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*> \brief \b ZLATM3
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* COMPLEX*16 FUNCTION ZLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
* IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
* SPARSE )
*
* .. Scalar Arguments ..
*
* INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
* $ KU, M, N
* DOUBLE PRECISION SPARSE
* ..
*
* .. Array Arguments ..
*
* INTEGER ISEED( 4 ), IWORK( * )
* COMPLEX*16 D( * ), DL( * ), DR( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of
*> dimension (M, N) described by the other parameters. (ISUB,JSUB)
*> is the final position of the (I,J) entry after pivoting
*> according to IPVTNG and IWORK. ZLATM3 is called by the
*> ZLATMR routine in order to build random test matrices. No error
*> checking on parameters is done, because this routine is called in
*> a tight loop by ZLATMR which has already checked the parameters.
*>
*> Use of ZLATM3 differs from CLATM2 in the order in which the random
*> number generator is called to fill in random matrix entries.
*> With ZLATM2, the generator is called to fill in the pivoted matrix
*> columnwise. With ZLATM3, the generator is called to fill in the
*> matrix columnwise, after which it is pivoted. Thus, ZLATM3 can
*> be used to construct random matrices which differ only in their
*> order of rows and/or columns. ZLATM2 is used to construct band
*> matrices while avoiding calling the random number generator for
*> entries outside the band (and therefore generating random numbers
*> in different orders for different pivot orders).
*>
*> The matrix whose (ISUB,JSUB) entry is returned is constructed as
*> follows (this routine only computes one entry):
*>
*> If ISUB is outside (1..M) or JSUB is outside (1..N), return zero
*> (this is convenient for generating matrices in band format).
*>
*> Generate a matrix A with random entries of distribution IDIST.
*>
*> Set the diagonal to D.
*>
*> Grade the matrix, if desired, from the left (by DL) and/or
*> from the right (by DR or DL) as specified by IGRADE.
*>
*> Permute, if desired, the rows and/or columns as specified by
*> IPVTNG and IWORK.
*>
*> Band the matrix to have lower bandwidth KL and upper
*> bandwidth KU.
*>
*> Set random entries to zero as specified by SPARSE.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> Number of rows of matrix. Not modified.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> Number of columns of matrix. Not modified.
*> \endverbatim
*>
*> \param[in] I
*> \verbatim
*> I is INTEGER
*> Row of unpivoted entry to be returned. Not modified.
*> \endverbatim
*>
*> \param[in] J
*> \verbatim
*> J is INTEGER
*> Column of unpivoted entry to be returned. Not modified.
*> \endverbatim
*>
*> \param[in,out] ISUB
*> \verbatim
*> ISUB is INTEGER
*> Row of pivoted entry to be returned. Changed on exit.
*> \endverbatim
*>
*> \param[in,out] JSUB
*> \verbatim
*> JSUB is INTEGER
*> Column of pivoted entry to be returned. Changed on exit.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*> KL is INTEGER
*> Lower bandwidth. Not modified.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> Upper bandwidth. Not modified.
*> \endverbatim
*>
*> \param[in] IDIST
*> \verbatim
*> IDIST is INTEGER
*> On entry, IDIST specifies the type of distribution to be
*> used to generate a random matrix .
*> 1 => real and imaginary parts each UNIFORM( 0, 1 )
*> 2 => real and imaginary parts each UNIFORM( -1, 1 )
*> 3 => real and imaginary parts each NORMAL( 0, 1 )
*> 4 => complex number uniform in DISK( 0 , 1 )
*> Not modified.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> ISEED is INTEGER array of dimension ( 4 )
*> Seed for random number generator.
*> Changed on exit.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is COMPLEX*16 array of dimension ( MIN( I , J ) )
*> Diagonal entries of matrix. Not modified.
*> \endverbatim
*>
*> \param[in] IGRADE
*> \verbatim
*> IGRADE is INTEGER
*> Specifies grading of matrix as follows:
*> 0 => no grading
*> 1 => matrix premultiplied by diag( DL )
*> 2 => matrix postmultiplied by diag( DR )
*> 3 => matrix premultiplied by diag( DL ) and
*> postmultiplied by diag( DR )
*> 4 => matrix premultiplied by diag( DL ) and
*> postmultiplied by inv( diag( DL ) )
*> 5 => matrix premultiplied by diag( DL ) and
*> postmultiplied by diag( CONJG(DL) )
*> 6 => matrix premultiplied by diag( DL ) and
*> postmultiplied by diag( DL )
*> Not modified.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*> DL is COMPLEX*16 array ( I or J, as appropriate )
*> Left scale factors for grading matrix. Not modified.
