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