+00
 20  (NRM RESID)/(NRM E)= 0.444E-15  RCOND(EST)= 0.214E-07 EST/TRUE= 0.288E+00
 30  (NRM RESID)/(NRM E)= 0.407E-15  RCOND(EST)= 0.209E-10 EST/TRUE= 0.288E+00
 40  (NRM RESID)/(NRM E)= 0.333E-15  RCOND(EST)= 0.204E-13 EST/TRUE= 0.288E+00

 M =  3   N =  4
  0  (NRM RESID)/(NRM E)= 0.293E-15  RCOND(EST)= 0.145E-02 EST/TRUE= 0.459E+00
 10  (NRM RESID)/(NRM E)= 0.109E-14  RCOND(EST)= 0.165E-04 EST/TRUE= 0.310E+00
 20  (NRM RESID)/(NRM E)= 0.918E-15  RCOND(EST)= 0.157E-07 EST/TRUE= 0.309E+00
 30  (NRM RESID)/(NRM E)= 0.503E-15  RCOND(EST)= 0.136E-10 EST/TRUE= 0.274E+00
 40  (NRM RESID)/(NRM E)= 0.533E-15  RCOND(EST)= 0.150E-13 EST/TRUE= 0.309E+00

 M =  3   N =  5
  0  (NRM RESID)/(NRM E)= 0.431E-15  RCOND(EST)= 0.726E-03 EST/TRUE= 0.411E+00
 10  (NRM RESID)/(NRM E)= 0.641E-15  RCOND(EST)= 0.123E-04 EST/TRUE= 0.332E+00
 20  (NRM RESID)/(NRM E)= 0.777E-15  RCOND(EST)= 0.117E-07 EST/TRUE= 0.332E+00
 30  (NRM RESID)/(NRM E)= 0.106E-14  RCOND(EST)= 0.114E-10 EST/TRUE= 0.332E+00
 40  (NRM RESID)/(NRM E)= 0.765E-15  RCOND(EST)= 0.112E-13 EST/TRUE= 0.333E+00

 M =  3   N =  6
  0  (NRM RESID)/(NRM E)= 0.539E-15  RCOND(EST)= 0.413E-03 EST/TRUE= 0.372E+00
 10  (NRM RESID)/(NRM E)= 0.740E-15  RCOND(EST)= 0.875E-05 EST/TRUE= 0.315E+00
 20  (NRM RESID)/(NRM E)= 0.133E-14  RCOND(EST)= 0.825E-08 EST/TRUE= 0.314E+00
 30  (NRM RESID)/(NRM E)= 0.634E-15  RCOND(EST)= 0.806E-11 EST/TRUE= 0.314E+00
 40  (NRM RESID)/(NRM E)= 0.825E-15  RCOND(EST)= 0.787E-14 EST/TRUE= 0.315E+00

 M =  3   N =  7
  0  (NRM RESID)/(NRM E)= 0.743E-15  RCOND(EST)= 0.264E-03 EST/TRUE= 0.351E+00
 10  (NRM RESID)/(NRM E)= 0.925E-15  RCOND(EST)= 0.849E-05 EST/TRUE= 0.389E+00
 20  (NRM RESID)/(NRM E)= 0.481E-15  RCOND(EST)= 0.795E-08 EST/TRUE= 0.388E+00
 30  (NRM RESID)/(NRM E)= 0.481E-15  RCOND(EST)= 0.777E-11 EST/TRUE= 0.388E+00
 40  (NRM RESID)/(NRM E)= 0.555E-15  RCOND(EST)= 0.759E-14 EST/TRUE= 0.389E+00

 M =  3   N =  8
  0  (NRM RESID)/(NRM E)= 0.108E-14  RCOND(EST)= 0.210E-03 EST/TRUE= 0.389E+00
 10  (NRM RESID)/(NRM E)= 0.145E-14  RCOND(EST)= 0.677E-05 EST/TRUE= 0.380E+00
 20  (NRM RESID)/(NRM E)= 0.724E-15  RCOND(EST)= 0.630E-08 EST/TRUE= 0.380E+00
 30  (NRM RESID)/(NRM E)= 0.987E-15  RCOND(EST)= 0.615E-11 EST/TRUE= 0.380E+00
 40  (NRM RESID)/(NRM E)= 0.921E-15  RCOND(EST)= 0.599E-14 EST/TRUE= 0.380E+00

 M =  4   N =  2
  0  (NRM RESID)/(NRM E)= 0.752E-15  RCOND(EST)= 0.118E-01 EST/TRUE= 0.432E+00
 10  (NRM RESID)/(NRM E)= 0.631E-15  RCOND(EST)= 0.437E-04 EST/TRUE= 0.536E+00
 20  (NRM RESID)/(NRM E)= 0.965E-15  RCOND(EST)= 0.424E-07 EST/TRUE= 0.535E+00
 30  (NRM RESID)/(NRM E)= 0.888E-15  RCOND(EST)= 0.414E-10 EST/TRUE= 0.535E+00
 40  (NRM RESID)/(NRM E)= 0.382E-15  RCOND(EST)= 0.404E-13 EST/TRUE= 0.535E+00

 M =  4   N =  3
  0  (NRM RESID)/(NRM E)= 0.205E-15  RCOND(EST)= 0.424E-02 EST/TRUE= 0.640E+00
 10  (NRM RESID)/(NRM E)= 0.438E-15  RCOND(EST)= 0.135E-04 EST/TRUE= 0.312E+00
 20  (NRM RESID)/(NRM E)= 0.411E-15  RCOND(EST)= 0.130E-07 EST/TRUE= 0.312E+00
 30  (NRM RESID)/(NRM E)= 0.488E-15  RCOND(EST)= 0.127E-10 EST/TRUE= 0.312E+00
 40  (NRM RESID)/(NRM E)= 0.222E-15  RCOND(EST)= 0.124E-13 EST/TRUE= 0.312E+00

 M =  4   N =  4
  0  (NRM RESID)/(NRM E)= 0.315E-15  RCOND(EST)= 0.167E-02 EST/TRUE= 0.563E+00
 10  (NRM RESID)/(NRM E)= 0.980E-15  RCOND(EST)= 0.944E-05 EST/TRUE= 0.307E+00
 20  (NRM RESID)/(NRM E)= 0.981E-15  RCOND(EST)= 0.902E-08 EST/TRUE= 0.307E+00
 30  (NRM RESID)/(NRM E)= 0.629E-15  RCOND(EST)= 0.702E-11 EST/TRUE= 0.244E+00
 40  (NRM RESID)/(NRM E)= 0.463E-15  RCOND(EST)= 0.860E-14 EST/TRUE= 0.307E+00

 M =  4   N =  5
  0  (NRM RESID)/(NRM E)= 0.258E-15  RCOND(EST)= 0.745E-03 EST/TRUE= 0.429E+00
 10  (NRM RESID)/(NRM E)= 0.507E-15  RCOND(EST)= 0.683E-05 EST/TRUE= 0.284E+00
 20  (NRM RESID)/(NRM E)= 0.539E-15  RCOND(EST)= 0.646E-08 EST/TRUE= 0.284E+00
 30  (NRM RESID)/(NRM E)= 0.983E-15  RCOND(EST)= 0.631E-11 EST/TRUE= 0.284E+00
 40  (NRM RESID)/(NRM E)= 0.476E-15  RCOND(EST)= 0.616E-14 EST/TRUE= 0.284E+00

 M =  4   N =  6
  0  (NRM RESID)/(NRM E)= 0.432E-15  RCOND(EST)= 0.409E-03 EST/TRUE= 0.354E+00
 10  (NRM RESID)/(NRM E)= 0.915E-15  RCOND(EST)= 0.502E-05 EST/TRUE= 0.281E+00
 20  (NRM RESID)/(NRM E)= 0.129E-14  RCOND(EST)= 0.472E-08 EST/TRUE= 0.281E+00
 30  (NRM RESID)/(NRM E)= 0.874E-15  RCOND(EST)= 0.461E-11 EST/TRUE= 0.281E+00
 40  (NRM RESID)/(NRM E)= 0.680E-15  RCOND(EST)= 0.450E-14 EST/TRUE= 0.282E+00

 M =  4   N =  7
  0  (NRM RESID)/(NRM E)= 0.645E-15  RCOND(EST)= 0.284E-03 EST/TRUE= 0.340E+00
 10  (NRM RESID)/(NRM E)= 0.690E-15  RCOND(EST)= 0.488E-05 EST/TRUE= 0.353E+00
 20  (NRM RESID)/(NRM E)= 0.518E-15  RCOND(EST)= 0.455E-08 EST/TRUE= 0.352E+00
 30  (NRM RESID)/(NRM E)= 0.475E-15  RCOND(EST)= 0.445E-11 EST/TRUE= 0.352E+00
 40  (NRM RESID)/(NRM E)= 0.765E-15  RCOND(EST)= 0.434E-14 EST/TRUE= 0.352E+00

 M =  4   N =  8
  0  (NRM RESID)/(NRM E)= 0.111E-14  RCOND(EST)= 0.452E-03 EST/TRUE= 0.719E+00
 10  (NRM RESID)/(NRM E)= 0.118E-14  RCOND(EST)= 0.395E-05 EST/TRUE= 0.355E+00
 20  (NRM RESID)/(NRM E)= 0.511E-15  RCOND(EST)= 0.366E-08 EST/TRUE= 0.354E+00
 30  (NRM RESID)/(NRM E)= 0.933E-15  RCOND(EST)= 0.357E-11 EST/TRUE= 0.354E+00
 40  (NRM RESID)/(NRM E)= 0.644E-15  RCOND(EST)= 0.349E-14 EST/TRUE= 0.353E+00

 M =  5   N =  2
  0  (NRM RESID)/(NRM E)= 0.607E-15  RCOND(EST)= 0.100E-01 EST/TRUE= 0.423E+00
 10  (NRM RESID)/(NRM E)= 0.773E-15  RCOND(EST)= 0.408E-04 EST/TRUE= 0.648E+00
 20  (NRM RESID)/(NRM E)= 0.759E-15  RCOND(EST)= 0.396E-07 EST/TRUE= 0.647E+00
 30  (NRM RESID)/(NRM E)= 0.746E-15  RCOND(EST)= 0.387E-10 EST/TRUE= 0.647E+00
 40  (NRM RESID)/(NRM E)= 0.289E-15  RCOND(EST)= 0.377E-13 EST/TRUE= 0.647E+00

