You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
262 lines
8.2 KiB
262 lines
8.2 KiB
2 years ago
|
*> \brief \b CHET22
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE CHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
|
||
|
|
* V, LDV, TAU, WORK, RWORK, RESULT )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* CHARACTER UPLO
|
||
|
|
* INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
|
||
|
|
* COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
|
||
|
|
* $ V( LDV, * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> CHET22 generally checks a decomposition of the form
|
||
|
|
*>
|
||
|
|
*> A U = U S
|
||
|
|
*>
|
||
|
|
*> where A is complex Hermitian, the columns of U are orthonormal,
|
||
|
|
*> and S is diagonal (if KBAND=0) or symmetric tridiagonal (if
|
||
|
|
*> KBAND=1). If ITYPE=1, then U is represented as a dense matrix,
|
||
|
|
*> otherwise the U is expressed as a product of Householder
|
||
|
|
*> transformations, whose vectors are stored in the array "V" and
|
||
|
|
*> whose scaling constants are in "TAU"; we shall use the letter
|
||
|
|
*> "V" to refer to the product of Householder transformations
|
||
|
|
*> (which should be equal to U).
|
||
|
|
*>
|
||
|
|
*> Specifically, if ITYPE=1, then:
|
||
|
|
*>
|
||
|
|
*> RESULT(1) = | U**H A U - S | / ( |A| m ulp ) and
|
||
|
|
*> RESULT(2) = | I - U**H U | / ( m ulp )
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \verbatim
|
||
|
|
*> ITYPE INTEGER
|
||
|
|
*> Specifies the type of tests to be performed.
|
||
|
|
*> 1: U expressed as a dense orthogonal matrix:
|
||
|
|
*> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
|
||
|
|
*> RESULT(2) = | I - U U**H | / ( n ulp )
|
||
|
|
*>
|
||
|
|
*> UPLO CHARACTER
|
||
|
|
*> If UPLO='U', the upper triangle of A will be used and the
|
||
|
|
*> (strictly) lower triangle will not be referenced. If
|
||
|
|
*> UPLO='L', the lower triangle of A will be used and the
|
||
|
|
*> (strictly) upper triangle will not be referenced.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> N INTEGER
|
||
|
|
*> The size of the matrix. If it is zero, CHET22 does nothing.
|
||
|
|
*> It must be at least zero.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> M INTEGER
|
||
|
|
*> The number of columns of U. If it is zero, CHET22 does
|
||
|
|
*> nothing. It must be at least zero.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> KBAND INTEGER
|
||
|
|
*> The bandwidth of the matrix. It may only be zero or one.
|
||
|
|
*> If zero, then S is diagonal, and E is not referenced. If
|
||
|
|
*> one, then S is symmetric tri-diagonal.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> A COMPLEX array, dimension (LDA , N)
|
||
|
|
*> The original (unfactored) matrix. It is assumed to be
|
||
|
|
*> symmetric, and only the upper (UPLO='U') or only the lower
|
||
|
|
*> (UPLO='L') will be referenced.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> LDA INTEGER
|
||
|
|
*> The leading dimension of A. It must be at least 1
|
||
|
|
*> and at least N.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> D REAL array, dimension (N)
|
||
|
|
*> The diagonal of the (symmetric tri-) diagonal matrix.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> E REAL array, dimension (N)
|
||
|
|
*> The off-diagonal of the (symmetric tri-) diagonal matrix.
|
||
|
|
*> E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc.
|
||
|
|
*> Not referenced if KBAND=0.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> U COMPLEX array, dimension (LDU, N)
|
||
|
|
*> If ITYPE=1, this contains the orthogonal matrix in
|
||
|
|
*> the decomposition, expressed as a dense matrix.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> LDU INTEGER
|
||
|
|
*> The leading dimension of U. LDU must be at least N and
|
||
|
|
*> at least 1.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> V COMPLEX array, dimension (LDV, N)
|
||
|
|
*> If ITYPE=2 or 3, the lower triangle of this array contains
|
||
|
|
*> the Householder vectors used to describe the orthogonal
|
||
|
|
*> matrix in the decomposition. If ITYPE=1, then it is not
|
||
|
|
*> referenced.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> LDV INTEGER
|
||
|
|
*> The leading dimension of V. LDV must be at least N and
|
||
|
|
*> at least 1.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> TAU COMPLEX array, dimension (N)
|
||
|
|
*> If ITYPE >= 2, then TAU(j) is the scalar factor of
|
||
|
|
*> v(j) v(j)**H in the Householder transformation H(j) of
|
||
|
|
*> the product U = H(1)...H(n-2)
|
||
|
|
*> If ITYPE < 2, then TAU is not referenced.
