*> \brief \b ZCHKHB * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZCHKHB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED, * THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK, * LWORK, RWORK, RESULT, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES, * $ NWDTHS * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER ISEED( 4 ), KK( * ), NN( * ) * DOUBLE PRECISION RESULT( * ), RWORK( * ), SD( * ), SE( * ) * COMPLEX*16 A( LDA, * ), U( LDU, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZCHKHB tests the reduction of a Hermitian band matrix to tridiagonal *> from, used with the Hermitian eigenvalue problem. *> *> ZHBTRD factors a Hermitian band matrix A as U S U* , where * means *> conjugate transpose, S is symmetric tridiagonal, and U is unitary. *> ZHBTRD can use either just the lower or just the upper triangle *> of A; ZCHKHB checks both cases. *> *> When ZCHKHB is called, a number of matrix "sizes" ("n's"), a number *> of bandwidths ("k's"), and a number of matrix "types" are *> specified. For each size ("n"), each bandwidth ("k") less than or *> equal to "n", and each type of matrix, one matrix will be generated *> and used to test the hermitian banded reduction routine. For each *> matrix, a number of tests will be performed: *> *> (1) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with *> UPLO='U' *> *> (2) | I - UU* | / ( n ulp ) *> *> (3) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with *> UPLO='L' *> *> (4) | I - UU* | / ( n ulp ) *> *> The "sizes" are specified by an array NN(1:NSIZES); the value of *> each element NN(j) specifies one size. *> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. *> Currently, the list of possible types is: *> *> (1) The zero matrix. *> (2) The identity matrix. *> *> (3) A diagonal matrix with evenly spaced entries *> 1, ..., ULP and random signs. *> (ULP = (first number larger than 1) - 1 ) *> (4) A diagonal matrix with geometrically spaced entries *> 1, ..., ULP and random signs. *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP *> and random signs. *> *> (6) Same as (4), but multiplied by SQRT( overflow threshold ) *> (7) Same as (4), but multiplied by SQRT( underflow threshold ) *> *> (8) A matrix of the form U* D U, where U is unitary and *> D has evenly spaced entries 1, ..., ULP with random signs *> on the diagonal. *> *> (9) A matrix of the form U* D U, where U is unitary and *> D has geometrically spaced entries 1, ..., ULP with random *> signs on the diagonal. *> *> (10) A matrix of the form U* D U, where U is unitary and *> D has "clustered" entries 1, ULP,..., ULP with random *> signs on the diagonal. *> *> (11) Same as (8), but multiplied by SQRT( overflow threshold ) *> (12) Same as (8), but multiplied by SQRT( underflow threshold ) *> *> (13) Hermitian matrix with random entries chosen from (-1,1). *> (14) Same as (13), but multiplied by SQRT( overflow threshold ) *> (15) Same as (13), but multiplied by SQRT( underflow threshold ) *> \endverbatim * * Arguments: * ========== * *> \param[in] NSIZES *> \verbatim *> NSIZES is INTEGER *> The number of sizes of matrices to use. If it is zero, *> ZCHKHB does nothing. It must be at least zero. *> \endverbatim *> *> \param[in] NN *> \verbatim *> NN is INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> \endverbatim *> *> \param[in] NWDTHS *> \verbatim *> NWDTHS is INTEGER *> The number of bandwidths to use. If it is zero, *> ZCHKHB does nothing. It must be at least zero. *> \endverbatim *> *> \param[in] KK *> \verbatim *> KK is INTEGER array, dimension (NWDTHS) *> An array containing the bandwidths to be used for the band *> matrices. The values must be at least zero. *> \endverbatim *> *> \param[in] NTYPES *> \verbatim *> NTYPES is INTEGER *> The number of elements in DOTYPE. If it is zero, ZCHKHB *> does nothing. It must be at least zero. If it is MAXTYP+1 *> and NSIZES is 1, then an additional type, MAXTYP+1 is *> defined, which is to use whatever matrix is in A. This *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> \endverbatim *> *> \param[in] DOTYPE *> \verbatim *> DOTYPE is LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. *> If NTYPES is smaller than the maximum number of types *> defined (PARAMETER MAXTYP), then types NTYPES+1 through *> MAXTYP will not be generated. If NTYPES is larger *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> \endverbatim *> *> \param[in,out] ISEED *> \verbatim *> ISEED is INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; *> if not they will be reduced mod 4096. Also, ISEED(4) must *> be odd. The random number generator uses a linear *> congruential sequence limited to small integers, and so *> should produce machine independent random numbers. The *> values of ISEED are changed on exit, and can be used in the *> next call to ZCHKHB to continue the same random number *> sequence. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is DOUBLE PRECISION *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error *> is scaled to be O(1), so THRESH should be a reasonably *> small multiple of 1, e.g., 10 or 100. In particular, *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> \endverbatim *> *> \param[in] NOUNIT *> \verbatim *> NOUNIT is INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension *> (LDA, max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of A. It must be at least 2 (not 1!) *> and at least max( KK )+1. *> \endverbatim *> *> \param[out] SD *> \verbatim *> SD is DOUBLE PRECISION array, dimension (max(NN)) *> Used to hold the diagonal of the tridiagonal matrix computed *> by ZHBTRD. *> \endverbatim *> *> \param[out] SE *> \verbatim *> SE is DOUBLE PRECISION array, dimension (max(NN)) *> Used to hold the off-diagonal of the tridiagonal matrix *> computed by ZHBTRD. *> \endverbatim *> *> \param[out] U *> \verbatim *> U is COMPLEX*16 array, dimension (LDU, max(NN)) *> Used to hold the unitary matrix computed by ZHBTRD. *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> The leading dimension of U. It must be at least 1 *> and at least max( NN ). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The number of entries in WORK. This must be at least *> max( LDA+1, max(NN)+1 )*max(NN). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (4) *> The values computed by the tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. *> *>----------------------------------------------------------------------- *> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NTEST The number of tests performed, or which can *> be performed so far, for the current matrix. *> NTESTT The total number of tests performed so far. *> NMAX Largest value in NN. *> NMATS The number of matrices generated so far. *> NERRS The number of tests which have exceeded THRESH *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. *> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix *> generator for type "j". *> KMAGN(j) The order of magnitude ( O(1), *> O(overflow^(1/2) ), O(underflow^(1/2) ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2011 * *> \ingroup complex16_eig * * ===================================================================== SUBROUTINE ZCHKHB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED, $ THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK, $ LWORK, RWORK, RESULT, INFO ) * * -- LAPACK test routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2011 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES, $ NWDTHS DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), KK( * ), NN( * ) DOUBLE PRECISION RESULT( * ), RWORK( * ), SD( * ), SE( * ) COMPLEX*16 A( LDA, * ), U( LDU, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) DOUBLE PRECISION ZERO, ONE, TWO, TEN PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, $ TEN = 10.0D+0 ) DOUBLE PRECISION HALF PARAMETER ( HALF = ONE / TWO ) INTEGER MAXTYP PARAMETER ( MAXTYP = 15 ) * .. * .. Local Scalars .. LOGICAL BADNN, BADNNB INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE, $ JTYPE, JWIDTH, K, KMAX, MTYPES, N, NERRS, $ NMATS, NMAX, NTEST, NTESTT DOUBLE PRECISION ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, $ TEMP1, ULP, ULPINV, UNFL * .. * .. Local Arrays .. INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ), $ KMODE( MAXTYP ), KTYPE( MAXTYP ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DLASUM, XERBLA, ZHBT21, ZHBTRD, ZLACPY, ZLASET, $ ZLATMR, ZLATMS * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCONJG, MAX, MIN, SQRT * .. * .. Data statements .. DATA KTYPE / 1, 2, 5*4, 5*5, 3*8 / DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1, $ 2, 3 / DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0, $ 0, 0 / * .. * .. Executable Statements .. * * Check for errors * NTESTT = 0 INFO = 0 * * Important constants * BADNN = .FALSE. NMAX = 1 DO 10 J = 1, NSIZES NMAX = MAX( NMAX, NN( J ) ) IF( NN( J ).LT.0 ) $ BADNN = .TRUE. 10 CONTINUE * BADNNB = .FALSE. KMAX = 0 DO 20 J = 1, NSIZES KMAX = MAX( KMAX, KK( J ) ) IF( KK( J ).LT.0 ) $ BADNNB = .TRUE. 20 CONTINUE KMAX = MIN( NMAX-1, KMAX ) * * Check for errors * IF( NSIZES.LT.0 ) THEN INFO = -1 ELSE IF( BADNN ) THEN INFO = -2 ELSE IF( NWDTHS.LT.0 ) THEN INFO = -3 ELSE IF( BADNNB ) THEN INFO = -4 ELSE IF( NTYPES.LT.0 ) THEN INFO = -5 ELSE IF( LDA.LT.KMAX+1 ) THEN INFO = -11 ELSE IF( LDU.LT.NMAX ) THEN INFO = -15 ELSE IF( ( MAX( LDA, NMAX )+1 )*NMAX.GT.LWORK ) THEN INFO = -17 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZCHKHB', -INFO ) RETURN END IF * * Quick return if possible * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 .OR. NWDTHS.EQ.0 ) $ RETURN * * More Important constants * UNFL = DLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' ) ULPINV = ONE / ULP RTUNFL = SQRT( UNFL ) RTOVFL = SQRT( OVFL ) * * Loop over sizes, types * NERRS = 0 NMATS = 0 * DO 190 JSIZE = 1, NSIZES N = NN( JSIZE ) ANINV = ONE / DBLE( MAX( 1, N ) ) * DO 180 JWIDTH = 1, NWDTHS K = KK( JWIDTH ) IF( K.GT.N ) $ GO TO 180 K = MAX( 0, MIN( N-1, K ) ) * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 170 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 170 NMATS = NMATS + 1 NTEST = 0 * DO 30 J = 1, 4 IOLDSD( J ) = ISEED( J ) 30 CONTINUE * * Compute "A". * Store as "Upper"; later, we will copy to other format. * * Control parameters: * * KMAGN KMODE KTYPE * =1 O(1) clustered 1 zero * =2 large clustered 2 identity * =3 small exponential (none) * =4 arithmetic diagonal, (w/ eigenvalues) * =5 random log hermitian, w/ eigenvalues * =6 random (none) * =7 random diagonal * =8 random hermitian * =9 positive definite * =10 diagonally dominant tridiagonal * IF( MTYPES.GT.MAXTYP ) $ GO TO 100 * ITYPE = KTYPE( JTYPE ) IMODE = KMODE( JTYPE ) * * Compute norm * GO TO ( 40, 50, 60 )KMAGN( JTYPE ) * 40 CONTINUE ANORM = ONE GO TO 70 * 50 CONTINUE ANORM = ( RTOVFL*ULP )*ANINV GO TO 70 * 60 CONTINUE ANORM = RTUNFL*N*ULPINV GO TO 70 * 70 CONTINUE * CALL ZLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA ) IINFO = 0 IF( JTYPE.LE.15 ) THEN COND = ULPINV ELSE COND = ULPINV*ANINV / TEN END IF * * Special Matrices -- Identity & Jordan block * * Zero * IF( ITYPE.EQ.1 ) THEN IINFO = 0 * ELSE IF( ITYPE.EQ.2 ) THEN * * Identity * DO 80 JCOL = 1, N A( K+1, JCOL ) = ANORM 80 CONTINUE * ELSE IF( ITYPE.EQ.4 ) THEN * * Diagonal Matrix, [Eigen]values Specified * CALL ZLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, $ COND, ANORM, 0, 0, 'Q', A( K+1, 1 ), LDA, $ WORK, IINFO ) * ELSE IF( ITYPE.EQ.5 ) THEN * * Hermitian, eigenvalues specified * CALL ZLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, $ COND, ANORM, K, K, 'Q', A, LDA, WORK, $ IINFO ) * ELSE IF( ITYPE.EQ.7 ) THEN * * Diagonal, random eigenvalues * CALL ZLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE, $ CONE, 'T', 'N', WORK( N+1 ), 1, ONE, $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0, $ ZERO, ANORM, 'Q', A( K+1, 1 ), LDA, $ IDUMMA, IINFO ) * ELSE IF( ITYPE.EQ.8 ) THEN * * Hermitian, random eigenvalues * CALL ZLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE, $ CONE, 'T', 'N', WORK( N+1 ), 1, ONE, $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, K, K, $ ZERO, ANORM, 'Q', A, LDA, IDUMMA, IINFO ) * ELSE