 M =  5   N =  3
  0  (NRM RESID)/(NRM E)= 0.233E-15  RCOND(EST)= 0.366E-02 EST/TRUE= 0.586E+00
 10  (NRM RESID)/(NRM E)= 0.473E-15  RCOND(EST)= 0.122E-04 EST/TRUE= 0.360E+00
 20  (NRM RESID)/(NRM E)= 0.681E-15  RCOND(EST)= 0.118E-07 EST/TRUE= 0.361E+00
 30  (NRM RESID)/(NRM E)= 0.563E-15  RCOND(EST)= 0.115E-10 EST/TRUE= 0.361E+00
 40  (NRM RESID)/(NRM E)= 0.178E-15  RCOND(EST)= 0.112E-13 EST/TRUE= 0.361E+00

 M =  5   N =  4
  0  (NRM RESID)/(NRM E)= 0.288E-15  RCOND(EST)= 0.124E-02 EST/TRUE= 0.861E+00
 10  (NRM RESID)/(NRM E)= 0.101E-14  RCOND(EST)= 0.665E-05 EST/TRUE= 0.302E+00
 20  (NRM RESID)/(NRM E)= 0.124E-14  RCOND(EST)= 0.635E-08 EST/TRUE= 0.302E+00
 30  (NRM RESID)/(NRM E)= 0.450E-15  RCOND(EST)= 0.562E-11 EST/TRUE= 0.274E+00
 40  (NRM RESID)/(NRM E)= 0.406E-15  RCOND(EST)= 0.605E-14 EST/TRUE= 0.302E+00

 M =  5   N =  5
  0  (NRM RESID)/(NRM E)= 0.499E-15  RCOND(EST)= 0.210E-03 EST/TRUE= 0.954E+00
 10  (NRM RESID)/(NRM E)= 0.471E-15  RCOND(EST)= 0.518E-05 EST/TRUE= 0.311E+00
 20  (NRM RESID)/(NRM E)= 0.450E-15  RCOND(EST)= 0.492E-08 EST/TRUE= 0.313E+00
 30  (NRM RESID)/(NRM E)= 0.977E-15  RCOND(EST)= 0.480E-11 EST/TRUE= 0.313E+00
 40  (NRM RESID)/(NRM E)= 0.422E-15  RCOND(EST)= 0.468E-14 EST/TRUE= 0.312E+00

 M =  5   N =  6
  0  (NRM RESID)/(NRM E)= 0.547E-15  RCOND(EST)= 0.627E-04 EST/TRUE= 0.926E+00
 10  (NRM RESID)/(NRM E)= 0.907E-15  RCOND(EST)= 0.358E-05 EST/TRUE= 0.265E+00
 20  (NRM RESID)/(NRM E)= 0.116E-14  RCOND(EST)= 0.337E-08 EST/TRUE= 0.266E+00
 30  (NRM RESID)/(NRM E)= 0.888E-15  RCOND(EST)= 0.329E-11 EST/TRUE= 0.266E+00
 40  (NRM RESID)/(NRM E)= 0.701E-15  RCOND(EST)= 0.322E-14 EST/TRUE= 0.265E+00

 M =  5   N =  7
  0  (NRM RESID)/(NRM E)= 0.820E-15  RCOND(EST)= 0.248E-04 EST/TRUE= 0.889E+00
 10  (NRM RESID)/(NRM E)= 0.985E-15  RCOND(EST)= 0.348E-05 EST/TRUE= 0.318E+00
 20  (NRM RESID)/(NRM E)= 0.497E-15  RCOND(EST)= 0.325E-08 EST/TRUE= 0.319E+00
 30  (NRM RESID)/(NRM E)= 0.506E-15  RCOND(EST)= 0.318E-11 EST/TRUE= 0.319E+00
 40  (NRM RESID)/(NRM E)= 0.853E-15  RCOND(EST)= 0.310E-14 EST/TRUE= 0.317E+00

 M =  5   N =  8
  0  (NRM RESID)/(NRM E)= 0.984E-15  RCOND(EST)= 0.114E-04 EST/TRUE= 0.841E+00
 10  (NRM RESID)/(NRM E)= 0.131E-14  RCOND(EST)= 0.287E-05 EST/TRUE= 0.328E+00
 20  (NRM RESID)/(NRM E)= 0.565E-15  RCOND(EST)= 0.266E-08 EST/TRUE= 0.330E+00
 30  (NRM RESID)/(NRM E)= 0.120E-14  RCOND(EST)= 0.260E-11 EST/TRUE= 0.330E+00
 40  (NRM RESID)/(NRM E)= 0.646E-15  RCOND(EST)= 0.254E-14 EST/TRUE= 0.328E+00

 M =  6   N =  2
  0  (NRM RESID)/(NRM E)= 0.911E-15  RCOND(EST)= 0.900E-02 EST/TRUE= 0.432E+00
 10  (NRM RESID)/(NRM E)= 0.555E-15  RCOND(EST)= 0.377E-04 EST/TRUE= 0.736E+00
 20  (NRM RESID)/(NRM E)= 0.904E-15  RCOND(EST)= 0.366E-07 EST/TRUE= 0.735E+00
 30  (NRM RESID)/(NRM E)= 0.802E-15  RCOND(EST)= 0.357E-10 EST/TRUE= 0.735E+00
 40  (NRM RESID)/(NRM E)= 0.549E-15  RCOND(EST)= 0.349E-13 EST/TRUE= 0.735E+00

 M =  6   N =  3
  0  (NRM RESID)/(NRM E)= 0.434E-15  RCOND(EST)= 0.317E-02 EST/TRUE= 0.546E+00
 10  (NRM RESID)/(NRM E)= 0.518E-15  RCOND(EST)= 0.115E-04 EST/TRUE= 0.417E+00
 20  (NRM RESID)/(NRM E)= 0.455E-15  RCOND(EST)= 0.112E-07 EST/TRUE= 0.418E+00
 30  (NRM RESID)/(NRM E)= 0.391E-15  RCOND(EST)= 0.109E-10 EST/TRUE= 0.418E+00
 40  (NRM RESID)/(NRM E)= 0.222E-15  RCOND(EST)= 0.107E-13 EST/TRUE= 0.418E+00

 M =  6   N =  4
  0  (NRM RESID)/(NRM E)= 0.645E-15  RCOND(EST)= 0.115E-02 EST/TRUE= 0.812E+00
 10  (NRM RESID)/(NRM E)= 0.869E-15  RCOND(EST)= 0.651E-05 EST/TRUE= 0.359E+00
 20  (NRM RESID)/(NRM E)= 0.114E-14  RCOND(EST)= 0.626E-08 EST/TRUE= 0.359E+00
 30  (NRM RESID)/(NRM E)= 0.282E-15  RCOND(EST)= 0.515E-11 EST/TRUE= 0.303E+00
 40  (NRM RESID)/(NRM E)= 0.463E-15  RCOND(EST)= 0.598E-14 EST/TRUE= 0.360E+00

 M =  6   N =  5
  0  (NRM RESID)/(NRM E)= 0.558E-15  RCOND(EST)= 0.387E-03 EST/TRUE= 0.114E+01
 10  (NRM RESID)/(NRM E)= 0.649E-15  RCOND(EST)= 0.430E-05 EST/TRUE= 0.328E+00
 20  (NRM RESID)/(NRM E)= 0.321E-15  RCOND(EST)= 0.407E-08 EST/TRUE= 0.328E+00
 30  (NRM RESID)/(NRM E)= 0.872E-15  RCOND(EST)= 0.397E-11 EST/TRUE= 0.328E+00
 40  (NRM RESID)/(NRM E)= 0.650E-15  RCOND(EST)= 0.389E-14 EST/TRUE= 0.328E+00

 M =  6   N =  6
  0  (NRM RESID)/(NRM E)= 0.631E-15  RCOND(EST)= 0.757E-04 EST/TRUE= 0.119E+01
 10  (NRM RESID)/(NRM E)= 0.821E-15  RCOND(EST)= 0.279E-05 EST/TRUE= 0.269E+00
 20  (NRM RESID)/(NRM E)= 0.117E-14  RCOND(EST)= 0.261E-08 EST/TRUE= 0.269E+00
 30  (NRM RESID)/(NRM E)= 0.866E-15  RCOND(EST)= 0.255E-11 EST/TRUE= 0.269E+00
 40  (NRM RESID)/(NRM E)= 0.703E-15  RCOND(EST)= 0.250E-14 EST/TRUE= 0.270E+00

 M =  6   N =  7
  0  (NRM RESID)/(NRM E)= 0.572E-15
 10  (NRM RESID)/(NRM E)= 0.974E-15
 20  (NRM RESID)/(NRM E)= 0.404E-15
 30  (NRM RESID)/(NRM E)= 0.481E-15
 40  (NRM RESID)/(NRM E)= 0.915E-15

 M =  6   N =  8
  0  (NRM RESID)/(NRM E)= 0.117E-14
 10  (NRM RESID)/(NRM E)= 0.142E-14
 20  (NRM RESID)/(NRM E)= 0.506E-15
 30  (NRM RESID)/(NRM E)= 0.102E-14
 40  (NRM RESID)/(NRM E)= 0.901E-15

 M =  7   N =  2
  0  (NRM RESID)/(NRM E)= 0.722E-15  RCOND(EST)= 0.802E-02 EST/TRUE= 0.433E+00
 10  (NRM RESID)/(NRM E)= 0.779E-15  RCOND(EST)= 0.348E-04 EST/TRUE= 0.806E+00
 20  (NRM RESID)/(NRM E)= 0.666E-15  RCOND(EST)= 0.338E-07 EST/TRUE= 0.805E+00
 30  (NRM RESID)/(NRM E)= 0.911E-15  RCOND(EST)= 0.330E-10 EST/TRUE= 0.805E+00
 40  (NRM RESID)/(NRM E)= 0.800E-15  RCOND(EST)= 0.322E-13 EST/TRUE= 0.805E+00

