# slatm3.f - Man Page

TESTING/MATGEN/slatm3.f

## Synopsis

### Functions/Subroutines

real function slatm3 (m, n, i, j, isub, jsub, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
SLATM3

## Function/Subroutine Documentation

### real function slatm3 (integer m, integer n, integer i, integer j, integer isub, integer jsub, integer kl, integer ku, integer idist, integer, dimension( 4 ) iseed, real, dimension( * ) d, integer igrade, real, dimension( * ) dl, real, dimension( * ) dr, integer ipvtng, integer, dimension( * ) iwork, real sparse)

SLATM3

Purpose:

```    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.```
Parameters

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 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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 223 of file slatm3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slatm3(3) is an alias of slatm3.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK