# clatmr.f - Man Page

TESTING/MATGEN/clatmr.f

## Synopsis

### Functions/Subroutines

subroutine clatmr (m, n, dist, iseed, sym, d, mode, cond, dmax, rsign, grade, dl, model, condl, dr, moder, condr, pivtng, ipivot, kl, ku, sparse, anorm, pack, a, lda, iwork, info)
CLATMR

## Function/Subroutine Documentation

### subroutine clatmr (integer m, integer n, character dist, integer, dimension( 4 ) iseed, character sym, complex, dimension( * ) d, integer mode, real cond, complex dmax, character rsign, character grade, complex, dimension( * ) dl, integer model, real condl, complex, dimension( * ) dr, integer moder, real condr, character pivtng, integer, dimension( * ) ipivot, integer kl, integer ku, real sparse, real anorm, character pack, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) iwork, integer info)

CLATMR

Purpose:

```    CLATMR generates random matrices of various types for testing
LAPACK programs.

CLATMR operates by applying the following sequence of
operations:

Generate a matrix A with random entries of distribution DIST
which is symmetric if SYM='S', Hermitian if SYM='H', and
nonsymmetric if SYM='N'.

Set the diagonal to D, where D may be input or
computed according to MODE, COND, DMAX and RSIGN
as described below.

Grade the matrix, if desired, from the left and/or right
as specified by GRADE. The inputs DL, MODEL, CONDL, DR,
MODER and CONDR also determine the grading as described
below.

Permute, if desired, the rows and/or columns as specified by
PIVTNG and IPIVOT.

Set random entries to zero, if desired, to get a random sparse
matrix as specified by SPARSE.

Make A a band matrix, if desired, by zeroing out the matrix
outside a band of lower bandwidth KL and upper bandwidth KU.

Scale A, if desired, to have maximum entry ANORM.

Pack the matrix if desired. Options specified by PACK are:
no packing
zero out upper half (if symmetric or Hermitian)
zero out lower half (if symmetric or Hermitian)
store the upper half columnwise (if symmetric or Hermitian
or square upper triangular)
store the lower half columnwise (if symmetric or Hermitian
or square lower triangular)
same as upper half rowwise if symmetric
same as conjugate upper half rowwise if Hermitian
store the lower triangle in banded format
(if symmetric or Hermitian)
store the upper triangle in banded format
(if symmetric or Hermitian)
store the entire matrix in banded format

Note: If two calls to CLATMR differ only in the PACK parameter,
they will generate mathematically equivalent matrices.

If two calls to CLATMR both have full bandwidth (KL = M-1
and KU = N-1), and differ only in the PIVTNG and PACK
parameters, then the matrices generated will differ only
in the order of the rows and/or columns, and otherwise
contain the same data. This consistency cannot be and
is not maintained with less than full bandwidth.```
Parameters

M

```          M is INTEGER
Number of rows of A. Not modified.```

N

```          N is INTEGER
Number of columns of A. Not modified.```

DIST

```          DIST is CHARACTER*1
On entry, DIST specifies the type of distribution to be used
to generate a random matrix .
'U' => real and imaginary parts are independent
UNIFORM( 0, 1 )  ( 'U' for uniform )
'S' => real and imaginary parts are independent
UNIFORM( -1, 1 ) ( 'S' for symmetric )
'N' => real and imaginary parts are independent
NORMAL( 0, 1 )   ( 'N' for normal )
'D' => uniform on interior of unit disk ( 'D' for disk )
Not modified.```

ISEED

```          ISEED is INTEGER array, dimension (4)
On entry ISEED specifies the seed of the random number
generator. They should lie between 0 and 4095 inclusive,
and ISEED(4) should be odd. The random number generator
uses a linear congruential sequence limited to small
integers, and so should produce machine independent
random numbers. The values of ISEED are changed on
exit, and can be used in the next call to CLATMR
to continue the same random number sequence.
Changed on exit.```

SYM

```          SYM is CHARACTER*1
If SYM='S', generated matrix is symmetric.
If SYM='H', generated matrix is Hermitian.
If SYM='N', generated matrix is nonsymmetric.
Not modified.```

D

```          D is COMPLEX array, dimension (min(M,N))
On entry this array specifies the diagonal entries
of the diagonal of A.  D may either be specified
on entry, or set according to MODE and COND as described
below. If the matrix is Hermitian, the real part of D
will be taken. May be changed on exit if MODE is nonzero.```

MODE

```          MODE is INTEGER
On entry describes how D is to be used:
MODE = 0 means use D as input
MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
MODE = 5 sets D to random numbers in the range
( 1/COND , 1 ) such that their logarithms
are uniformly distributed.
MODE = 6 set D to random numbers from same distribution
as the rest of the matrix.
MODE < 0 has the same meaning as ABS(MODE), except that
the order of the elements of D is reversed.
Thus if MODE is positive, D has entries ranging from
1 to 1/COND, if negative, from 1/COND to 1,
Not modified.```

COND

```          COND is REAL
On entry, used as described under MODE above.
If used, it must be >= 1. Not modified.```

DMAX