IF( ITYPE.EQ.9 ) THEN * * Positive definite, eigenvalues specified. * CALL ZLATMS( N, N, 'S', ISEED, 'P', RWORK, IMODE, $ COND, ANORM, K, K, 'Q', A, LDA, $ WORK( N+1 ), IINFO ) * ELSE IF( ITYPE.EQ.10 ) THEN * * Positive definite tridiagonal, eigenvalues specified. * IF( N.GT.1 ) $ K = MAX( 1, K ) CALL ZLATMS( N, N, 'S', ISEED, 'P', RWORK, IMODE, $ COND, ANORM, 1, 1, 'Q', A( K, 1 ), LDA, $ WORK, IINFO ) DO 90 I = 2, N TEMP1 = ABS( A( K, I ) ) / $ SQRT( ABS( A( K+1, I-1 )*A( K+1, I ) ) ) IF( TEMP1.GT.HALF ) THEN A( K, I ) = HALF*SQRT( ABS( A( K+1, $ I-1 )*A( K+1, I ) ) ) END IF 90 CONTINUE * ELSE * IINFO = 1 END IF * IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF * 100 CONTINUE * * Call ZHBTRD to compute S and U from upper triangle. * CALL ZLACPY( ' ', K+1, N, A, LDA, WORK, LDA ) * NTEST = 1 CALL ZHBTRD( 'V', 'U', N, K, WORK, LDA, SD, SE, U, LDU, $ WORK( LDA*N+1 ), IINFO ) * IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'ZHBTRD(U)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) THEN RETURN ELSE RESULT( 1 ) = ULPINV GO TO 150 END IF END IF * * Do tests 1 and 2 * CALL ZHBT21( 'Upper', N, K, 1, A, LDA, SD, SE, U, LDU, $ WORK, RWORK, RESULT( 1 ) ) * * Convert A from Upper-Triangle-Only storage to * Lower-Triangle-Only storage. * DO 120 JC = 1, N DO 110 JR = 0, MIN( K, N-JC ) A( JR+1, JC ) = DCONJG( A( K+1-JR, JC+JR ) ) 110 CONTINUE 120 CONTINUE DO 140 JC = N + 1 - K, N DO 130 JR = MIN( K, N-JC ) + 1, K A( JR+1, JC ) = ZERO 130 CONTINUE 140 CONTINUE * * Call ZHBTRD to compute S and U from lower triangle * CALL ZLACPY( ' ', K+1, N, A, LDA, WORK, LDA ) * NTEST = 3 CALL ZHBTRD( 'V', 'L', N, K, WORK, LDA, SD, SE, U, LDU, $ WORK( LDA*N+1 ), IINFO ) * IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'ZHBTRD(L)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) IF( IINFO.LT.0 ) THEN RETURN ELSE RESULT( 3 ) = ULPINV GO TO 150 END IF END IF NTEST = 4 * * Do tests 3 and 4 * CALL ZHBT21( 'Lower', N, K, 1, A, LDA, SD, SE, U, LDU, $ WORK, RWORK, RESULT( 3 ) ) * * End of Loop -- Check for RESULT(j) > THRESH * 150 CONTINUE NTESTT = NTESTT + NTEST * * Print out tests which fail. * DO 160 JR = 1, NTEST IF( RESULT( JR ).GE.THRESH ) THEN * * If this is the first test to fail, * print a header to the data file. * IF( NERRS.EQ.0 ) THEN WRITE( NOUNIT, FMT = 9998 )'ZHB' WRITE( NOUNIT, FMT = 9997 ) WRITE( NOUNIT, FMT = 9996 ) WRITE( NOUNIT, FMT = 9995 )'Hermitian' WRITE( NOUNIT, FMT = 9994 )'unitary', '*', $ 'conjugate transpose', ( '*', J = 1, 4 ) END IF NERRS = NERRS + 1 WRITE( NOUNIT, FMT = 9993 )N, K, IOLDSD, JTYPE, $ JR, RESULT( JR ) END IF 160 CONTINUE * 170 CONTINUE 180 CONTINUE 190 CONTINUE * * Summary * CALL DLASUM( 'ZHB', NOUNIT, NERRS, NTESTT ) RETURN * 9999 FORMAT( ' ZCHKHB: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) 9998 FORMAT( / 1X, A3, $ ' -- Complex Hermitian Banded Tridiagonal Reduction Routines' $ ) 9997 FORMAT( ' Matrix types (see DCHK23 for details): ' ) * 9996 FORMAT( / ' Special Matrices:', $ / ' 1=Zero matrix. ', $ ' 5=Diagonal: clustered entries.', $ / ' 2=Identity matrix. ', $ ' 6=Diagonal: large, evenly spaced.', $ / ' 3=Diagonal: evenly spaced entries. ', $ ' 7=Diagonal: small, evenly spaced.', $ / ' 4=Diagonal: geometr. spaced entries.' ) 9995 FORMAT( ' Dense ', A, ' Banded Matrices:', $ / ' 8=Evenly spaced eigenvals. ', $ ' 12=Small, evenly spaced eigenvals.', $ / ' 9=Geometrically spaced eigenvals. ', $ ' 13=Matrix with random O(1) entries.', $ / ' 10=Clustered eigenvalues. ', $ ' 14=Matrix with large random entries.', $ / ' 11=Large, evenly spaced eigenvals. ', $ ' 15=Matrix with small random entries.' ) * 9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', A, ',', $ / 20X, A, ' means ', A, '.', / ' UPLO=''U'':', $ / ' 1= | A - U S U', A1, ' | / ( |A| n ulp ) ', $ ' 2= | I - U U', A1, ' | / ( n ulp )', / ' UPLO=''L'':', $ / ' 3= | A - U S U', A1, ' | / ( |A| n ulp ) ', $ ' 4= | I - U U', A1, ' | / ( n ulp )' ) 9993 FORMAT( ' N=', I5, ', K=', I4, ', seed=', 4( I4, ',' ), ' type ', $ I2, ', test(', I2, ')=', G10.3 ) * * End of ZCHKHB * END