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*> \brief \b DLATM2
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLATM2( M, N, I, J, KL, KU, IDIST,
* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
*
* .. Scalar Arguments ..
*
* INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N
* DOUBLE PRECISION SPARSE
* ..
*
* .. Array Arguments ..
*
* INTEGER ISEED( 4 ), IWORK( * )
* DOUBLE PRECISION D( * ), DL( * ), DR( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLATM2 returns the (I,J) entry of a random matrix of dimension
*> (M, N) described by the other parameters. It is called by the
*> DLATMR 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 DLATMR which has already checked the parameters.
*>
*> Use of DLATM2 differs from SLATM3 in the order in which the random
*> number generator is called to fill in random matrix entries.
*> With DLATM2, the generator is called to fill in the pivoted matrix
*> columnwise. With DLATM3, the generator is called to fill in the
*> matrix columnwise, after which it is pivoted. Thus, DLATM3 can
*> be used to construct random matrices which differ only in their
*> order of rows and/or columns. DLATM2 is used to construct band
*> matrices while avoiding calling the random number generator for
*> entries outside the band (and therefore generating random numbers
*>
*> The matrix whose (I,J) entry is returned is constructed as
*> follows (this routine only computes one entry):
*>
*> If I is outside (1..M) or J 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 entry to be returned. Not modified.
*> \endverbatim
*>
*> \param[in] J
*> \verbatim
*> J is INTEGER
*> Column of entry to be returned. Not modified.
*> \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 => UNIFORM( 0, 1 )
*> 2 => UNIFORM( -1, 1 )
*> 3 => NORMAL( 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 DOUBLE PRECISION 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( DL )
*> Not modified.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*> DL is DOUBLE PRECISION array ( I or J, as appropriate )
*> Left scale factors for grading matrix. Not modified.
*> \endverbatim
*>
*> \param[in] DR
*> \verbatim
*> DR is DOUBLE PRECISION 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[out] IWORK
*> \verbatim
*> IWORK is INTEGER array ( I or J, as appropriate )
*> This array specifies the permutation used. The
*> row (or column) in position K was originally in
*> position IWORK( K ).
*> This differs from IWORK for DLATM3. 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 matix 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.
*
*> \date June 2016
*
*> \ingroup double_matgen
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLATM2( M, N, I, J, KL, KU, IDIST,
$ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2016
*
* .. Scalar Arguments ..
*
INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N
DOUBLE PRECISION SPARSE
* ..
*
* .. Array Arguments ..
*
INTEGER ISEED( 4 ), IWORK( * )
DOUBLE PRECISION D( * ), DL( * ), DR( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
*
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
* ..
*
* .. Local Scalars ..
*
INTEGER ISUB, JSUB
DOUBLE PRECISION TEMP
* ..
*
* .. External Functions ..
*
DOUBLE PRECISION DLARAN, DLARND
EXTERNAL DLARAN, DLARND
* ..
*
*-----------------------------------------------------------------------
*
* .. 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
DLATM2 = ZERO
RETURN
END IF
*
* Check for banding
*
IF( J.GT.I+KU .OR. J.LT.I-KL ) THEN
DLATM2 = ZERO
RETURN
END IF
*
* Check for sparsity
*
IF( SPARSE.GT.ZERO ) THEN
IF( DLARAN( ISEED ).LT.SPARSE ) THEN
DLATM2 = ZERO
RETURN
END IF
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
*
* Compute entry and grade it according to IGRADE
*
IF( ISUB.EQ.JSUB ) THEN
TEMP = D( ISUB )
ELSE
TEMP = DLARND( IDIST, ISEED )
END IF
IF( IGRADE.EQ.1 ) THEN
TEMP = TEMP*DL( ISUB )
ELSE IF( IGRADE.EQ.2 ) THEN
TEMP = TEMP*DR( JSUB )
ELSE IF( IGRADE.EQ.3 ) THEN
TEMP = TEMP*DL( ISUB )*DR( JSUB )
ELSE IF( IGRADE.EQ.4 .AND. ISUB.NE.JSUB ) THEN
TEMP = TEMP*DL( ISUB ) / DL( JSUB )
ELSE IF( IGRADE.EQ.5 ) THEN
TEMP = TEMP*DL( ISUB )*DL( JSUB )
END IF
DLATM2 = TEMP
RETURN
*
* End of DLATM2
*
END
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