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309 lines
8.3 KiB
309 lines
8.3 KiB
2 years ago
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*> \brief \b ZUNT03
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZUNT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
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* RWORK, RESULT, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER*( * ) RC
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* INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N
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* DOUBLE PRECISION RESULT
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 U( LDU, * ), V( LDV, * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZUNT03 compares two unitary matrices U and V to see if their
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*> corresponding rows or columns span the same spaces. The rows are
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*> checked if RC = 'R', and the columns are checked if RC = 'C'.
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*>
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*> RESULT is the maximum of
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*>
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*> | V*V' - I | / ( MV ulp ), if RC = 'R', or
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*>
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*> | V'*V - I | / ( MV ulp ), if RC = 'C',
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*>
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*> and the maximum over rows (or columns) 1 to K of
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*>
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*> | U(i) - S*V(i) |/ ( N ulp )
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*>
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*> where abs(S) = 1 (chosen to minimize the expression), U(i) is the
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*> i-th row (column) of U, and V(i) is the i-th row (column) of V.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] RC
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*> \verbatim
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*> RC is CHARACTER*1
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*> If RC = 'R' the rows of U and V are to be compared.
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*> If RC = 'C' the columns of U and V are to be compared.
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*> \endverbatim
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*>
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*> \param[in] MU
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*> \verbatim
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*> MU is INTEGER
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*> The number of rows of U if RC = 'R', and the number of
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*> columns if RC = 'C'. If MU = 0 ZUNT03 does nothing.
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*> MU must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] MV
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*> \verbatim
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*> MV is INTEGER
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*> The number of rows of V if RC = 'R', and the number of
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*> columns if RC = 'C'. If MV = 0 ZUNT03 does nothing.
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*> MV must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> If RC = 'R', the number of columns in the matrices U and V,
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*> and if RC = 'C', the number of rows in U and V. If N = 0
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*> ZUNT03 does nothing. N must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of rows or columns of U and V to compare.
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*> 0 <= K <= max(MU,MV).
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*> \endverbatim
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*>
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*> \param[in] U
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*> \verbatim
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*> U is COMPLEX*16 array, dimension (LDU,N)
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*> The first matrix to compare. If RC = 'R', U is MU by N, and
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*> if RC = 'C', U is N by MU.
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*> \endverbatim
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*>
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*> \param[in] LDU
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*> \verbatim
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*> LDU is INTEGER
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*> The leading dimension of U. If RC = 'R', LDU >= max(1,MU),
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*> and if RC = 'C', LDU >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] V
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*> \verbatim
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*> V is COMPLEX*16 array, dimension (LDV,N)
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*> The second matrix to compare. If RC = 'R', V is MV by N, and
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*> if RC = 'C', V is N by MV.
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*> \endverbatim
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*>
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*> \param[in] LDV
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*> \verbatim
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*> LDV is INTEGER
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*> The leading dimension of V. If RC = 'R', LDV >= max(1,MV),
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*> and if RC = 'C', LDV >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK. For best performance, LWORK
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*> should be at least N*N if RC = 'C' or M*M if RC = 'R', but
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*> the tests will be done even if LWORK is 0.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (max(MV,N))
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is DOUBLE PRECISION
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*> The value computed by the test described above. RESULT is
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*> limited to 1/ulp to avoid overflow.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> 0 indicates a successful exit
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*> -k indicates the k-th parameter had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16_eig
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*
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* =====================================================================
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SUBROUTINE ZUNT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
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$ RWORK, RESULT, INFO )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER*( * ) RC
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INTEGER INFO, K, LDU, LDV, LWORK, MU, MV, N
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DOUBLE PRECISION RESULT
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 U( LDU, * ), V( LDV, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, IRC, J, LMX
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DOUBLE PRECISION RES1, RES2, ULP
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COMPLEX*16 S, SU, SV
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER IZAMAX
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DOUBLE PRECISION DLAMCH
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EXTERNAL LSAME, IZAMAX, DLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DCMPLX, MAX, MIN
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZUNT01
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* ..
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* .. Executable Statements ..
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*
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* Check inputs
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*
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INFO = 0
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IF( LSAME( RC, 'R' ) ) THEN
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IRC = 0
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ELSE IF( LSAME( RC, 'C' ) ) THEN
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IRC = 1
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ELSE
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IRC = -1
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END IF
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IF( IRC.EQ.-1 ) THEN
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INFO = -1
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ELSE IF( MU.LT.0 ) THEN
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INFO = -2
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ELSE IF( MV.LT.0 ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( K.LT.0 .OR. K.GT.MAX( MU, MV ) ) THEN
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INFO = -5
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ELSE IF( ( IRC.EQ.0 .AND. LDU.LT.MAX( 1, MU ) ) .OR.
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$ ( IRC.EQ.1 .AND. LDU.LT.MAX( 1, N ) ) ) THEN
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INFO = -7
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ELSE IF( ( IRC.EQ.0 .AND. LDV.LT.MAX( 1, MV ) ) .OR.
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$ ( IRC.EQ.1 .AND. LDV.LT.MAX( 1, N ) ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZUNT03', -INFO )
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RETURN
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END IF
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*
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* Initialize result
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*
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RESULT = ZERO
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IF( MU.EQ.0 .OR. MV.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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* Machine constants
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*
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ULP = DLAMCH( 'Precision' )
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*
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IF( IRC.EQ.0 ) THEN
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*
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* Compare rows
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*
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RES1 = ZERO
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DO 20 I = 1, K
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LMX = IZAMAX( N, U( I, 1 ), LDU )
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IF( V( I, LMX ).EQ.DCMPLX( ZERO ) ) THEN
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SV = ONE
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ELSE
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SV = ABS( V( I, LMX ) ) / V( I, LMX )
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END IF
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IF( U( I, LMX ).EQ.DCMPLX( ZERO ) ) THEN
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SU = ONE
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ELSE
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SU = ABS( U( I, LMX ) ) / U( I, LMX )
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END IF
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S = SV / SU
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DO 10 J = 1, N
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RES1 = MAX( RES1, ABS( U( I, J )-S*V( I, J ) ) )
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10 CONTINUE
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20 CONTINUE
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RES1 = RES1 / ( DBLE( N )*ULP )
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*
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* Compute orthogonality of rows of V.
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*
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CALL ZUNT01( 'Rows', MV, N, V, LDV, WORK, LWORK, RWORK, RES2 )
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*
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ELSE
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*
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* Compare columns
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*
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RES1 = ZERO
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DO 40 I = 1, K
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LMX = IZAMAX( N, U( 1, I ), 1 )
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IF( V( LMX, I ).EQ.DCMPLX( ZERO ) ) THEN
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SV = ONE
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ELSE
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SV = ABS( V( LMX, I ) ) / V( LMX, I )
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END IF
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IF( U( LMX, I ).EQ.DCMPLX( ZERO ) ) THEN
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SU = ONE
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ELSE
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SU = ABS( U( LMX, I ) ) / U( LMX, I )
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END IF
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S = SV / SU
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DO 30 J = 1, N
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RES1 = MAX( RES1, ABS( U( J, I )-S*V( J, I ) ) )
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30 CONTINUE
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40 CONTINUE
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RES1 = RES1 / ( DBLE( N )*ULP )
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*
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* Compute orthogonality of columns of V.
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*
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CALL ZUNT01( 'Columns', N, MV, V, LDV, WORK, LWORK, RWORK,
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$ RES2 )
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END IF
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*
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RESULT = MIN( MAX( RES1, RES2 ), ONE / ULP )
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RETURN
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*
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* End of ZUNT03
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*
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END
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