 M =  7   N =  3
  0  (NRM RESID)/(NRM E)= 0.336E-15  RCOND(EST)= 0.283E-02 EST/TRUE= 0.525E+00
 10  (NRM RESID)/(NRM E)= 0.333E-15  RCOND(EST)= 0.107E-04 EST/TRUE= 0.457E+00
 20  (NRM RESID)/(NRM E)= 0.539E-15  RCOND(EST)= 0.104E-07 EST/TRUE= 0.458E+00
 30  (NRM RESID)/(NRM E)= 0.591E-15  RCOND(EST)= 0.102E-10 EST/TRUE= 0.458E+00
 40  (NRM RESID)/(NRM E)= 0.151E-15  RCOND(EST)= 0.993E-14 EST/TRUE= 0.458E+00

 M =  7   N =  4
  0  (NRM RESID)/(NRM E)= 0.408E-15  RCOND(EST)= 0.105E-02 EST/TRUE= 0.772E+00
 10  (NRM RESID)/(NRM E)= 0.873E-15  RCOND(EST)= 0.598E-05 EST/TRUE= 0.387E+00
 20  (NRM RESID)/(NRM E)= 0.846E-15  RCOND(EST)= 0.577E-08 EST/TRUE= 0.388E+00
 30  (NRM RESID)/(NRM E)= 0.338E-15  RCOND(EST)= 0.474E-11 EST/TRUE= 0.327E+00
 40  (NRM RESID)/(NRM E)= 0.486E-15  RCOND(EST)= 0.550E-14 EST/TRUE= 0.390E+00

 M =  7   N =  5
  0  (NRM RESID)/(NRM E)= 0.543E-15  RCOND(EST)= 0.393E-03 EST/TRUE= 0.116E+01
 10  (NRM RESID)/(NRM E)= 0.615E-15  RCOND(EST)= 0.377E-05 EST/TRUE= 0.337E+00
 20  (NRM RESID)/(NRM E)= 0.634E-15  RCOND(EST)= 0.358E-08 EST/TRUE= 0.336E+00
 30  (NRM RESID)/(NRM E)= 0.110E-14  RCOND(EST)= 0.350E-11 EST/TRUE= 0.336E+00
 40  (NRM RESID)/(NRM E)= 0.723E-15  RCOND(EST)= 0.342E-14 EST/TRUE= 0.337E+00

 M =  7   N =  6
  0  (NRM RESID)/(NRM E)= 0.696E-15
 10  (NRM RESID)/(NRM E)= 0.858E-15
 20  (NRM RESID)/(NRM E)= 0.946E-15
 30  (NRM RESID)/(NRM E)= 0.105E-14
 40  (NRM RESID)/(NRM E)= 0.721E-15

 M =  7   N =  7
  0  (NRM RESID)/(NRM E)= 0.630E-15
 10  (NRM RESID)/(NRM E)= 0.898E-15
 20  (NRM RESID)/(NRM E)= 0.434E-15
 30  (NRM RESID)/(NRM E)= 0.486E-15
 40  (NRM RESID)/(NRM E)= 0.108E-14

 M =  7   N =  8
  0  (NRM RESID)/(NRM E)= 0.114E-14
 10  (NRM RESID)/(NRM E)= 0.106E-14
 20  (NRM RESID)/(NRM E)= 0.590E-15
 30  (NRM RESID)/(NRM E)= 0.937E-15
 40  (NRM RESID)/(NRM E)= 0.810E-15

 M =  8   N =  2
  0  (NRM RESID)/(NRM E)= 0.496E-15  RCOND(EST)= 0.701E-02 EST/TRUE= 0.420E+00
 10  (NRM RESID)/(NRM E)= 0.666E-15  RCOND(EST)= 0.321E-04 EST/TRUE= 0.861E+00
 20  (NRM RESID)/(NRM E)= 0.914E-15  RCOND(EST)= 0.312E-07 EST/TRUE= 0.860E+00
 30  (NRM RESID)/(NRM E)= 0.770E-15  RCOND(EST)= 0.305E-10 EST/TRUE= 0.860E+00
 40  (NRM RESID)/(NRM E)= 0.670E-15  RCOND(EST)= 0.298E-13 EST/TRUE= 0.860E+00

 M =  8   N =  3
  0  (NRM RESID)/(NRM E)= 0.407E-15  RCOND(EST)= 0.256E-02 EST/TRUE= 0.509E+00
 10  (NRM RESID)/(NRM E)= 0.401E-15  RCOND(EST)= 0.985E-05 EST/TRUE= 0.483E+00
 20  (NRM RESID)/(NRM E)= 0.540E-15  RCOND(EST)= 0.955E-08 EST/TRUE= 0.485E+00
 30  (NRM RESID)/(NRM E)= 0.629E-15  RCOND(EST)= 0.933E-11 EST/TRUE= 0.485E+00
 40  (NRM RESID)/(NRM E)= 0.281E-15  RCOND(EST)= 0.911E-14 EST/TRUE= 0.484E+00

 M =  8   N =  4
  0  (NRM RESID)/(NRM E)= 0.388E-15  RCOND(EST)= 0.950E-03 EST/TRUE= 0.734E+00
 10  (NRM RESID)/(NRM E)= 0.887E-15  RCOND(EST)= 0.562E-05 EST/TRUE= 0.418E+00
 20  (NRM RESID)/(NRM E)= 0.118E-14  RCOND(EST)= 0.542E-08 EST/TRUE= 0.419E+00
 30  (NRM RESID)/(NRM E)= 0.416E-15  RCOND(EST)= 0.465E-11 EST/TRUE= 0.368E+00
 40  (NRM RESID)/(NRM E)= 0.444E-15  RCOND(EST)= 0.518E-14 EST/TRUE= 0.420E+00

 M =  8   N =  5
  0  (NRM RESID)/(NRM E)= 0.479E-15  RCOND(EST)= 0.362E-03 EST/TRUE= 0.109E+01
 10  (NRM RESID)/(NRM E)= 0.640E-15  RCOND(EST)= 0.385E-05 EST/TRUE= 0.395E+00
 20  (NRM RESID)/(NRM E)= 0.585E-15  RCOND(EST)= 0.368E-08 EST/TRUE= 0.394E+00
 30  (NRM RESID)/(NRM E)= 0.118E-14  RCOND(EST)= 0.359E-11 EST/TRUE= 0.394E+00
 40  (NRM RESID)/(NRM E)= 0.707E-15  RCOND(EST)= 0.351E-14 EST/TRUE= 0.394E+00

 M =  8   N =  6
  0  (NRM RESID)/(NRM E)= 0.923E-15
 10  (NRM RESID)/(NRM E)= 0.832E-15
 20  (NRM RESID)/(NRM E)= 0.851E-15
 30  (NRM RESID)/(NRM E)= 0.860E-15
 40  (NRM RESID)/(NRM E)= 0.465E-15

 M =  8   N =  7
  0  (NRM RESID)/(NRM E)= 0.536E-15
 10  (NRM RESID)/(NRM E)= 0.109E-14
 20  (NRM RESID)/(NRM E)= 0.564E-15
 30  (NRM RESID)/(NRM E)= 0.623E-15
 40  (NRM RESID)/(NRM E)= 0.114E-14

 M =  8   N =  8
  0  (NRM RESID)/(NRM E)= 0.864E-15
 10  (NRM RESID)/(NRM E)= 0.132E-14
 20  (NRM RESID)/(NRM E)= 0.674E-15
 30  (NRM RESID)/(NRM E)= 0.108E-14
 40  (NRM RESID)/(NRM E)= 0.948E-15

 M =  9   N =  2
  0  (NRM RESID)/(NRM E)= 0.722E-15  RCOND(EST)= 0.637E-02 EST/TRUE= 0.420E+00
 10  (NRM RESID)/(NRM E)= 0.618E-15  RCOND(EST)= 0.298E-04 EST/TRUE= 0.906E+00
 20  (NRM RESID)/(NRM E)= 0.119E-14  RCOND(EST)= 0.289E-07 EST/TRUE= 0.905E+00
 30  (NRM RESID)/(NRM E)= 0.358E-15  RCOND(EST)= 0.282E-10 EST/TRUE= 0.905E+00
 40  (NRM RESID)/(NRM E)= 0.615E-15  RCOND(EST)= 0.276E-13 EST/TRUE= 0.907E+00

 M =  9   N =  3
  0  (NRM RESID)/(NRM E)= 0.358E-15  RCOND(EST)= 0.232E-02 EST/TRUE= 0.495E+00
 10  (NRM RESID)/(NRM E)= 0.493E-15  RCOND(EST)= 0.928E-05 EST/TRUE= 0.516E+00
 20  (NRM RESID)/(NRM E)= 0.770E-15  RCOND(EST)= 0.901E-08 EST/TRUE= 0.517E+00
 30  (NRM RESID)/(NRM E)= 0.348E-15  RCOND(EST)= 0.880E-11 EST/TRUE= 0.517E+00
 40  (NRM RESID)/(NRM E)= 0.348E-15  RCOND(EST)= 0.859E-14 EST/TRUE= 0.517E+00

 M =  9   N =  4
  0  (NRM RESID)/(NRM E)= 0.449E-15  RCOND(EST)= 0.872E-03 EST/TRUE= 0.706E+00
 10  (NRM RESID)/(NRM E)= 0.968E-15  RCOND(EST)= 0.533E-05 EST/TRUE= 0.448E+00
 20  (NRM RESID)/(NRM E)= 0.938E-15  RCOND(EST)= 0.515E-08 EST/TRUE= 0.450E+00
 30  (NRM RESID)/(NRM E)= 0.318E-15  RCOND(EST)= 0.449E-11 EST/TRUE= 0.401E+00
 40  (NRM RESID)/(NRM E)= 0.507E-15  RCOND(EST)= 0.492E-14 EST/TRUE= 0.449E+00

 M =  9   N =  5
  0  (NRM RESID)/(NRM E)= 0.359E-15
 10  (NRM RESID)/(NRM E)= 0.528E-15
 20  (NRM RESID)/(NRM E)= 0.401E-15
 30  (NRM RESID)/(NRM E)= 0.954E-15
 40  (NRM RESID)/(NRM E)= 0.718E-15

