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SUBROUTINE ZGET22( TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W,
$ WORK, RWORK, RESULT )
*
* -- LAPACK test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER TRANSA, TRANSE, TRANSW
INTEGER LDA, LDE, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION RESULT( 2 ), RWORK( * )
COMPLEX*16 A( LDA, * ), E( LDE, * ), W( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* ZGET22 does an eigenvector check.
*
* The basic test is:
*
* RESULT(1) = | A E - E W | / ( |A| |E| ulp )
*
* using the 1-norm. It also tests the normalization of E:
*
* RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
* j
*
* where E(j) is the j-th eigenvector, and m-norm is the max-norm of a
* vector. The max-norm of a complex n-vector x in this case is the
* maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n.
*
* Arguments
* ==========
*
* TRANSA (input) CHARACTER*1
* Specifies whether or not A is transposed.
* = 'N': No transpose
* = 'T': Transpose
* = 'C': Conjugate transpose
*
* TRANSE (input) CHARACTER*1
* Specifies whether or not E is transposed.
* = 'N': No transpose, eigenvectors are in columns of E
* = 'T': Transpose, eigenvectors are in rows of E
* = 'C': Conjugate transpose, eigenvectors are in rows of E
*
* TRANSW (input) CHARACTER*1
* Specifies whether or not W is transposed.
* = 'N': No transpose
* = 'T': Transpose, same as TRANSW = 'N'
* = 'C': Conjugate transpose, use -WI(j) instead of WI(j)
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input) COMPLEX*16 array, dimension (LDA,N)
* The matrix whose eigenvectors are in E.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* E (input) COMPLEX*16 array, dimension (LDE,N)
* The matrix of eigenvectors. If TRANSE = 'N', the eigenvectors
* are stored in the columns of E, if TRANSE = 'T' or 'C', the
* eigenvectors are stored in the rows of E.
*
* LDE (input) INTEGER
* The leading dimension of the array E. LDE >= max(1,N).
*
* W (input) COMPLEX*16 array, dimension (N)
* The eigenvalues of A.
*
* WORK (workspace) COMPLEX*16 array, dimension (N*N)
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RESULT (output) DOUBLE PRECISION array, dimension (2)
* RESULT(1) = | A E - E W | / ( |A| |E| ulp )
* RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
* j
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
CHARACTER NORMA, NORME
INTEGER ITRNSE, ITRNSW, J, JCOL, JOFF, JROW, JVEC
DOUBLE PRECISION ANORM, ENORM, ENRMAX, ENRMIN, ERRNRM, TEMP1,
$ ULP, UNFL
COMPLEX*16 WTEMP
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANGE
EXTERNAL LSAME, DLAMCH, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL ZGEMM, ZLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN
* ..
* .. Executable Statements ..
*
* Initialize RESULT (in case N=0)
*
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
IF( N.LE.0 )
$ RETURN
*
UNFL = DLAMCH( 'Safe minimum' )
ULP = DLAMCH( 'Precision' )
*
ITRNSE = 0
ITRNSW = 0
NORMA = 'O'
NORME = 'O'
*
IF( LSAME( TRANSA, 'T' ) .OR. LSAME( TRANSA, 'C' ) ) THEN
NORMA = 'I'
END IF
*
IF( LSAME( TRANSE, 'T' ) ) THEN
ITRNSE = 1
NORME = 'I'
ELSE IF( LSAME( TRANSE, 'C' ) ) THEN
ITRNSE = 2
NORME = 'I'
END IF
*
IF( LSAME( TRANSW, 'C' ) ) THEN
ITRNSW = 1
END IF
*
* Normalization of E:
*
ENRMIN = ONE / ULP
ENRMAX = ZERO
IF( ITRNSE.EQ.0 ) THEN
DO 20 JVEC = 1, N
TEMP1 = ZERO
DO 10 J = 1, N
TEMP1 = MAX( TEMP1, ABS( DBLE( E( J, JVEC ) ) )+
$ ABS( DIMAG( E( J, JVEC ) ) ) )
10 CONTINUE
ENRMIN = MIN( ENRMIN, TEMP1 )
ENRMAX = MAX( ENRMAX, TEMP1 )
20 CONTINUE
ELSE
DO 30 JVEC = 1, N
RWORK( JVEC ) = ZERO
30 CONTINUE
*
DO 50 J = 1, N
DO 40 JVEC = 1, N
RWORK( JVEC ) = MAX( RWORK( JVEC ),
$ ABS( DBLE( E( JVEC, J ) ) )+
$ ABS( DIMAG( E( JVEC, J ) ) ) )
40 CONTINUE
50 CONTINUE
*
DO 60 JVEC = 1, N
ENRMIN = MIN( ENRMIN, RWORK( JVEC ) )
ENRMAX = MAX( ENRMAX, RWORK( JVEC ) )
60 CONTINUE
END IF
*
* Norm of A:
*
ANORM = MAX( ZLANGE( NORMA, N, N, A, LDA, RWORK ), UNFL )
*
* Norm of E:
*
ENORM = MAX( ZLANGE( NORME, N, N, E, LDE, RWORK ), ULP )
*
* Norm of error:
*
* Error = AE - EW
*
CALL ZLASET( 'Full', N, N, CZERO, CZERO, WORK, N )
*
JOFF = 0
DO 100 JCOL = 1, N
IF( ITRNSW.EQ.0 ) THEN
WTEMP = W( JCOL )
ELSE
WTEMP = DCONJG( W( JCOL ) )
END IF
*
IF( ITRNSE.EQ.0 ) THEN
DO 70 JROW = 1, N
WORK( JOFF+JROW ) = E( JROW, JCOL )*WTEMP
70 CONTINUE
ELSE IF( ITRNSE.EQ.1 ) THEN
DO 80 JROW = 1, N
WORK( JOFF+JROW ) = E( JCOL, JROW )*WTEMP
80 CONTINUE
ELSE
DO 90 JROW = 1, N
WORK( JOFF+JROW ) = DCONJG( E( JCOL, JROW ) )*WTEMP
90 CONTINUE
END IF
JOFF = JOFF + N
100 CONTINUE
*
CALL ZGEMM( TRANSA, TRANSE, N, N, N, CONE, A, LDA, E, LDE, -CONE,
$ WORK, N )
*
ERRNRM = ZLANGE( 'One', N, N, WORK, N, RWORK ) / ENORM
*
* Compute RESULT(1) (avoiding under/overflow)
*
IF( ANORM.GT.ERRNRM ) THEN
RESULT( 1 ) = ( ERRNRM / ANORM ) / ULP
ELSE
IF( ANORM.LT.ONE ) THEN
RESULT( 1 ) = ( MIN( ERRNRM, ANORM ) / ANORM ) / ULP
ELSE
RESULT( 1 ) = MIN( ERRNRM / ANORM, ONE ) / ULP
END IF
END IF
*
* Compute RESULT(2) : the normalization error in E.
*
RESULT( 2 ) = MAX( ABS( ENRMAX-ONE ), ABS( ENRMIN-ONE ) ) /
$ ( DBLE( N )*ULP )
*
RETURN
*
* End of ZGET22
*
END
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