CLATM3
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
June 2010
June 2010
Purpose
CLATM3 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. CLATM3 is called by the
CLATMR 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 CLATMR which has already checked the parameters.
Use of CLATM3 differs from CLATM2 in the order in which the random
number generator is called to fill in random matrix entries.
With CLATM2, the generator is called to fill in the pivoted matrix
columnwise. With CLATM3, the generator is called to fill in the
matrix columnwise, after which it is pivoted. Thus, CLATM3 can
be used to construct random matrices which differ only in their
order of rows and/or columns. CLATM2 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.
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. CLATM3 is called by the
CLATMR 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 CLATMR which has already checked the parameters.
Use of CLATM3 differs from CLATM2 in the order in which the random
number generator is called to fill in random matrix entries.
With CLATM2, the generator is called to fill in the pivoted matrix
columnwise. With CLATM3, the generator is called to fill in the
matrix columnwise, after which it is pivoted. Thus, CLATM3 can
be used to construct random matrices which differ only in their
order of rows and/or columns. CLATM2 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 => 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. |
| ISEED |
(input/output) INTEGER array of dimension ( 4 )
Seed for random number generator.
Changed on exit. |
| D |
(input) COMPLEX 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( CONJG(DL) ) 6 => matrix premultiplied by diag( DL ) and postmultiplied by diag( DL ) Not modified. |
| DL |
(input) COMPLEX array ( I or J, as appropriate )
Left scale factors for grading matrix. Not modified.
|
| DR |
(input) COMPLEX 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 CLATM2. 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. |