 M =  9   N =  6
  0  (NRM RESID)/(NRM E)= 0.698E-15
 10  (NRM RESID)/(NRM E)= 0.872E-15
 20  (NRM RESID)/(NRM E)= 0.820E-15
 30  (NRM RESID)/(NRM E)= 0.660E-15
 40  (NRM RESID)/(NRM E)= 0.501E-15

 M =  9   N =  7
  0  (NRM RESID)/(NRM E)= 0.592E-15
 10  (NRM RESID)/(NRM E)= 0.982E-15
 20  (NRM RESID)/(NRM E)= 0.458E-15
 30  (NRM RESID)/(NRM E)= 0.712E-15
 40  (NRM RESID)/(NRM E)= 0.130E-14

 M =  9   N =  8
  0  (NRM RESID)/(NRM E)= 0.113E-14
 10  (NRM RESID)/(NRM E)= 0.179E-14
 20  (NRM RESID)/(NRM E)= 0.809E-15
 30  (NRM RESID)/(NRM E)= 0.954E-15
 40  (NRM RESID)/(NRM E)= 0.822E-15

 WORST CASE RESIDUAL IS 0.179E-14
 WORST CASE RCOND RATIOS (EST/TRUE) ARE 0.244E+00 (LOW) AND 0.119E+01 (HIGH)


 THE RESIDUAL SHOULD BE ON THE ORDER OF 1E-14 OR SMALLER ON MOST MACHINES.
 THE RCOND RATIOS SHOULD BE ON THE ORDER OF 1, I.E., BETWEEN .1 AND 10.
SHAR_EOF
fi # end of overwriting check
if test -f 'res2'
then
	echo shar: will not over-write existing file "'res2'"
else
cat << "SHAR_EOF" > 'res2'
             T        T
 SOLVE  A*X*E  + E*X*A  + Q = 0  USING SYLGC

 N =  1
  0  (NRM RESID)/(NRM Q)= 0.000E+00  RCOND(EST)= 0.100E+01 EST/TRUE= 0.100E+01
 10  (NRM RESID)/(NRM Q)= 0.000E+00  RCOND(EST)= 0.100E+01 EST/TRUE= 0.100E+01
 20  (NRM RESID)/(NRM Q)= 0.000E+00  RCOND(EST)= 0.100E+01 EST/TRUE= 0.100E+01
 30  (NRM RESID)/(NRM Q)= 0.000E+00  RCOND(EST)= 0.100E+01 EST/TRUE= 0.100E+01
 40  (NRM RESID)/(NRM Q)= 0.000E+00  RCOND(EST)= 0.100E+01 EST/TRUE= 0.100E+01

 N =  2
  0  (NRM RESID)/(NRM Q)= 0.000E+00  RCOND(EST)= 0.117E+00 EST/TRUE= 0.852E+00
 10  (NRM RESID)/(NRM Q)= 0.296E-15  RCOND(EST)= 0.487E-03 EST/TRUE= 0.128E+01
 20  (NRM RESID)/(NRM Q)= 0.296E-15  RCOND(EST)= 0.477E-06 EST/TRUE= 0.128E+01
 30  (NRM RESID)/(NRM Q)= 0.296E-15  RCOND(EST)= 0.466E-09 EST/TRUE= 0.128E+01
 40  (NRM RESID)/(NRM Q)= 0.296E-15  RCOND(EST)= 0.455E-12 EST/TRUE= 0.128E+01

 N =  3
  0  (NRM RESID)/(NRM Q)= 0.763E-15  RCOND(EST)= 0.286E-01 EST/TRUE= 0.508E+00
 10  (NRM RESID)/(NRM Q)= 0.148E-15  RCOND(EST)= 0.143E-03 EST/TRUE= 0.723E+00
 20  (NRM RESID)/(NRM Q)= 0.493E-15  RCOND(EST)= 0.140E-06 EST/TRUE= 0.725E+00
 30  (NRM RESID)/(NRM Q)= 0.209E-15  RCOND(EST)= 0.136E-09 EST/TRUE= 0.725E+00
 40  (NRM RESID)/(NRM Q)= 0.299E-15  RCOND(EST)= 0.133E-12 EST/TRUE= 0.725E+00

 N =  4
  0  (NRM RESID)/(NRM Q)= 0.136E-14  RCOND(EST)= 0.127E-01 EST/TRUE= 0.460E+00
 10  (NRM RESID)/(NRM Q)= 0.789E-15  RCOND(EST)= 0.682E-04 EST/TRUE= 0.512E+00
 20  (NRM RESID)/(NRM Q)= 0.666E-15  RCOND(EST)= 0.668E-07 EST/TRUE= 0.513E+00
 30  (NRM RESID)/(NRM Q)= 0.641E-15  RCOND(EST)= 0.964E-10 EST/TRUE= 0.758E+00
 40  (NRM RESID)/(NRM Q)= 0.148E-14  RCOND(EST)= 0.942E-13 EST/TRUE= 0.759E+00

 N =  5
  0  (NRM RESID)/(NRM Q)= 0.102E-14  RCOND(EST)= 0.520E-02 EST/TRUE= 0.379E+00
 10  (NRM RESID)/(NRM Q)= 0.120E-14  RCOND(EST)= 0.778E-04 EST/TRUE= 0.772E+00
 20  (NRM RESID)/(NRM Q)= 0.933E-15  RCOND(EST)= 0.764E-07 EST/TRUE= 0.776E+00
 30  (NRM RESID)/(NRM Q)= 0.629E-15  RCOND(EST)= 0.746E-10 EST/TRUE= 0.776E+00
 40  (NRM RESID)/(NRM Q)= 0.355E-15  RCOND(EST)= 0.728E-13 EST/TRUE= 0.775E+00

 N =  6
  0  (NRM RESID)/(NRM Q)= 0.164E-14  RCOND(EST)= 0.221E-02 EST/TRUE= 0.372E+00
 10  (NRM RESID)/(NRM Q)= 0.203E-14  RCOND(EST)= 0.429E-04 EST/TRUE= 0.530E+00
 20  (NRM RESID)/(NRM Q)= 0.533E-15  RCOND(EST)= 0.423E-07 EST/TRUE= 0.534E+00
 30  (NRM RESID)/(NRM Q)= 0.612E-15  RCOND(EST)= 0.413E-10 EST/TRUE= 0.534E+00
 40  (NRM RESID)/(NRM Q)= 0.829E-15  RCOND(EST)= 0.403E-13 EST/TRUE= 0.534E+00

 N =  7
  0  (NRM RESID)/(NRM Q)= 0.220E-14
 10  (NRM RESID)/(NRM Q)= 0.128E-14
 20  (NRM RESID)/(NRM Q)= 0.126E-14
 30  (NRM RESID)/(NRM Q)= 0.525E-15
 40  (NRM RESID)/(NRM Q)= 0.846E-15

 N =  8
  0  (NRM RESID)/(NRM Q)= 0.135E-14
 10  (NRM RESID)/(NRM Q)= 0.178E-14
 20  (NRM RESID)/(NRM Q)= 0.825E-15
 30  (NRM RESID)/(NRM Q)= 0.994E-15
 40  (NRM RESID)/(NRM Q)= 0.166E-14

 WORST CASE RESIDUAL IS 0.220E-14
 WORST CASE RCOND RATIOS (EST/TRUE) ARE 0.372E+00 (LOW) AND 0.128E+01 (HIGH)


 THE RESIDUAL SHOULD BE ON THE ORDER OF 1E-14 OR SMALLER ON MOST MACHINES.
 THE RCOND RATIOS SHOULD BE ON THE ORDER OF 1, I.E., BETWEEN .1 AND 10.
SHAR_EOF
fi # end of overwriting check
if test -f 'res3'
then
	echo shar: will not over-write existing file "'res3'"
else
cat << "SHAR_EOF" > 'res3'
             T        T
 SOLVE  A*X*A  - E*X*E  + Q = 0  USING SYLGD

 N =  2
  0  (NRM RESID)/(NRM Q)= 0.000E+00  RCOND(EST)= 0.236E+00 EST/TRUE= 0.720E+00
 10  (NRM RESID)/(NRM Q)= 0.311E-15  RCOND(EST)= 0.390E-03 EST/TRUE= 0.872E+00
 20  (NRM RESID)/(NRM Q)= 0.111E-15  RCOND(EST)= 0.381E-06 EST/TRUE= 0.874E+00
 30  (NRM RESID)/(NRM Q)= 0.222E-15  RCOND(EST)= 0.373E-09 EST/TRUE= 0.874E+00
 40  (NRM RESID)/(NRM Q)= 0.222E-15  RCOND(EST)= 0.364E-12 EST/TRUE= 0.874E+00

 N =  3
  0  (NRM RESID)/(NRM Q)= 0.760E-15  RCOND(EST)= 0.665E-01 EST/TRUE= 0.395E+00
 10  (NRM RESID)/(NRM Q)= 0.523E-15  RCOND(EST)= 0.952E-04 EST/TRUE= 0.561E+00
 20  (NRM RESID)/(NRM Q)= 0.708E-15  RCOND(EST)= 0.931E-07 EST/TRUE= 0.562E+00
 30  (NRM RESID)/(NRM Q)= 0.605E-15  RCOND(EST)= 0.909E-10 EST/TRUE= 0.562E+00
 40  (NRM RESID)/(NRM Q)= 0.272E-15  RCOND(EST)= 0.888E-13 EST/TRUE= 0.562E+00

 N =  4
  0  (NRM RESID)/(NRM Q)= 0.563E-15  RCOND(EST)= 0.656E-01 EST/TRUE= 0.635E+00
 10  (NRM RESID)/(NRM Q)= 0.351E-15  RCOND(EST)= 0.329E-04 EST/TRUE= 0.363E+00
 20  (NRM RESID)/(NRM Q)= 0.442E-15  RCOND(EST)= 0.322E-07 EST/TRUE= 0.364E+00
 30  (NRM RESID)/(NRM Q)= 0.489E-15  RCOND(EST)= 0.315E-10 EST/TRUE= 0.364E+00
 40  (NRM RESID)/(NRM Q)= 0.854E-15  RCOND(EST)= 0.307E-13 EST/TRUE= 0.364E+00

 N =  5
  0  (NRM RESID)/(NRM Q)= 0.164E-14  RCOND(EST)= 0.278E-01 EST/TRUE= 0.398E+00
 10  (NRM RESID)/(NRM Q)= 0.461E-15  RCOND(EST)= 0.364E-04 EST/TRUE= 0.642E+00
 20  (NRM RESID)/(NRM Q)= 0.691E-15  RCOND(EST)= 0.357E-07 EST/TRUE= 0.645E+00
 30  (NRM RESID)/(NRM Q)= 0.751E-15  RCOND(EST)= 0.348E-10 EST/TRUE= 0.645E+00
 40  (NRM RESID)/(NRM Q)= 0.544E-15  RCOND(EST)= 0.340E-13 EST/TRUE= 0.645E+00

 N =  6
  0  (NRM RESID)/(NRM Q)= 0.203E-14  RCOND(EST)= 0.225E-01 EST/TRUE= 0.445E+00
 10  (NRM RESID)/(NRM Q)= 0.162E-14  RCOND(EST)= 0.148E-04 EST/TRUE= 0.381E+00
 20  (NRM RESID)/(NRM Q)= 0.102E-14  RCOND(EST)= 0.145E-07 EST/TRUE= 0.383E+00
 30  (NRM RESID)/(NRM Q)= 0.682E-15  RCOND(EST)= 0.142E-10 EST/TRUE= 0.383E+00
 40  (NRM RESID)/(NRM Q)= 0.170E-14  RCOND(EST)= 0.139E-13 EST/TRUE= 0.383E+00

 N =  7
  0  (NRM RESID)/(NRM Q)= 0.173E-14
 10  (NRM RESID)/(NRM Q)= 0.149E-14
 20  (NRM RESID)/(NRM Q)= 0.643E-15
 30  (NRM RESID)/(NRM Q)= 0.845E-15
 40  (NRM RESID)/(NRM Q)= 0.887E-15

 N =  8
  0  (NRM RESID)/(NRM Q)= 0.990E-15
 10  (NRM RESID)/(NRM Q)= 0.140E-14
 20  (NRM RESID)/(NRM Q)= 0.151E-14
 30  (NRM RESID)/(NRM Q)= 0.135E-14
 40  (NRM RESID)/(NRM Q)= 0.973E-15

 WORST CASE RESIDUAL IS 0.203E-14
 WORST CASE RCOND RATIOS (EST/TRUE) ARE 0.363E+00 (LOW) AND 0.874E+00 (HIGH)


 THE RESIDUAL SHOULD BE ON THE ORDER OF 1E-14 OR SMALLER ON MOST MACHINES.
 THE RCOND RATIOS SHOULD BE ON THE ORDER OF 1, I.E., BETWEEN .1 AND 10.
SHAR_EOF
fi # end of overwriting check
if test -f 'res4'
then
	echo shar: will not over-write existing file "'res4'"
else
cat << "SHAR_EOF" > 'res4'
             T        T
 SOLVE  A*X*B  + C*X*D  = E  USING SYLG

 M = 2, N = 1
  -0.1000E+01
  -0.1000E+01
   (NRM RESID)/(NRM E)= 0.000E+00  RCOND(EST)= 0.149E+00

 DO YOU WISH TO HAVE THE ACTUAL CONDITION NUMBER COMPUTED? (Y OR N) 
   RCOND(TRUE)= 0.205E+00 EST/TRUE= 0.727E+00
SHAR_EOF
fi # end of overwriting check
if test -f 'res5'
then
	echo shar: will not over-write existing file "'res5'"
else
cat << "SHAR_EOF" > 'res5'
             T        T
 SOLVE  A*X*E  + E*X*A  + Q = 0  USING SYLGC

 N = 3
  -0.2828E+00  0.1207E+00  0.7553E-01
   0.1207E+00  0.3802E-01 -0.1554E+00
   0.7553E-01 -0.1554E+00  0.9797E-01
   (NRM RESID)/(NRM Q)= 0.246E-14  RCOND(EST)= 0.847E-02

 DO YOU WISH TO HAVE THE ACTUAL CONDITION NUMBER COMPUTED? (Y OR N) 
   RCOND(TRUE)= 0.203E-01 EST/TRUE= 0.418E+00
SHAR_EOF
fi # end of overwriting check
if test -f 'res6'
then
	echo shar: will not over-write existing file "'res6'"
else
cat << "SHAR_EOF" > 'res6'
             T        T
 SOLVE  A*X*A  - E*X*E  + Q = 0  USING SYLGD

 N = 5
   0.9957E+01 -0.2289E+02 -0.3361E+02  0.2581E+02  0.1963E+02
  -0.2289E+02 -0.4787E+02 -0.2944E+02  0.4595E+02  0.4209E+02
  -0.3361E+02 -0.2944E+02  0.1919E+00  0.2509E+02  0.2677E+02
   0.2581E+02  0.4595E+02  0.2509E+02 -0.4278E+02 -0.4072E+02
   0.1963E+02  0.4209E+02  0.2677E+02 -0.4072E+02 -0.3895E+02
   (NRM RESID)/(NRM Q)= 0.141E+01  RCOND(EST)= 0.506E-04

 DO YOU WISH TO HAVE THE ACTUAL CONDITION NUMBER COMPUTED? (Y OR N) 
   RCOND(TRUE)= 0.424E-04 EST/TRUE= 0.119E+01
SHAR_EOF
fi # end of overwriting check
if test -f 'res7'
then
	echo shar: will not over-write existing file "'res7'"
else
cat << "SHAR_EOF" > 'res7'
             T        T
 SOLVE  A*X*B  + C*X*D  = E  USING SYLG

 M =  1   N =  1
  1  (NRM RESID)/(NRM E)= 0.385E-16  RCOND(EST)= 0.710E+00 EST/TRUE= 0.710E+00
  2  (NRM RESID)/(NRM E)= 0.155E-15  RCOND(EST)= 0.685E+00 EST/TRUE= 0.685E+00
  3  (NRM RESID)/(NRM E)= 0.127E-15  RCOND(EST)= 0.100E+01 EST/TRUE= 0.100E+01
  4  (NRM RESID)/(NRM E)= 0.267E-15  RCOND(EST)= 0.538E+00 EST/TRUE= 0.538E+00
  5  (NRM RESID)/(NRM E)= 0.000E+00  RCOND(EST)= 0.100E+01 EST/TRUE= 0.100E+01

 M =  1   N =  2
  1  (NRM RESID)/(NRM E)= 0.333E-14  RCOND(EST)= 0.686E-01 EST/TRUE= 0.502E+00
  2  (NRM RESID)/(NRM E)= 0.141E-14  RCOND(EST)= 0.241E+00 EST/TRUE= 0.514E+00
  3  (NRM RESID)/(NRM E)= 0.327E-14  RCOND(EST)= 0.234E-01 EST/TRUE= 0.909E+00
  4  (NRM RESID)/(NRM E)= 0.441E-15  RCOND(EST)= 0.638E+00 EST/TRUE= 0.162E+01
  5  (NRM RESID)/(NRM E)= 0.207E-15  RCOND(EST)= 0.197E+00 EST/TRUE= 0.570E+00

 M =  1   N =  3
  1  (NRM RESID)/(NRM E)= 0.109E-14  RCOND(EST)= 0.578E+00 EST/TRUE= 0.902E+00
  2  (NRM RESID)/(NRM E)= 0.600E-15  RCOND(EST)= 0.408E+00 EST/TRUE= 0.108E+01
  3  (NRM RESID)/(NRM E)= 0.588E-15  RCOND(EST)= 0.480E-01 EST/TRUE= 0.179E+01
  4  (NRM RESID)/(NRM E)= 0.704E-15  RCOND(EST)= 0.179E+00 EST/TRUE= 0.134E+01
  5  (NRM RESID)/(NRM E)= 0.647E-14  RCOND(EST)= 0.688E-01 EST/TRUE= 0.739E+00

 M =  1   N =  4
  1  (NRM RESID)/(NRM E)= 0.471E-15  RCOND(EST)= 0.855E-01 EST/TRUE= 0.613E+00
  2  (NRM RESID)/(NRM E)= 0.292E-15  RCOND(EST)= 0.267E+00 EST/TRUE= 0.902E+00
  3  (NRM RESID)/(NRM E)= 0.583E-15  RCOND(EST)= 0.343E+00 EST/TRUE= 0.145E+01
  4  (NRM RESID)/(NRM E)= 0.267E-14  RCOND(EST)= 0.605E-01 EST/TRUE= 0.879E+00
  5  (NRM RESID)/(NRM E)= 0.371E-15  RCOND(EST)= 0.113E+00 EST/TRUE= 0.111E+01

 M =  1   N =  5
  1  (NRM RESID)/(NRM E)= 0.411E-14  RCOND(EST)= 0.624E-01 EST/TRUE= 0.865E+00
  2  (NRM RESID)/(NRM E)= 0.121E-14  RCOND(EST)= 0.166E-01 EST/TRUE= 0.854E+00
  3  (NRM RESID)/(NRM E)= 0.697E-14  RCOND(EST)= 0.286E-01 EST/TRUE= 0.182E+01
  4  (NRM RESID)/(NRM E)= 0.379E-14  RCOND(EST)= 0.331E-01 EST/TRUE= 0.792E+00
  5  (NRM RESID)/(NRM E)= 0.149E-14  RCOND(EST)= 0.160E-01 EST/TRUE= 0.540E+00

 M =  1   N =  6
  1  (NRM RESID)/(NRM E)= 0.455E-15  RCOND(EST)= 0.171E+00 EST/TRUE= 0.118E+01
  2  (NRM RESID)/(NRM E)= 0.865E-15  RCOND(EST)= 0.135E+00 EST/TRUE= 0.994E+00
  3  (NRM RESID)/(NRM E)= 0.296E-14  RCOND(EST)= 0.545E-01 EST/TRUE= 0.101E+01
  4  (NRM RESID)/(NRM E)= 0.202E-13  RCOND(EST)= 0.527E-02 EST/TRUE= 0.772E+00
  5  (NRM RESID)/(NRM E)= 0.129E-13  RCOND(EST)= 0.820E-02 EST/TRUE= 0.125E+01