*> \endverbatim
*>
*> \param[in] DR
*> \verbatim
*> DR is COMPLEX*16 array ( I or J, as appropriate )
*> Right scale factors for grading matrix. Not modified.
*> \endverbatim
*>
*> \param[in] IPVTNG
*> \verbatim
*> IPVTNG is INTEGER
*> On entry specifies pivoting permutations as follows:
*> 0 => none.
*> 1 => row pivoting.
*> 2 => column pivoting.
*> 3 => full pivoting, i.e., on both sides.
*> Not modified.
*> \endverbatim
*>
*> \param[in] IWORK
*> \verbatim
*> IWORK is INTEGER array ( I or J, as appropriate )
*> This array specifies the permutation used. The
*> row (or column) originally in position K is in
*> position IWORK( K ) after pivoting.
*> This differs from IWORK for ZLATM2. Not modified.
*> \endverbatim
*>
*> \param[in] SPARSE
*> \verbatim
*> SPARSE is DOUBLE PRECISION between 0. and 1.
*> On entry specifies the sparsity of the matrix
*> if sparse matrix is to be generated.
*> SPARSE should lie between 0 and 1.
*> A uniform ( 0, 1 ) random number x is generated and
*> compared to SPARSE; if x is larger the matrix entry
*> is unchanged and if x is smaller the entry is set
*> to zero. Thus on the average a fraction SPARSE of the
*> entries will be set to zero.
*> Not modified.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_matgen
*
* =====================================================================
COMPLEX*16 FUNCTION ZLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
$ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
$ SPARSE )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
*
INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
$ KU, M, N
DOUBLE PRECISION SPARSE
* ..
*
* .. Array Arguments ..
*
INTEGER ISEED( 4 ), IWORK( * )
COMPLEX*16 D( * ), DL( * ), DR( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
*
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
COMPLEX*16 CZERO
PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ) )
* ..
*
* .. Local Scalars ..
*
COMPLEX*16 CTEMP
* ..
*
* .. External Functions ..
*
DOUBLE PRECISION DLARAN
COMPLEX*16 ZLARND
EXTERNAL DLARAN, ZLARND
* ..
*
* .. Intrinsic Functions ..
*
INTRINSIC DCONJG
* ..
*
*-----------------------------------------------------------------------
*
* .. Executable Statements ..
*
*
* Check for I and J in range
*
IF( I.LT.1 .OR. I.GT.M .OR. J.LT.1 .OR. J.GT.N ) THEN
ISUB = I
JSUB = J
ZLATM3 = CZERO
RETURN
END IF
*
* Compute subscripts depending on IPVTNG
*
IF( IPVTNG.EQ.0 ) THEN
ISUB = I
JSUB = J
ELSE IF( IPVTNG.EQ.1 ) THEN
ISUB = IWORK( I )
JSUB = J
ELSE IF( IPVTNG.EQ.2 ) THEN
ISUB = I
JSUB = IWORK( J )
ELSE IF( IPVTNG.EQ.3 ) THEN
ISUB = IWORK( I )
JSUB = IWORK( J )
END IF
*
* Check for banding
*
IF( JSUB.GT.ISUB+KU .OR. JSUB.LT.ISUB-KL ) THEN
ZLATM3 = CZERO
RETURN
END IF
*
* Check for sparsity
*
IF( SPARSE.GT.ZERO ) THEN
IF( DLARAN( ISEED ).LT.SPARSE ) THEN
ZLATM3 = CZERO
RETURN
END IF
END IF
*
* Compute entry and grade it according to IGRADE
*
IF( I.EQ.J ) THEN
CTEMP = D( I )
ELSE
CTEMP = ZLARND( IDIST, ISEED )
END IF
IF( IGRADE.EQ.1 ) THEN
CTEMP = CTEMP*DL( I )
ELSE IF( IGRADE.EQ.2 ) THEN
CTEMP = CTEMP*DR( J )
ELSE IF( IGRADE.EQ.3 ) THEN
CTEMP = CTEMP*DL( I )*DR( J )
ELSE IF( IGRADE.EQ.4 .AND. I.NE.J ) THEN
CTEMP = CTEMP*DL( I ) / DL( J )
ELSE IF( IGRADE.EQ.5 ) THEN
CTEMP = CTEMP*DL( I )*DCONJG( DL( J ) )
ELSE IF( IGRADE.EQ.6 ) THEN
CTEMP = CTEMP*DL( I )*DL( J )
END IF
ZLATM3 = CTEMP
RETURN
*
* End of ZLATM3
*
END
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