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SUBROUTINE SCHKEQ( THRESH, NOUT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER NOUT
REAL THRESH
* ..
*
* Purpose
* =======
*
* SCHKEQ tests SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU
*
* Arguments
* =========
*
* THRESH (input) REAL
* Threshold for testing routines. Should be between 2 and 10.
*
* NOUT (input) INTEGER
* The unit number for output.
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE, TEN
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E+0, TEN = 1.0E1 )
INTEGER NSZ, NSZB
PARAMETER ( NSZ = 5, NSZB = 3*NSZ-2 )
INTEGER NSZP, NPOW
PARAMETER ( NSZP = ( NSZ*( NSZ+1 ) ) / 2,
$ NPOW = 2*NSZ+1 )
* ..
* .. Local Scalars ..
LOGICAL OK
CHARACTER*3 PATH
INTEGER I, INFO, J, KL, KU, M, N
REAL CCOND, EPS, NORM, RATIO, RCMAX, RCMIN, RCOND
* ..
* .. Local Arrays ..
REAL A( NSZ, NSZ ), AB( NSZB, NSZ ), AP( NSZP ),
$ C( NSZ ), POW( NPOW ), R( NSZ ), RESLTS( 5 ),
$ RPOW( NPOW )
* ..
* .. External Functions ..
REAL SLAMCH
EXTERNAL SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SGBEQU, SGEEQU, SPBEQU, SPOEQU, SPPEQU
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
* ..
* .. Executable Statements ..
*
PATH( 1:1 ) = 'Single precision'
PATH( 2:3 ) = 'EQ'
*
EPS = SLAMCH( 'P' )
DO 10 I = 1, 5
RESLTS( I ) = ZERO
10 CONTINUE
DO 20 I = 1, NPOW
POW( I ) = TEN**( I-1 )
RPOW( I ) = ONE / POW( I )
20 CONTINUE
*
* Test SGEEQU
*
DO 80 N = 0, NSZ
DO 70 M = 0, NSZ
*
DO 40 J = 1, NSZ
DO 30 I = 1, NSZ
IF( I.LE.M .AND. J.LE.N ) THEN
A( I, J ) = POW( I+J+1 )*( -1 )**( I+J )
ELSE
A( I, J ) = ZERO
END IF
30 CONTINUE
40 CONTINUE
*
CALL SGEEQU( M, N, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 1 ) = ONE
ELSE
IF( N.NE.0 .AND. M.NE.0 ) THEN
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( RCOND-RPOW( M ) ) / RPOW( M ) ) )
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( CCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( NORM-POW( N+M+1 ) ) / POW( N+M+
$ 1 ) ) )
DO 50 I = 1, M
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( R( I )-RPOW( I+N+1 ) ) /
$ RPOW( I+N+1 ) ) )
50 CONTINUE
DO 60 J = 1, N
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( C( J )-POW( N-J+1 ) ) /
$ POW( N-J+1 ) ) )
60 CONTINUE
END IF
END IF
*
70 CONTINUE
80 CONTINUE
*
* Test with zero rows and columns
*
DO 90 J = 1, NSZ
A( MAX( NSZ-1, 1 ), J ) = ZERO
90 CONTINUE
CALL SGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
IF( INFO.NE.MAX( NSZ-1, 1 ) )
$ RESLTS( 1 ) = ONE
*
DO 100 J = 1, NSZ
A( MAX( NSZ-1, 1 ), J ) = ONE
100 CONTINUE
DO 110 I = 1, NSZ
A( I, MAX( NSZ-1, 1 ) ) = ZERO
110 CONTINUE
CALL SGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
IF( INFO.NE.NSZ+MAX( NSZ-1, 1 ) )
$ RESLTS( 1 ) = ONE
RESLTS( 1 ) = RESLTS( 1 ) / EPS
*
* Test SGBEQU
*
DO 250 N = 0, NSZ
DO 240 M = 0, NSZ
DO 230 KL = 0, MAX( M-1, 0 )
DO 220 KU = 0, MAX( N-1, 0 )
*
DO 130 J = 1, NSZ
DO 120 I = 1, NSZB
AB( I, J ) = ZERO
120 CONTINUE
130 CONTINUE
DO 150 J = 1, N
DO 140 I = 1, M
IF( I.LE.MIN( M, J+KL ) .AND. I.GE.