 M =  1   N =  7
  1  (NRM RESID)/(NRM E)= 0.149E-13  RCOND(EST)= 0.137E-01 EST/TRUE= 0.133E+01
  2  (NRM RESID)/(NRM E)= 0.259E-14  RCOND(EST)= 0.348E-01 EST/TRUE= 0.831E+00
  3  (NRM RESID)/(NRM E)= 0.453E-14  RCOND(EST)= 0.380E-01 EST/TRUE= 0.183E+01
  4  (NRM RESID)/(NRM E)= 0.208E-14  RCOND(EST)= 0.441E-01 EST/TRUE= 0.103E+01
  5  (NRM RESID)/(NRM E)= 0.104E-13  RCOND(EST)= 0.251E-01 EST/TRUE= 0.135E+01

 M =  1   N =  8
  1  (NRM RESID)/(NRM E)= 0.281E-14  RCOND(EST)= 0.721E-01 EST/TRUE= 0.841E+00
  2  (NRM RESID)/(NRM E)= 0.215E-13  RCOND(EST)= 0.540E-01 EST/TRUE= 0.298E+01
  3  (NRM RESID)/(NRM E)= 0.227E-14  RCOND(EST)= 0.159E+00 EST/TRUE= 0.119E+01
  4  (NRM RESID)/(NRM E)= 0.130E-14  RCOND(EST)= 0.401E-01 EST/TRUE= 0.146E+01
  5  (NRM RESID)/(NRM E)= 0.124E-13  RCOND(EST)= 0.635E-01 EST/TRUE= 0.137E+01

 M =  2   N =  1
  1  (NRM RESID)/(NRM E)= 0.160E-15  RCOND(EST)= 0.494E+00 EST/TRUE= 0.596E+00
  2  (NRM RESID)/(NRM E)= 0.530E-15  RCOND(EST)= 0.402E+00 EST/TRUE= 0.548E+00
  3  (NRM RESID)/(NRM E)= 0.151E-15  RCOND(EST)= 0.446E+00 EST/TRUE= 0.543E+00
  4  (NRM RESID)/(NRM E)= 0.501E-15  RCOND(EST)= 0.113E+00 EST/TRUE= 0.506E+00
  5  (NRM RESID)/(NRM E)= 0.110E-14  RCOND(EST)= 0.104E+00 EST/TRUE= 0.947E+00

 M =  2   N =  2
  1  (NRM RESID)/(NRM E)= 0.153E-14  RCOND(EST)= 0.195E-01 EST/TRUE= 0.748E+00
  2  (NRM RESID)/(NRM E)= 0.977E-15  RCOND(EST)= 0.302E-01 EST/TRUE= 0.113E+01
  3  (NRM RESID)/(NRM E)= 0.604E-15  RCOND(EST)= 0.766E-01 EST/TRUE= 0.876E+00
  4  (NRM RESID)/(NRM E)= 0.918E-15  RCOND(EST)= 0.186E-01 EST/TRUE= 0.721E+00
  5  (NRM RESID)/(NRM E)= 0.900E-15  RCOND(EST)= 0.702E-01 EST/TRUE= 0.727E+00

 M =  2   N =  3
  1  (NRM RESID)/(NRM E)= 0.149E-14  RCOND(EST)= 0.284E-01 EST/TRUE= 0.844E+00
  2  (NRM RESID)/(NRM E)= 0.406E-14  RCOND(EST)= 0.198E-01 EST/TRUE= 0.763E+00
  3  (NRM RESID)/(NRM E)= 0.693E-15  RCOND(EST)= 0.763E-01 EST/TRUE= 0.909E+00
  4  (NRM RESID)/(NRM E)= 0.178E-14  RCOND(EST)= 0.207E-01 EST/TRUE= 0.149E+01
  5  (NRM RESID)/(NRM E)= 0.174E-14  RCOND(EST)= 0.112E-01 EST/TRUE= 0.938E+00

 M =  2   N =  4
  1  (NRM RESID)/(NRM E)= 0.446E-14  RCOND(EST)= 0.209E-01 EST/TRUE= 0.620E+00
  2  (NRM RESID)/(NRM E)= 0.282E-14  RCOND(EST)= 0.437E-01 EST/TRUE= 0.129E+01
  3  (NRM RESID)/(NRM E)= 0.189E-13  RCOND(EST)= 0.596E-02 EST/TRUE= 0.481E+00
  4  (NRM RESID)/(NRM E)= 0.648E-14  RCOND(EST)= 0.199E-01 EST/TRUE= 0.110E+01
  5  (NRM RESID)/(NRM E)= 0.288E-14  RCOND(EST)= 0.171E-01 EST/TRUE= 0.412E+00

 M =  2   N =  5
  1  (NRM RESID)/(NRM E)= 0.235E-14  RCOND(EST)= 0.271E-01 EST/TRUE= 0.854E+00
  2  (NRM RESID)/(NRM E)= 0.312E-14  RCOND(EST)= 0.153E-01 EST/TRUE= 0.107E+01
  3  (NRM RESID)/(NRM E)= 0.134E-14  RCOND(EST)= 0.145E-01 EST/TRUE= 0.535E+00
  4  (NRM RESID)/(NRM E)= 0.128E-14  RCOND(EST)= 0.499E-01 EST/TRUE= 0.849E+00
  5  (NRM RESID)/(NRM E)= 0.229E-13  RCOND(EST)= 0.650E-02 EST/TRUE= 0.762E+00

 M =  2   N =  6
  1  (NRM RESID)/(NRM E)= 0.164E-14  RCOND(EST)= 0.361E-01 EST/TRUE= 0.862E+00
  2  (NRM RESID)/(NRM E)= 0.592E-14  RCOND(EST)= 0.234E-01 EST/TRUE= 0.618E+00
  3  (NRM RESID)/(NRM E)= 0.245E-13  RCOND(EST)= 0.347E-02 EST/TRUE= 0.986E+00
  4  (NRM RESID)/(NRM E)= 0.392E-14  RCOND(EST)= 0.421E-01 EST/TRUE= 0.114E+01
  5  (NRM RESID)/(NRM E)= 0.714E-14  RCOND(EST)= 0.219E-01 EST/TRUE= 0.174E+01

 M =  2   N =  7
  1  (NRM RESID)/(NRM E)= 0.374E-14  RCOND(EST)= 0.169E-01 EST/TRUE= 0.863E+00
  2  (NRM RESID)/(NRM E)= 0.378E-14  RCOND(EST)= 0.279E-01 EST/TRUE= 0.828E+00
  3  (NRM RESID)/(NRM E)= 0.381E-14  RCOND(EST)= 0.649E-01 EST/TRUE= 0.194E+01
  4  (NRM RESID)/(NRM E)= 0.738E-14  RCOND(EST)= 0.580E-02 EST/TRUE= 0.126E+01
  5  (NRM RESID)/(NRM E)= 0.184E-13  RCOND(EST)= 0.380E-02 EST/TRUE= 0.373E+00

 M =  2   N =  8
  1  (NRM RESID)/(NRM E)= 0.402E-14  RCOND(EST)= 0.241E-01 EST/TRUE= 0.809E+00
  2  (NRM RESID)/(NRM E)= 0.209E-14  RCOND(EST)= 0.219E-01 EST/TRUE= 0.834E+00
  3  (NRM RESID)/(NRM E)= 0.108E-13  RCOND(EST)= 0.208E-02 EST/TRUE= 0.721E+00
  4  (NRM RESID)/(NRM E)= 0.222E-13  RCOND(EST)= 0.244E-02 EST/TRUE= 0.680E+00
  5  (NRM RESID)/(NRM E)= 0.436E-14  RCOND(EST)= 0.274E-01 EST/TRUE= 0.129E+01

 M =  3   N =  1
  1  (NRM RESID)/(NRM E)= 0.223E-14  RCOND(EST)= 0.568E-01 EST/TRUE= 0.998E+00
  2  (NRM RESID)/(NRM E)= 0.161E-15  RCOND(EST)= 0.200E+00 EST/TRUE= 0.532E+00
  3  (NRM RESID)/(NRM E)= 0.140E-15  RCOND(EST)= 0.158E+00 EST/TRUE= 0.556E+00
  4  (NRM RESID)/(NRM E)= 0.278E-15  RCOND(EST)= 0.631E-01 EST/TRUE= 0.663E+00
  5  (NRM RESID)/(NRM E)= 0.533E-15  RCOND(EST)= 0.147E+00 EST/TRUE= 0.672E+00

 M =  3   N =  2
  1  (NRM RESID)/(NRM E)= 0.698E-15  RCOND(EST)= 0.316E-01 EST/TRUE= 0.596E+00
  2  (NRM RESID)/(NRM E)= 0.151E-14  RCOND(EST)= 0.344E-01 EST/TRUE= 0.569E+00
  3  (NRM RESID)/(NRM E)= 0.121E-14  RCOND(EST)= 0.453E-01 EST/TRUE= 0.403E+00
  4  (NRM RESID)/(NRM E)= 0.685E-15  RCOND(EST)= 0.425E-01 EST/TRUE= 0.590E+00
  5  (NRM RESID)/(NRM E)= 0.724E-15  RCOND(EST)= 0.507E-01 EST/TRUE= 0.725E+00

 M =  3   N =  3
  1  (NRM RESID)/(NRM E)= 0.227E-14  RCOND(EST)= 0.129E-01 EST/TRUE= 0.678E+00
  2  (NRM RESID)/(NRM E)= 0.302E-14  RCOND(EST)= 0.150E-01 EST/TRUE= 0.759E+00
  3  (NRM RESID)/(NRM E)= 0.266E-14  RCOND(EST)= 0.405E-02 EST/TRUE= 0.544E+00
  4  (NRM RESID)/(NRM E)= 0.102E-14  RCOND(EST)= 0.475E-01 EST/TRUE= 0.694E+00
  5  (NRM RESID)/(NRM E)= 0.283E-14  RCOND(EST)= 0.634E-02 EST/TRUE= 0.347E+00

