TESTING/MATGEN/clatm3.f(3)

💖 NAME 💖

TESTING/MATGEN/clatm3.f — the page title is TESTING/MATGEN/clatm3.f(3), and we’re in the Library Functions Manual. Welcome to the CLATM3 page, bestie. 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

       complex function clatm3 (m, n, i, j, isub, jsub, kl, ku, idist, iseed,
           d, igrade, dl, dr, ipvtng, iwork, sparse)
           CLATM3

🧚 Function/Subroutine Documentation 🧚

       complex function clatm3 (integer m, integer n, integer i, integer j, integer
           isub, integer jsub, integer kl, integer ku, integer idist, integer,
           dimension( 4 ) iseed, complex, dimension( * ) d, integer igrade,
           complex, dimension( * ) dl, complex, dimension( * ) dr, integer ipvtng,
           integer, dimension( * ) iwork, real sparse)
           CLATM3

✨ Purpose ✨

okay so here’s the tea: CLATM3 returns the (ISUB,JSUB) entry of a random matrix of dimension (M, N) described by the other parameters. The (ISUB,JSUB) spot is the final position of the (I,J) entry after pivoting according to IPVTNG and IWORK. CLATM3 gets called by CLATMR to build random test matrices. No error checking on parameters is done here, because this routine is called in a tight loop by CLATMR, which has already checked the parameters. no cap. 💅

The way CLATM3 works 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). iconic behavior, honestly. 🦋

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 — INTEGER. Number of rows of matrix. Not modified.
• N — INTEGER. Number of columns of matrix. Not modified.
• I — INTEGER. Row of unpivoted entry to be returned. Not modified.
• J — INTEGER. Column of unpivoted entry to be returned. Not modified.
• ISUB — INTEGER. Row of pivoted entry to be returned. Changed on exit.
• JSUB — INTEGER. Column of pivoted entry to be returned. Changed on exit.
• KL — INTEGER. Lower bandwidth. Not modified.
• KU — INTEGER. Upper bandwidth. Not modified.
• IDIST — INTEGER. On entry, IDIST specifies the type of distribution to be used to generate a random matrix. Not modified.
  • 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 )
• ISEED — INTEGER array of dimension ( 4 ). Seed for random number generator. Changed on exit.
• D — COMPLEX array of dimension ( MIN( I , J ) ). Diagonal entries of matrix. Not modified.
• IGRADE — INTEGER. Specifies grading of matrix as follows. Not modified.
  • 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 )
• DL — COMPLEX array ( I or J, as appropriate ). Left scale factors for grading matrix. Not modified.
• DR — COMPLEX array ( I or J, as appropriate ). Right scale factors for grading matrix. Not modified.
• IPVTNG — INTEGER. On entry specifies pivoting permutations as follows. Not modified.
  • 0 => none.
  • 1 => row pivoting.
  • 2 => column pivoting.
  • 3 => full pivoting, i.e., on both sides.
• IWORK — 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 — 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 226 of file clatm3.f.

💜 Author 💜

This page was generated automatically by Doxygen for LAPACK from the source code.

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