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SUBROUTINE PZGET22( TRANSA, TRANSE, TRANSW, N, A, DESCA, E, DESCE,
$ W, WORK, DESCW, RWORK, RESULT )
*
* -- ScaLAPACK testing routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* August 14, 2001
*
* .. Scalar Arguments ..
CHARACTER TRANSA, TRANSE, TRANSW
INTEGER N
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCE( * ), DESCW( * )
DOUBLE PRECISION RESULT( 2 ), RWORK( * )
COMPLEX*16 A( * ), E( * ), W( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PZGET22 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 (*)
* The matrix whose eigenvectors are in E.
*
* DESCA (input) INTEGER array, dimension(*)
*
* E (input) COMPLEX*16 array, dimension (*)
* 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.
*
* DESCE (input) INTEGER array, dimension(*)
*
* W (input) COMPLEX*16 array, dimension (N)
* The eigenvalues of A.
*
* WORK (workspace) COMPLEX*16 array, dimension (*)
* DESCW (input) INTEGER array, dimension(*)
*
* 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
* Further Details
* ===============
*
* Contributed by Mark Fahey, June, 2000
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
$ MB_, NB_, RSRC_, CSRC_, LLD_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
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 ICOL, II, IROW, ITRNSE, ITRNSW, J, JCOL, JJ,
$ JROW, JVEC, LDA, LDE, LDW, MB, MYCOL, MYROW,
$ NB, NPCOL, NPROW, CONTXT, CA, CSRC, RA, RSRC
DOUBLE PRECISION ANORM, ENORM, ENRMAX, ENRMIN, ERRNRM, TEMP1,
$ ULP, UNFL
COMPLEX*16 CDUM, WTEMP
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION PDLAMCH, PZLANGE
EXTERNAL LSAME, PDLAMCH, PZLANGE
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DGAMN2D, DGAMX2D, INFOG2L,
$ PZAXPY, PZGEMM, PZLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function definitions ..
CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
* ..
* .. Executable Statements ..
*
* Initialize RESULT (in case N=0)
*
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
IF( N.LE.0 )
$ RETURN
*
CONTXT = DESCA( CTXT_ )
RSRC = DESCA( RSRC_ )
CSRC = DESCA( CSRC_ )
NB = DESCA( NB_ )
MB = DESCA( MB_ )
LDA = DESCA( LLD_ )
LDE = DESCE( LLD_ )
LDW = DESCW( LLD_ )
CALL BLACS_GRIDINFO( CONTXT, NPROW, NPCOL, MYROW, MYCOL )
*
UNFL = PDLAMCH( CONTXT, 'Safe minimum' )
ULP = PDLAMCH( CONTXT, '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
CALL INFOG2L( J, JVEC, DESCE, NPROW, NPCOL, MYROW, MYCOL,
$ IROW, ICOL, II, JJ )
IF( ( MYROW.EQ.II ) .AND. ( MYCOL.EQ.JJ ) ) THEN
TEMP1 = MAX( TEMP1, CABS1( E( ( ICOL-1 )*LDE+
$ IROW ) ) )
END IF
10 CONTINUE
IF( MYCOL.EQ.JJ ) THEN
CALL DGAMX2D( CONTXT, 'Col', ' ', 1, 1, TEMP1, 1, RA, CA,
$ -1, -1, -1 )
ENRMIN = MIN( ENRMIN, TEMP1 )
ENRMAX = MAX( ENRMAX, TEMP1 )
END IF
20 CONTINUE
CALL DGAMX2D( CONTXT, 'Row', ' ', 1, 1, ENRMAX, 1, RA, CA, -1,
$ -1, -1 )
CALL DGAMN2D( CONTXT, 'Row', ' ', 1, 1, ENRMIN, 1, RA, CA, -1,
$ -1, -1 )
ELSE
DO 40 J = 1, N
TEMP1 = ZERO
DO 30 JVEC = 1, N
CALL INFOG2L( J, JVEC, DESCE, NPROW, NPCOL, MYROW, MYCOL,
$ IROW, ICOL, II, JJ )
IF( ( MYROW.EQ.II ) .AND. ( MYCOL.EQ.JJ ) ) THEN
TEMP1 = MAX( TEMP1, CABS1( E( ( ICOL-1 )*LDE+
$ IROW ) ) )
END IF
30 CONTINUE
IF( MYROW.EQ.II ) THEN
CALL DGAMX2D( CONTXT, 'Row', ' ', 1, 1, TEMP1, 1, RA, CA,
$ -1, -1, -1 )
ENRMIN = MIN( ENRMIN, TEMP1 )
ENRMAX = MAX( ENRMAX, TEMP1 )
END IF
40 CONTINUE
CALL DGAMX2D( CONTXT, 'Row', ' ', 1, 1, ENRMAX, 1, RA, CA, -1,
$ -1, -1 )
CALL DGAMN2D( CONTXT, 'Row', ' ', 1, 1, ENRMIN, 1, RA, CA, -1,
$ -1, -1 )
END IF
*
* Norm of A:
*
ANORM = MAX( PZLANGE( NORMA, N, N, A, 1, 1, DESCA, RWORK ), UNFL )
*
* Norm of E:
*
ENORM = MAX( PZLANGE( NORME, N, N, E, 1, 1, DESCE, RWORK ), ULP )
*
* Norm of error:
*
* Error = AE - EW
*
CALL PZLASET( 'Full', N, N, CZERO, CZERO, WORK, 1, 1, DESCW )
*
DO 60 JCOL = 1, N
IF( ITRNSW.EQ.0 ) THEN
WTEMP = W( JCOL )
ELSE
WTEMP = DCONJG( W( JCOL ) )
END IF
*
IF( ITRNSE.EQ.0 ) THEN
CALL PZAXPY( N, WTEMP, E, 1, JCOL, DESCE, 1, WORK, 1, JCOL,
$ DESCW, 1 )
ELSE IF( ITRNSE.EQ.1 ) THEN
CALL PZAXPY( N, WTEMP, E, JCOL, 1, DESCE, N, WORK, 1, JCOL,
$ DESCW, 1 )
ELSE
CALL PZAXPY( N, DCONJG( WTEMP ), E, JCOL, 1, DESCE, N, WORK,
$ 1, JCOL, DESCW, 1 )
DO 50 JROW = 1, N
CALL INFOG2L( JROW, JCOL, DESCW, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF( ( MYROW.EQ.II ) .AND. ( MYCOL.EQ.JJ ) ) THEN
WORK( ( JCOL-1 )*LDW+JROW )
$ = DCONJG( WORK( ( JCOL-1 )*LDW+JROW ) )
END IF
50 CONTINUE
END IF
60 CONTINUE
*
CALL PZGEMM( TRANSA, TRANSE, N, N, N, CONE, A, 1, 1, DESCA, E, 1,
$ 1, DESCE, -CONE, WORK, 1, 1, DESCW )
*
ERRNRM = PZLANGE( 'One', N, N, WORK, 1, 1, DESCW, 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 PZGET22
*
END
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