 M =  3   N =  4
  1  (NRM RESID)/(NRM E)= 0.160E-14  RCOND(EST)= 0.432E-01 EST/TRUE= 0.110E+01
  2  (NRM RESID)/(NRM E)= 0.239E-14  RCOND(EST)= 0.116E-01 EST/TRUE= 0.993E+00
  3  (NRM RESID)/(NRM E)= 0.265E-14  RCOND(EST)= 0.653E-02 EST/TRUE= 0.421E+00
  4  (NRM RESID)/(NRM E)= 0.420E-14  RCOND(EST)= 0.547E-01 EST/TRUE= 0.150E+01
  5  (NRM RESID)/(NRM E)= 0.715E-14  RCOND(EST)= 0.787E-02 EST/TRUE= 0.873E+00

 M =  3   N =  5
  1  (NRM RESID)/(NRM E)= 0.967E-14  RCOND(EST)= 0.634E-02 EST/TRUE= 0.604E+00
  2  (NRM RESID)/(NRM E)= 0.316E-14  RCOND(EST)= 0.981E-02 EST/TRUE= 0.539E+00
  3  (NRM RESID)/(NRM E)= 0.399E-14  RCOND(EST)= 0.367E-02 EST/TRUE= 0.512E+00
  4  (NRM RESID)/(NRM E)= 0.817E-14  RCOND(EST)= 0.832E-02 EST/TRUE= 0.431E+00
  5  (NRM RESID)/(NRM E)= 0.621E-14  RCOND(EST)= 0.119E-01 EST/TRUE= 0.187E+01

 M =  3   N =  6
  1  (NRM RESID)/(NRM E)= 0.117E-13  RCOND(EST)= 0.301E-02 EST/TRUE= 0.790E+00
  2  (NRM RESID)/(NRM E)= 0.142E-14  RCOND(EST)= 0.259E-01 EST/TRUE= 0.581E+00
  3  (NRM RESID)/(NRM E)= 0.225E-14  RCOND(EST)= 0.486E-01 EST/TRUE= 0.112E+01
  4  (NRM RESID)/(NRM E)= 0.701E-14  RCOND(EST)= 0.156E-01 EST/TRUE= 0.150E+01
  5  (NRM RESID)/(NRM E)= 0.190E-14  RCOND(EST)= 0.501E-01 EST/TRUE= 0.922E+00

 M =  3   N =  7
  1  (NRM RESID)/(NRM E)= 0.605E-14  RCOND(EST)= 0.453E-02 EST/TRUE= 0.816E+00
  2  (NRM RESID)/(NRM E)= 0.235E-14  RCOND(EST)= 0.192E-01 EST/TRUE= 0.103E+01
  3  (NRM RESID)/(NRM E)= 0.108E-13  RCOND(EST)= 0.245E-02 EST/TRUE= 0.632E+00
  4  (NRM RESID)/(NRM E)= 0.187E-13  RCOND(EST)= 0.139E-02 EST/TRUE= 0.639E+00
  5  (NRM RESID)/(NRM E)= 0.161E-14  RCOND(EST)= 0.804E-02 EST/TRUE= 0.623E+00

 M =  3   N =  8
  1  (NRM RESID)/(NRM E)= 0.241E-14  RCOND(EST)= 0.821E-02 EST/TRUE= 0.514E+00
  2  (NRM RESID)/(NRM E)= 0.156E-13  RCOND(EST)= 0.314E-02 EST/TRUE= 0.795E+00
  3  (NRM RESID)/(NRM E)= 0.613E-14  RCOND(EST)= 0.277E-02 EST/TRUE= 0.550E+00
  4  (NRM RESID)/(NRM E)= 0.132E-13  RCOND(EST)= 0.216E-02 EST/TRUE= 0.376E+00
  5  (NRM RESID)/(NRM E)= 0.311E-14  RCOND(EST)= 0.183E-01 EST/TRUE= 0.110E+01

 M =  4   N =  1
  1  (NRM RESID)/(NRM E)= 0.645E-15  RCOND(EST)= 0.385E-01 EST/TRUE= 0.474E+00
  2  (NRM RESID)/(NRM E)= 0.311E-14  RCOND(EST)= 0.111E-01 EST/TRUE= 0.126E+01
  3  (NRM RESID)/(NRM E)= 0.105E-14  RCOND(EST)= 0.815E-01 EST/TRUE= 0.632E+00
  4  (NRM RESID)/(NRM E)= 0.769E-15  RCOND(EST)= 0.131E+00 EST/TRUE= 0.808E+00
  5  (NRM RESID)/(NRM E)= 0.138E-13  RCOND(EST)= 0.391E-02 EST/TRUE= 0.682E+00

 M =  4   N =  2
  1  (NRM RESID)/(NRM E)= 0.393E-13  RCOND(EST)= 0.521E-03 EST/TRUE= 0.349E+00
  2  (NRM RESID)/(NRM E)= 0.896E-15  RCOND(EST)= 0.461E-01 EST/TRUE= 0.483E+00
  3  (NRM RESID)/(NRM E)= 0.769E-15  RCOND(EST)= 0.443E-01 EST/TRUE= 0.515E+00
  4  (NRM RESID)/(NRM E)= 0.443E-15  RCOND(EST)= 0.460E-01 EST/TRUE= 0.643E+00
  5  (NRM RESID)/(NRM E)= 0.194E-13  RCOND(EST)= 0.119E-02 EST/TRUE= 0.430E+00

 M =  4   N =  3
  1  (NRM RESID)/(NRM E)= 0.668E-14  RCOND(EST)= 0.127E-02 EST/TRUE= 0.105E+01
  2  (NRM RESID)/(NRM E)= 0.103E-13  RCOND(EST)= 0.129E-02 EST/TRUE= 0.288E+00
  3  (NRM RESID)/(NRM E)= 0.113E-14  RCOND(EST)= 0.239E-01 EST/TRUE= 0.406E+00
  4  (NRM RESID)/(NRM E)= 0.784E-15  RCOND(EST)= 0.261E-01 EST/TRUE= 0.938E+00
  5  (NRM RESID)/(NRM E)= 0.248E-14  RCOND(EST)= 0.116E-01 EST/TRUE= 0.430E+00

 M =  4   N =  4
  1  (NRM RESID)/(NRM E)= 0.812E-14  RCOND(EST)= 0.290E-02 EST/TRUE= 0.338E+00
  2  (NRM RESID)/(NRM E)= 0.304E-14  RCOND(EST)= 0.295E-02 EST/TRUE= 0.770E+00
  3  (NRM RESID)/(NRM E)= 0.578E-14  RCOND(EST)= 0.181E-01 EST/TRUE= 0.990E+00
  4  (NRM RESID)/(NRM E)= 0.163E-14  RCOND(EST)= 0.249E-01 EST/TRUE= 0.482E+00
  5  (NRM RESID)/(NRM E)= 0.621E-14  RCOND(EST)= 0.138E-02 EST/TRUE= 0.604E+00

 M =  4   N =  5
  1  (NRM RESID)/(NRM E)= 0.523E-14  RCOND(EST)= 0.141E-02 EST/TRUE= 0.328E+00
  2  (NRM RESID)/(NRM E)= 0.206E-14  RCOND(EST)= 0.569E-02 EST/TRUE= 0.421E+00
  3  (NRM RESID)/(NRM E)= 0.212E-14  RCOND(EST)= 0.230E-01 EST/TRUE= 0.842E+00
  4  (NRM RESID)/(NRM E)= 0.194E-14  RCOND(EST)= 0.233E-01 EST/TRUE= 0.108E+01
  5  (NRM RESID)/(NRM E)= 0.392E-14  RCOND(EST)= 0.117E-01 EST/TRUE= 0.114E+01

 M =  4   N =  6
  1  (NRM RESID)/(NRM E)= 0.146E-12  RCOND(EST)= 0.108E-03 EST/TRUE= 0.686E+00
  2  (NRM RESID)/(NRM E)= 0.365E-14  RCOND(EST)= 0.144E-01 EST/TRUE= 0.100E+01
  3  (NRM RESID)/(NRM E)= 0.564E-13  RCOND(EST)= 0.764E-04 EST/TRUE= 0.274E+00
  4  (NRM RESID)/(NRM E)= 0.403E-14  RCOND(EST)= 0.111E-01 EST/TRUE= 0.111E+01
  5  (NRM RESID)/(NRM E)= 0.496E-14  RCOND(EST)= 0.260E-01 EST/TRUE= 0.590E+00

 M =  4   N =  7
  1  (NRM RESID)/(NRM E)= 0.420E-13  RCOND(EST)= 0.988E-03 EST/TRUE= 0.496E+00
  2  (NRM RESID)/(NRM E)= 0.134E-13  RCOND(EST)= 0.220E-02 EST/TRUE= 0.102E+01
  3  (NRM RESID)/(NRM E)= 0.550E-14  RCOND(EST)= 0.343E-02 EST/TRUE= 0.564E+00
  4  (NRM RESID)/(NRM E)= 0.122E-13  RCOND(EST)= 0.141E-02 EST/TRUE= 0.327E+00
  5  (NRM RESID)/(NRM E)= 0.618E-14  RCOND(EST)= 0.710E-02 EST/TRUE= 0.875E+00

 M =  4   N =  8
  1  (NRM RESID)/(NRM E)= 0.500E-13  RCOND(EST)= 0.164E-02 EST/TRUE= 0.876E+00
  2  (NRM RESID)/(NRM E)= 0.569E-14  RCOND(EST)= 0.298E-02 EST/TRUE= 0.607E+00
  3  (NRM RESID)/(NRM E)= 0.474E-13  RCOND(EST)= 0.266E-03 EST/TRUE= 0.625E+00
  4  (NRM RESID)/(NRM E)= 0.520E-12  RCOND(EST)= 0.185E-03 EST/TRUE= 0.158E+01
  5  (NRM RESID)/(NRM E)= 0.364E-13  RCOND(EST)= 0.541E-03 EST/TRUE= 0.599E+00

