REAL FUNCTION SLATM3( M, N, I, J, ISUB, JSUB, KL, KU,
$ IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
$ SPARSE )
*
* -- LAPACK auxiliary test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* June 2010
*
* .. Scalar Arguments ..
*
INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
$ KU, M, N
REAL SPARSE
* ..
*
* .. Array Arguments ..
*
INTEGER ISEED( 4 ), IWORK( * )
REAL D( * ), DL( * ), DR( * )
* ..
*
* Purpose
* =======
*
* SLATM3 returns the (ISUB,JSUB) entry of a random matrix of
* dimension (M, N) described by the other paramters. (ISUB,JSUB)
* is the final position of the (I,J) entry after pivoting
* according to IPVTNG and IWORK. SLATM3 is called by the
* SLATMR 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 SLATMR which has already checked the parameters.
*
* Use of SLATM3 differs from SLATM2 in the order in which the random
* number generator is called to fill in random matrix entries.
* With SLATM2, the generator is called to fill in the pivoted matrix
* columnwise. With SLATM3, the generator is called to fill in the
* matrix columnwise, after which it is pivoted. Thus, SLATM3 can
* be used to construct random matrices which differ only in their
* order of rows and/or columns. SLATM2 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.
*
* Arguments
* =========
*
* M (input) INTEGER
* Number of rows of matrix. Not modified.
*
* N (input) INTEGER
* Number of columns of matrix. Not modified.
*
* I (input) INTEGER
* Row of unpivoted entry to be returned. Not modified.
*
* J (input) INTEGER
* Column of unpivoted entry to be returned. Not modified.
*
* ISUB (input/output) INTEGER
* Row of pivoted entry to be returned. Changed on exit.
*
* JSUB (input/output) INTEGER
* Column of pivoted entry to be returned. Changed on exit.
*
* KL (input) INTEGER
* Lower bandwidth. Not modified.
*
* KU (input) INTEGER
* Upper bandwidth. Not modified.
*
* IDIST (input) 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.
*
* ISEED (input/output) INTEGER array of dimension ( 4 )
* Seed for random number generator.
* Changed on exit.
*
* D (input) REAL array of dimension ( MIN( I , J ) )
* Diagonal entries of matrix. Not modified.
*
* IGRADE (input) 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.
*
* DL (input) REAL array ( I or J, as appropriate )
* Left scale factors for grading matrix. Not modified.
*
* DR (input) REAL array ( I or J, as appropriate )
* Right scale factors for grading matrix. Not modified.
*
* IPVTNG (input) 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.
*
* IWORK (input) 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 SLATM2. Not modified.
*
* SPARSE (input) REAL 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.
*
* =====================================================================
*
* .. Parameters ..
*
REAL ZERO
PARAMETER ( ZERO = 0.0E0 )
* ..
*
* .. Local Scalars ..
*
REAL TEMP
* ..
*
* .. External Functions ..
*
REAL SLARAN, SLARND
EXTERNAL SLARAN, SLARND
* ..
*
*-----------------------------------------------------------------------
*
* .. 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
SLATM3 = ZERO
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
SLATM3 = ZERO
RETURN
END IF
*
* Check for sparsity
*
IF( SPARSE.GT.ZERO ) THEN
IF( SLARAN( ISEED ).LT.SPARSE ) THEN
SLATM3 = ZERO
RETURN
END IF
END IF
*
* Compute entry and grade it according to IGRADE
*
IF( I.EQ.J ) THEN
TEMP = D( I )
ELSE
TEMP = SLARND( IDIST, ISEED )
END IF
IF( IGRADE.EQ.1 ) THEN
TEMP = TEMP*DL( I )
ELSE IF( IGRADE.EQ.2 ) THEN
TEMP = TEMP*DR( J )
ELSE IF( IGRADE.EQ.3 ) THEN
TEMP = TEMP*DL( I )*DR( J )
ELSE IF( IGRADE.EQ.4 .AND. I.NE.J ) THEN
TEMP = TEMP*DL( I ) / DL( J )
ELSE IF( IGRADE.EQ.5 ) THEN
TEMP = TEMP*DL( I )*DL( J )
END IF
SLATM3 = TEMP
RETURN
*
* End of SLATM3
*
END