|
||
|
|
*> Not modified.
|
||
|
|
*>
|
||
|
|
*> WORK COMPLEX array, dimension (2*N**2)
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> RWORK REAL array, dimension (N)
|
||
|
|
*> Workspace.
|
||
|
|
*> Modified.
|
||
|
|
*>
|
||
|
|
*> RESULT REAL array, dimension (2)
|
||
|
|
*> The values computed by the two tests described above. The
|
||
|
|
*> values are currently limited to 1/ulp, to avoid overflow.
|
||
|
|
*> RESULT(1) is always modified. RESULT(2) is modified only
|
||
|
|
*> if LDU is at least N.
|
||
|
|
*> Modified.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup complex_eig
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE CHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU,
|
||
|
|
$ V, LDV, TAU, WORK, RWORK, RESULT )
|
||
|
|
*
|
||
|
|
* -- LAPACK test routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
CHARACTER UPLO
|
||
|
|
INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
|
||
|
|
COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
|
||
|
|
$ V( LDV, * ), WORK( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
REAL ZERO, ONE
|
||
|
|
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
|
||
|
|
COMPLEX CZERO, CONE
|
||
|
|
PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ),
|
||
|
|
$ CONE = ( 1.0E0, 0.0E0 ) )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
INTEGER J, JJ, JJ1, JJ2, NN, NNP1
|
||
|
|
REAL ANORM, ULP, UNFL, WNORM
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
REAL CLANHE, SLAMCH
|
||
|
|
EXTERNAL CLANHE, SLAMCH
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL CGEMM, CHEMM
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC MAX, MIN, REAL
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
RESULT( 1 ) = ZERO
|
||
|
|
RESULT( 2 ) = ZERO
|
||
|
|
IF( N.LE.0 .OR. M.LE.0 )
|
||
|
|
$ RETURN
|
||
|
|
*
|
||
|
|
UNFL = SLAMCH( 'Safe minimum' )
|
||
|
|
ULP = SLAMCH( 'Precision' )
|
||
|
|
*
|
||
|
|
* Do Test 1
|
||
|
|
*
|
||
|
|
* Norm of A:
|
||
|
|
*
|
||
|
|
ANORM = MAX( CLANHE( '1', UPLO, N, A, LDA, RWORK ), UNFL )
|
||
|
|
*
|
||
|
|
* Compute error matrix:
|
||
|
|
*
|
||
|
|
* ITYPE=1: error = U**H A U - S
|
||
|
|
*
|
||
|
|
CALL CHEMM( 'L', UPLO, N, M, CONE, A, LDA, U, LDU, CZERO, WORK,
|
||
|
|
$ N )
|
||
|
|
NN = N*N
|
||
|
|
NNP1 = NN + 1
|
||
|
|
CALL CGEMM( 'C', 'N', M, M, N, CONE, U, LDU, WORK, N, CZERO,
|
||
|
|
$ WORK( NNP1 ), N )
|
||
|
|
DO 10 J = 1, M
|
||
|
|
JJ = NN + ( J-1 )*N + J
|
||
|
|
WORK( JJ ) = WORK( JJ ) - D( J )
|
||
|
|
10 CONTINUE
|
||
|
|
IF( KBAND.EQ.1 .AND. N.GT.1 ) THEN
|
||
|
|
DO 20 J = 2, M
|
||
|
|
JJ1 = NN + ( J-1 )*N + J - 1
|
||
|
|
JJ2 = NN + ( J-2 )*N + J
|
||
|
|
WORK( JJ1 ) = WORK( JJ1 ) - E( J-1 )
|
||
|
|
WORK( JJ2 ) = WORK( JJ2 ) - E( J-1 )
|
||
|
|
20 CONTINUE
|
||
|
|
END IF
|
||
|
|
WNORM = CLANHE( '1', UPLO, M, WORK( NNP1 ), N, RWORK )
|
||
|
|
*
|
||
|
|
IF( ANORM.GT.WNORM ) THEN
|
||
|
|
RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP )
|
||
|
|
ELSE
|
||
|
|
IF( ANORM.LT.ONE ) THEN
|
||
|
|
RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP )
|
||
|
|
ELSE
|
||
|
|
RESULT( 1 ) = MIN( WNORM / ANORM, REAL( M ) ) / ( M*ULP )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do Test 2
|
||
|
|
*
|
||
|
|
* Compute U**H U - I
|
||
|
|
*
|
||
|
|
IF( ITYPE.EQ.1 )
|
||
|
|
$ CALL CUNT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, RWORK,
|
||
|
|
$ RESULT( 2 ) )
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of CHET22
|
||
|
|
*
|
||
|
|
END
|