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.
326 lines
9.4 KiB
326 lines
9.4 KiB
2 years ago
|
*> \brief \b ZLATM2
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* COMPLEX*16 FUNCTION ZLATM2( 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( * )
|
||
|
|
* COMPLEX*16 D( * ), DL( * ), DR( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> ZLATM2 returns the (I,J) entry of a random matrix of dimension
|
||
|
|
*> (M, N) described by the other parameters. It 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 ZLATM2 differs from CLATM3 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
|
||
|
|
*>
|
||
|
|
*> 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 => 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[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 ZLATM3. 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 ZLATM2( M, N, I, J, 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, J, KL, KU, M, N
|
||
|
|
DOUBLE PRECISION SPARSE
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* .. Array Arguments ..
|
||
|
|
*
|
||
|
|
INTEGER ISEED( 4 ), IWORK( * )
|
||
|
|
COMPLEX*16 D( * ), DL( * ), DR( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
*
|
||
|
|
COMPLEX*16 CZERO
|
||
|
|
PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ) )
|
||
|
|
DOUBLE PRECISION ZERO
|
||
|
|
PARAMETER ( ZERO = 0.0D0 )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* .. Local Scalars ..
|
||
|
|
*
|
||
|
|
INTEGER ISUB, JSUB
|
||
|
|
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
|
||
|
|
ZLATM2 = CZERO
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Check for banding
|
||
|
|
*
|
||
|
|
IF( J.GT.I+KU .OR. J.LT.I-KL ) THEN
|
||
|
|
ZLATM2 = CZERO
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Check for sparsity
|
||
|
|
*
|
||
|
|
IF( SPARSE.GT.ZERO ) THEN
|
||
|
|
IF( DLARAN( ISEED ).LT.SPARSE ) THEN
|
||
|
|
ZLATM2 = CZERO
|
||
|
|
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
|
||
|
|
CTEMP = D( ISUB )
|
||
|
|
ELSE
|
||
|
|
CTEMP = ZLARND( IDIST, ISEED )
|
||
|
|
END IF
|
||
|
|
IF( IGRADE.EQ.1 ) THEN
|
||
|
|
CTEMP = CTEMP*DL( ISUB )
|
||
|
|
ELSE IF( IGRADE.EQ.2 ) THEN
|
||
|
|
CTEMP = CTEMP*DR( JSUB )
|
||
|
|
ELSE IF( IGRADE.EQ.3 ) THEN
|
||
|
|
CTEMP = CTEMP*DL( ISUB )*DR( JSUB )
|
||
|
|
ELSE IF( IGRADE.EQ.4 .AND. ISUB.NE.JSUB ) THEN
|
||
|
|
CTEMP = CTEMP*DL( ISUB ) / DL( JSUB )
|
||
|
|
ELSE IF( IGRADE.EQ.5 ) THEN
|
||
|
|
CTEMP = CTEMP*DL( ISUB )*DCONJG( DL( JSUB ) )
|
||
|
|
ELSE IF( IGRADE.EQ.6 ) THEN
|
||
|
|
CTEMP = CTEMP*DL( ISUB )*DL( JSUB )
|
||
|
|
END IF
|
||
|
|
ZLATM2 = CTEMP
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of ZLATM2
|
||
|
|
*
|
||
|
|
END
|