 M =  5   N =  1
  1  (NRM RESID)/(NRM E)= 0.133E-14  RCOND(EST)= 0.769E-01 EST/TRUE= 0.996E+00
  2  (NRM RESID)/(NRM E)= 0.569E-15  RCOND(EST)= 0.186E+00 EST/TRUE= 0.635E+00
  3  (NRM RESID)/(NRM E)= 0.668E-15  RCOND(EST)= 0.616E-01 EST/TRUE= 0.663E+00
  4  (NRM RESID)/(NRM E)= 0.137E-14  RCOND(EST)= 0.372E-01 EST/TRUE= 0.634E+00
  5  (NRM RESID)/(NRM E)= 0.382E-15  RCOND(EST)= 0.153E+00 EST/TRUE= 0.561E+00

 M =  5   N =  2
  1  (NRM RESID)/(NRM E)= 0.123E-14  RCOND(EST)= 0.247E-02 EST/TRUE= 0.167E+01
  2  (NRM RESID)/(NRM E)= 0.482E-14  RCOND(EST)= 0.125E-01 EST/TRUE= 0.522E+00
  3  (NRM RESID)/(NRM E)= 0.657E-14  RCOND(EST)= 0.414E-02 EST/TRUE= 0.557E+00
  4  (NRM RESID)/(NRM E)= 0.204E-14  RCOND(EST)= 0.587E-02 EST/TRUE= 0.619E+00
  5  (NRM RESID)/(NRM E)= 0.523E-14  RCOND(EST)= 0.690E-02 EST/TRUE= 0.308E+00

 M =  5   N =  3
  1  (NRM RESID)/(NRM E)= 0.422E-14  RCOND(EST)= 0.469E-02 EST/TRUE= 0.563E+00
  2  (NRM RESID)/(NRM E)= 0.114E-13  RCOND(EST)= 0.473E-03 EST/TRUE= 0.820E+00
  3  (NRM RESID)/(NRM E)= 0.578E-14  RCOND(EST)= 0.452E-02 EST/TRUE= 0.409E+00
  4  (NRM RESID)/(NRM E)= 0.352E-14  RCOND(EST)= 0.131E-01 EST/TRUE= 0.619E+00
  5  (NRM RESID)/(NRM E)= 0.242E-13  RCOND(EST)= 0.111E-02 EST/TRUE= 0.949E+00

 M =  5   N =  4
  1  (NRM RESID)/(NRM E)= 0.283E-14  RCOND(EST)= 0.122E-01 EST/TRUE= 0.806E+00
  2  (NRM RESID)/(NRM E)= 0.280E-14  RCOND(EST)= 0.578E-02 EST/TRUE= 0.921E+00
  3  (NRM RESID)/(NRM E)= 0.634E-14  RCOND(EST)= 0.417E-02 EST/TRUE= 0.554E+00
  4  (NRM RESID)/(NRM E)= 0.445E-12  RCOND(EST)= 0.605E-04 EST/TRUE= 0.582E+00
  5  (NRM RESID)/(NRM E)= 0.125E-13  RCOND(EST)= 0.263E-02 EST/TRUE= 0.643E+00

 M =  5   N =  5
  1  (NRM RESID)/(NRM E)= 0.416E-14  RCOND(EST)= 0.651E-02 EST/TRUE= 0.561E+00
  2  (NRM RESID)/(NRM E)= 0.359E-14  RCOND(EST)= 0.167E-01 EST/TRUE= 0.760E+00
  3  (NRM RESID)/(NRM E)= 0.102E-13  RCOND(EST)= 0.739E-02 EST/TRUE= 0.492E+00
  4  (NRM RESID)/(NRM E)= 0.978E-14  RCOND(EST)= 0.978E-02 EST/TRUE= 0.788E+00
  5  (NRM RESID)/(NRM E)= 0.569E-14  RCOND(EST)= 0.141E-01 EST/TRUE= 0.110E+01

 M =  5   N =  6
  1  (NRM RESID)/(NRM E)= 0.298E-14  RCOND(EST)= 0.736E-02 EST/TRUE= 0.602E+00
  2  (NRM RESID)/(NRM E)= 0.307E-14  RCOND(EST)= 0.185E-02 EST/TRUE= 0.306E+00
  3  (NRM RESID)/(NRM E)= 0.293E-14  RCOND(EST)= 0.413E-02 EST/TRUE= 0.327E+00
  4  (NRM RESID)/(NRM E)= 0.294E-13  RCOND(EST)= 0.890E-03 EST/TRUE= 0.102E+01
  5  (NRM RESID)/(NRM E)= 0.552E-14  RCOND(EST)= 0.433E-02 EST/TRUE= 0.480E+00

 M =  5   N =  7
  1  (NRM RESID)/(NRM E)= 0.144E-13  RCOND(EST)= 0.933E-03 EST/TRUE= 0.519E+00
  2  (NRM RESID)/(NRM E)= 0.681E-14  RCOND(EST)= 0.809E-03 EST/TRUE= 0.131E+01
  3  (NRM RESID)/(NRM E)= 0.470E-13  RCOND(EST)= 0.938E-03 EST/TRUE= 0.737E+00
  4  (NRM RESID)/(NRM E)= 0.242E-13  RCOND(EST)= 0.299E-02 EST/TRUE= 0.489E+00
  5  (NRM RESID)/(NRM E)= 0.128E-13  RCOND(EST)= 0.809E-03 EST/TRUE= 0.124E+01

 M =  5   N =  8
  1  (NRM RESID)/(NRM E)= 0.111E-13  RCOND(EST)= 0.235E-02 EST/TRUE= 0.387E+00
  2  (NRM RESID)/(NRM E)= 0.714E-14  RCOND(EST)= 0.359E-02 EST/TRUE= 0.583E+00
  3  (NRM RESID)/(NRM E)= 0.371E-13  RCOND(EST)= 0.151E-02 EST/TRUE= 0.681E+00
  4  (NRM RESID)/(NRM E)= 0.418E-13  RCOND(EST)= 0.835E-03 EST/TRUE= 0.360E+00
  5  (NRM RESID)/(NRM E)= 0.831E-14  RCOND(EST)= 0.138E-01 EST/TRUE= 0.556E+00

 M =  6   N =  1
  1  (NRM RESID)/(NRM E)= 0.855E-15  RCOND(EST)= 0.406E-01 EST/TRUE= 0.623E+00
  2  (NRM RESID)/(NRM E)= 0.314E-14  RCOND(EST)= 0.175E-01 EST/TRUE= 0.786E+00
  3  (NRM RESID)/(NRM E)= 0.881E-15  RCOND(EST)= 0.610E-01 EST/TRUE= 0.521E+00
  4  (NRM RESID)/(NRM E)= 0.191E-13  RCOND(EST)= 0.380E-02 EST/TRUE= 0.942E+00
  5  (NRM RESID)/(NRM E)= 0.786E-14  RCOND(EST)= 0.101E-01 EST/TRUE= 0.599E+00

 M =  6   N =  2
  1  (NRM RESID)/(NRM E)= 0.910E-14  RCOND(EST)= 0.227E-02 EST/TRUE= 0.510E+00
  2  (NRM RESID)/(NRM E)= 0.145E-14  RCOND(EST)= 0.185E-01 EST/TRUE= 0.380E+00
  3  (NRM RESID)/(NRM E)= 0.273E-14  RCOND(EST)= 0.210E-02 EST/TRUE= 0.426E+00
  4  (NRM RESID)/(NRM E)= 0.162E-14  RCOND(EST)= 0.460E-02 EST/TRUE= 0.490E+00
  5  (NRM RESID)/(NRM E)= 0.217E-13  RCOND(EST)= 0.107E-02 EST/TRUE= 0.304E+00

 M =  6   N =  3
  1  (NRM RESID)/(NRM E)= 0.144E-13  RCOND(EST)= 0.101E-02 EST/TRUE= 0.402E+00
  2  (NRM RESID)/(NRM E)= 0.285E-14  RCOND(EST)= 0.986E-02 EST/TRUE= 0.626E+00
  3  (NRM RESID)/(NRM E)= 0.159E-14  RCOND(EST)= 0.540E-02 EST/TRUE= 0.347E+00
  4  (NRM RESID)/(NRM E)= 0.397E-13  RCOND(EST)= 0.861E-03 EST/TRUE= 0.359E+00
  5  (NRM RESID)/(NRM E)= 0.812E-14  RCOND(EST)= 0.127E-01 EST/TRUE= 0.567E+00

 M =  6   N =  4
  1  (NRM RESID)/(NRM E)= 0.295E-13  RCOND(EST)= 0.303E-03 EST/TRUE= 0.532E+00
  2  (NRM RESID)/(NRM E)= 0.148E-13  RCOND(EST)= 0.320E-02 EST/TRUE= 0.454E+00
  3  (NRM RESID)/(NRM E)= 0.803E-14  RCOND(EST)= 0.207E-02 EST/TRUE= 0.540E+00
  4  (NRM RESID)/(NRM E)= 0.224E-14  RCOND(EST)= 0.135E-01 EST/TRUE= 0.584E+00
  5  (NRM RESID)/(NRM E)= 0.659E-14  RCOND(EST)= 0.154E-02 EST/TRUE= 0.812E+00

 M =  6   N =  5
  1  (NRM RESID)/(NRM E)= 0.116E-13  RCOND(EST)= 0.374E-02 EST/TRUE= 0.994E+00
  2  (NRM RESID)/(NRM E)= 0.105E-13  RCOND(EST)= 0.308E-02 EST/TRUE= 0.544E+00
  3  (NRM RESID)/(NRM E)= 0.890E-13  RCOND(EST)= 0.246E-03 EST/TRUE= 0.426E+00
  4  (NRM RESID)/(NRM E)= 0.637E-14  RCOND(EST)= 0.105E-01 EST/TRUE= 0.784E+00
  5  (NRM RESID)/(NRM E)= 0.203E-13  RCOND(EST)= 0.156E-02 EST/TRUE= 0.864E+00

 M =  6   N =  6
  1  (NRM RESID)/(NRM E)= 0.602E-14  RCOND(EST)= 0.99