$ MAX( 1, J-KU ) .AND. J.LE.N ) THEN
AB( KU+1+I-J, J ) = POW( I+J+1 )*
$ ( -1 )**( I+J )
END IF
140 CONTINUE
150 CONTINUE
*
CALL SGBEQU( M, N, KL, KU, AB, NSZB, R, C, RCOND,
$ CCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
IF( .NOT.( ( N+KL.LT.M .AND. INFO.EQ.N+KL+1 ) .OR.
$ ( M+KU.LT.N .AND. INFO.EQ.2*M+KU+1 ) ) ) THEN
RESLTS( 2 ) = ONE
END IF
ELSE
IF( N.NE.0 .AND. M.NE.0 ) THEN
*
RCMIN = R( 1 )
RCMAX = R( 1 )
DO 160 I = 1, M
RCMIN = MIN( RCMIN, R( I ) )
RCMAX = MAX( RCMAX, R( I ) )
160 CONTINUE
RATIO = RCMIN / RCMAX
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ( RCOND-RATIO ) / RATIO ) )
*
RCMIN = C( 1 )
RCMAX = C( 1 )
DO 170 J = 1, N
RCMIN = MIN( RCMIN, C( J ) )
RCMAX = MAX( RCMAX, C( J ) )
170 CONTINUE
RATIO = RCMIN / RCMAX
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ( CCOND-RATIO ) / RATIO ) )
*
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ( NORM-POW( N+M+1 ) ) /
$ POW( N+M+1 ) ) )
DO 190 I = 1, M
RCMAX = ZERO
DO 180 J = 1, N
IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN
RATIO = ABS( R( I )*POW( I+J+1 )*
$ C( J ) )
RCMAX = MAX( RCMAX, RATIO )
END IF
180 CONTINUE
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ONE-RCMAX ) )
190 CONTINUE
*
DO 210 J = 1, N
RCMAX = ZERO
DO 200 I = 1, M
IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN
RATIO = ABS( R( I )*POW( I+J+1 )*
$ C( J ) )
RCMAX = MAX( RCMAX, RATIO )
END IF
200 CONTINUE
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ONE-RCMAX ) )
210 CONTINUE
END IF
END IF
*
220 CONTINUE
230 CONTINUE
240 CONTINUE
250 CONTINUE
RESLTS( 2 ) = RESLTS( 2 ) / EPS
*
* Test SPOEQU
*
DO 290 N = 0, NSZ
*
DO 270 I = 1, NSZ
DO 260 J = 1, NSZ
IF( I.LE.N .AND. J.EQ.I ) THEN
A( I, J ) = POW( I+J+1 )*( -1 )**( I+J )
ELSE
A( I, J ) = ZERO
END IF
260 CONTINUE
270 CONTINUE
*
CALL SPOEQU( N, A, NSZ, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 3 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 3 ) = MAX( RESLTS( 3 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 3 ) = MAX( RESLTS( 3 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 280 I = 1, N
RESLTS( 3 ) = MAX( RESLTS( 3 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
$ 1 ) ) )
280 CONTINUE
END IF
END IF
290 CONTINUE
A( MAX( NSZ-1, 1 ), MAX( NSZ-1, 1 ) ) = -ONE
CALL SPOEQU( NSZ, A, NSZ, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( NSZ-1, 1 ) )
$ RESLTS( 3 ) = ONE
RESLTS( 3 ) = RESLTS( 3 ) / EPS
*
* Test SPPEQU
*
DO 360 N = 0, NSZ
*
* Upper triangular packed storage
*
DO 300 I = 1, ( N*( N+1 ) ) / 2
AP( I ) = ZERO
300 CONTINUE
DO 310 I = 1, N
AP( ( I*( I+1 ) ) / 2 ) = POW( 2*I+1 )
310 CONTINUE
*
CALL SPPEQU( 'U', N, AP, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 4 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 320 I = 1, N
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
$ 1 ) ) )
320 CONTINUE
END IF
END IF
*
* Lower triangular packed storage
*
DO 330 I = 1, ( N*( N+1 ) ) / 2
AP( I ) = ZERO
330 CONTINUE
J = 1
DO 340 I = 1, N
AP( J ) = POW( 2*I+1 )
J = J + ( N-I+1 )
340 CONTINUE
