SLATM3 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. 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.

M

          M is INTEGER


           Number of rows of matrix. Not modified.

N

          N is INTEGER


           Number of columns of matrix. Not modified.

I

          I is INTEGER


           Row of unpivoted entry to be returned. Not modified.

J

          J is INTEGER


           Column of unpivoted entry to be returned. Not modified.

ISUB

          ISUB is INTEGER


           Row of pivoted entry to be returned. Changed on exit.

JSUB

          JSUB is INTEGER


           Column of pivoted entry to be returned. Changed on exit.

KL

          KL is INTEGER


           Lower bandwidth. Not modified.

KU

          KU is INTEGER


           Upper bandwidth. Not modified.

IDIST

          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.

ISEED

          ISEED is INTEGER array of dimension ( 4 )


           Seed for random number generator.


           Changed on exit.

D

          D is REAL array of dimension ( MIN( I , J ) )


           Diagonal entries of matrix. Not modified.

IGRADE

          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.

DL

          DL is REAL array ( I or J, as appropriate )


           Left scale factors for grading matrix.  Not modified.

DR

          DR is REAL array ( I or J, as appropriate )


           Right scale factors for grading matrix.  Not modified.

IPVTNG

          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.

IWORK

          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 SLATM2. Not modified.

SPARSE

          SPARSE is REAL 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.

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