```          DMAX is COMPLEX
If MODE neither -6, 0 nor 6, the diagonal is scaled by
DMAX / max(abs(D(i))), so that maximum absolute entry
of diagonal is abs(DMAX). If DMAX is complex (or zero),
diagonal will be scaled by a complex number (or zero).```

RSIGN

```          RSIGN is CHARACTER*1
If MODE neither -6, 0 nor 6, specifies sign of diagonal
as follows:
'T' => diagonal entries are multiplied by a random complex
number uniformly distributed with absolute value 1
'F' => diagonal unchanged
Not modified.```

GRADE

```          GRADE is CHARACTER*1
Specifies grading of matrix as follows:
'N'  => no grading
'L'  => matrix premultiplied by diag( DL )
(only if matrix nonsymmetric)
'R'  => matrix postmultiplied by diag( DR )
(only if matrix nonsymmetric)
'B'  => matrix premultiplied by diag( DL ) and
postmultiplied by diag( DR )
(only if matrix nonsymmetric)
'H'  => matrix premultiplied by diag( DL ) and
postmultiplied by diag( CONJG(DL) )
(only if matrix Hermitian or nonsymmetric)
'S'  => matrix premultiplied by diag( DL ) and
postmultiplied by diag( DL )
(only if matrix symmetric or nonsymmetric)
'E'  => matrix premultiplied by diag( DL ) and
postmultiplied by inv( diag( DL ) )
( 'S' for similarity )
(only if matrix nonsymmetric)
Note: if GRADE='S', then M must equal N.
Not modified.```

DL

```          DL is COMPLEX array, dimension (M)
If MODEL=0, then on entry this array specifies the diagonal
entries of a diagonal matrix used as described under GRADE
above. If MODEL is not zero, then DL will be set according
to MODEL and CONDL, analogous to the way D is set according
to MODE and COND (except there is no DMAX parameter for DL).
If GRADE='E', then DL cannot have zero entries.
Not referenced if GRADE = 'N' or 'R'. Changed on exit.```

MODEL

```          MODEL is INTEGER
This specifies how the diagonal array DL is to be computed,
just as MODE specifies how D is to be computed.
Not modified.```

CONDL

```          CONDL is REAL
When MODEL is not zero, this specifies the condition number
of the computed DL.  Not modified.```

DR

```          DR is COMPLEX array, dimension (N)
If MODER=0, then on entry this array specifies the diagonal
entries of a diagonal matrix used as described under GRADE
above. If MODER is not zero, then DR will be set according
to MODER and CONDR, analogous to the way D is set according
to MODE and COND (except there is no DMAX parameter for DR).
Not referenced if GRADE = 'N', 'L', 'H' or 'S'.
Changed on exit.```

MODER

```          MODER is INTEGER
This specifies how the diagonal array DR is to be computed,
just as MODE specifies how D is to be computed.
Not modified.```

CONDR

```          CONDR is REAL
When MODER is not zero, this specifies the condition number
of the computed DR.  Not modified.```

PIVTNG

```          PIVTNG is CHARACTER*1
On entry specifies pivoting permutations as follows:
'N' or ' ' => none.
'L' => left or row pivoting (matrix must be nonsymmetric).
'R' => right or column pivoting (matrix must be
nonsymmetric).
'B' or 'F' => both or full pivoting, i.e., on both sides.
In this case, M must equal N

If two calls to CLATMR both have full bandwidth (KL = M-1
and KU = N-1), and differ only in the PIVTNG and PACK
parameters, then the matrices generated will differ only
in the order of the rows and/or columns, and otherwise
contain the same data. This consistency cannot be
maintained with less than full bandwidth.```

IPIVOT

```          IPIVOT is INTEGER array, dimension (N or M)
This array specifies the permutation used.  After the
basic matrix is generated, the rows, columns, or both
are permuted.   If, say, row pivoting is selected, CLATMR
starts with the *last* row and interchanges the M-th and
IPIVOT(M)-th rows, then moves to the next-to-last row,
interchanging the (M-1)-th and the IPIVOT(M-1)-th rows,
and so on.  In terms of '2-cycles', the permutation is
(1 IPIVOT(1)) (2 IPIVOT(2)) ... (M IPIVOT(M))
where the rightmost cycle is applied first.  This is the
*inverse* of the effect of pivoting in LINPACK.  The idea
is that factoring (with pivoting) an identity matrix
which has been inverse-pivoted in this way should
result in a pivot vector identical to IPIVOT.
Not referenced if PIVTNG = 'N'. Not modified.```

KL

```          KL is INTEGER
On entry specifies the lower bandwidth of the  matrix. For
example, KL=0 implies upper triangular, KL=1 implies upper
Hessenberg, and KL at least M-1 implies the matrix is not
banded. Must equal KU if matrix is symmetric or Hermitian.
Not modified.```

KU