*
CALL SPPEQU( 'L', N, AP, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 4 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 350 I = 1, N
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
$ 1 ) ) )
350 CONTINUE
END IF
END IF
*
360 CONTINUE
I = ( NSZ*( NSZ+1 ) ) / 2 - 2
AP( I ) = -ONE
CALL SPPEQU( 'L', NSZ, AP, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( NSZ-1, 1 ) )
$ RESLTS( 4 ) = ONE
RESLTS( 4 ) = RESLTS( 4 ) / EPS
*
* Test SPBEQU
*
DO 460 N = 0, NSZ
DO 450 KL = 0, MAX( N-1, 0 )
*
* Test upper triangular storage
*
DO 380 J = 1, NSZ
DO 370 I = 1, NSZB
AB( I, J ) = ZERO
370 CONTINUE
380 CONTINUE
DO 390 J = 1, N
AB( KL+1, J ) = POW( 2*J+1 )
390 CONTINUE
*
CALL SPBEQU( 'U', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 5 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 400 I = 1, N
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) /
$ RPOW( I+1 ) ) )
400 CONTINUE
END IF
END IF
IF( N.NE.0 ) THEN
AB( KL+1, MAX( N-1, 1 ) ) = -ONE
CALL SPBEQU( 'U', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( N-1, 1 ) )
$ RESLTS( 5 ) = ONE
END IF
*
* Test lower triangular storage
*
DO 420 J = 1, NSZ
DO 410 I = 1, NSZB
AB( I, J ) = ZERO
410 CONTINUE
420 CONTINUE
DO 430 J = 1, N
AB( 1, J ) = POW( 2*J+1 )
430 CONTINUE
*
CALL SPBEQU( 'L', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 5 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 440 I = 1, N
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) /
$ RPOW( I+1 ) ) )
440 CONTINUE
END IF
END IF
IF( N.NE.0 ) THEN
AB( 1, MAX( N-1, 1 ) ) = -ONE
CALL SPBEQU( 'L', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( N-1, 1 ) )
$ RESLTS( 5 ) = ONE
END IF
450 CONTINUE
460 CONTINUE
RESLTS( 5 ) = RESLTS( 5 ) / EPS
OK = ( RESLTS( 1 ).LE.THRESH ) .AND.
$ ( RESLTS( 2 ).LE.THRESH ) .AND.
$ ( RESLTS( 3 ).LE.THRESH ) .AND.
$ ( RESLTS( 4 ).LE.THRESH ) .AND. ( RESLTS( 5 ).LE.THRESH )
WRITE( NOUT, FMT = * )
IF( OK ) THEN
WRITE( NOUT, FMT = 9999 )PATH
ELSE
IF( RESLTS( 1 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9998 )RESLTS( 1 ), THRESH
IF( RESLTS( 2 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9997 )RESLTS( 2 ), THRESH
IF( RESLTS( 3 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9996 )RESLTS( 3 ), THRESH
IF( RESLTS( 4 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9995 )RESLTS( 4 ), THRESH
IF( RESLTS( 5 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9994 )RESLTS( 5 ), THRESH
END IF
9999 FORMAT( 1X, 'All tests for ', A3,
$ ' routines passed the threshold' )
9998 FORMAT( ' SGEEQU failed test with value ', E10.3, ' exceeding',
$ ' threshold ', E10.3 )
9997 FORMAT( ' SGBEQU failed test with value ', E10.3, ' exceeding',
$ ' threshold ', E10.3 )
9996 FORMAT( ' SPOEQU failed test with value ', E10.3, ' exceeding',
$ ' threshold ', E10.3 )
9995 FORMAT( ' SPPEQU failed test with value ', E10.3, ' exceeding',
$ ' threshold ', E10.3 )
9994 FORMAT( ' SPBEQU failed test with value ', E10.3, ' exceeding',
$ ' threshold ', E10.3 )
RETURN
*
* End of SCHKEQ
*
END
|