```          KU is INTEGER
On entry specifies the upper bandwidth of the  matrix. For
example, KU=0 implies lower triangular, KU=1 implies lower
Hessenberg, and KU at least N-1 implies the matrix is not
banded. Must equal KL if matrix is symmetric or Hermitian.
Not modified.```

SPARSE

```          SPARSE is REAL
On entry specifies the sparsity of the matrix if a sparse
matrix is to be generated. SPARSE should lie between
0 and 1. To generate a sparse matrix, for each matrix entry
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.```

ANORM

```          ANORM is REAL
On entry specifies maximum entry of output matrix
(output matrix will by multiplied by a constant so that
its largest absolute entry equal ANORM)
if ANORM is nonnegative. If ANORM is negative no scaling
is done. Not modified.```

PACK

```          PACK is CHARACTER*1
On entry specifies packing of matrix as follows:
'N' => no packing
'U' => zero out all subdiagonal entries
(if symmetric or Hermitian)
'L' => zero out all superdiagonal entries
(if symmetric or Hermitian)
'C' => store the upper triangle columnwise
(only if matrix symmetric or Hermitian or
square upper triangular)
'R' => store the lower triangle columnwise
(only if matrix symmetric or Hermitian or
square lower triangular)
(same as upper half rowwise if symmetric)
(same as conjugate upper half rowwise if Hermitian)
'B' => store the lower triangle in band storage scheme
(only if matrix symmetric or Hermitian)
'Q' => store the upper triangle in band storage scheme
(only if matrix symmetric or Hermitian)
'Z' => store the entire matrix in band storage scheme
(pivoting can be provided for by using this
option to store A in the trailing rows of
the allocated storage)

Using these options, the various LAPACK packed and banded
storage schemes can be obtained:
GB               - use 'Z'
PB, HB or TB     - use 'B' or 'Q'
PP, HP or TP     - use 'C' or 'R'

If two calls to CLATMR differ only in the PACK parameter,
they will generate mathematically equivalent matrices.
Not modified.```

A

```          A is COMPLEX array, dimension (LDA,N)
On exit A is the desired test matrix. Only those
entries of A which are significant on output
will be referenced (even if A is in packed or band
storage format). The 'unoccupied corners' of A in
band format will be zeroed out.```

LDA

```          LDA is INTEGER
on entry LDA specifies the first dimension of A as
declared in the calling program.
If PACK='N', 'U' or 'L', LDA must be at least max ( 1, M ).
If PACK='C' or 'R', LDA must be at least 1.
If PACK='B', or 'Q', LDA must be MIN ( KU+1, N )
If PACK='Z', LDA must be at least KUU+KLL+1, where
KUU = MIN ( KU, N-1 ) and KLL = MIN ( KL, M-1 )
Not modified.```

IWORK

```          IWORK is INTEGER array, dimension (N or M)
Workspace. Not referenced if PIVTNG = 'N'. Changed on exit.```

INFO

```          INFO is INTEGER
Error parameter on exit:
0 => normal return
-1 => M negative or unequal to N and SYM='S' or 'H'
-2 => N negative
-3 => DIST illegal string
-5 => SYM illegal string
-7 => MODE not in range -6 to 6
-8 => COND less than 1.0, and MODE neither -6, 0 nor 6
-10 => MODE neither -6, 0 nor 6 and RSIGN illegal string
-11 => GRADE illegal string, or GRADE='E' and
M not equal to N, or GRADE='L', 'R', 'B', 'S' or 'E'
and SYM = 'H', or GRADE='L', 'R', 'B', 'H' or 'E'
and SYM = 'S'
-12 => GRADE = 'E' and DL contains zero
-13 => MODEL not in range -6 to 6 and GRADE= 'L', 'B', 'H',
'S' or 'E'
-14 => CONDL less than 1.0, GRADE='L', 'B', 'H', 'S' or 'E',
and MODEL neither -6, 0 nor 6
-16 => MODER not in range -6 to 6 and GRADE= 'R' or 'B'
-17 => CONDR less than 1.0, GRADE='R' or 'B', and
MODER neither -6, 0 nor 6
-18 => PIVTNG illegal string, or PIVTNG='B' or 'F' and
M not equal to N, or PIVTNG='L' or 'R' and SYM='S'
or 'H'
-19 => IPIVOT contains out of range number and
PIVTNG not equal to 'N'
-20 => KL negative
-21 => KU negative, or SYM='S' or 'H' and KU not equal to KL
-22 => SPARSE not in range 0. to 1.
-24 => PACK illegal string, or PACK='U', 'L', 'B' or 'Q'
and SYM='N', or PACK='C' and SYM='N' and either KL
not equal to 0 or N not equal to M, or PACK='R' and
SYM='N', and either KU not equal to 0 or N not equal
to M
-26 => LDA too small
1 => Error return from CLATM1 (computing D)
2 => Cannot scale diagonal to DMAX (max. entry is 0)
3 => Error return from CLATM1 (computing DL)
4 => Error return from CLATM1 (computing DR)
5 => ANORM is positive, but matrix constructed prior to
attempting to scale it to have norm ANORM, is zero```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 486 of file clatmr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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