TESTING/MATGEN/clatm2.f(3)

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version 3.12.1 · 2 versions
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🌸 NAME 🌸

okay bestie, this is TESTING/MATGEN/clatm2.f — a Library Functions Manual page for the one and only clatm2.f in TESTING/MATGEN. It’s giving “tiny Fortran icon that does one very specific job and does it flawlessly.” 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines

complex function clatm2 (m, n, i, j, kl, ku, idist, iseed, d, igrade,
    dl, dr, ipvtng, iwork, sparse)
    CLATM2

🦋 Function/Subroutine Documentation 🦋

💖 complex function clatm2 (...) 💖

complex function clatm2 (integer m, integer n, integer i, integer j, 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)
    CLATM2

This is CLATM2, and yes, it is exactly as specific as the signature looks. 🫶

🔥 Purpose 🔥

So, CLATM2 returns the (I,J) entry of a random matrix of dimension (M, N) described by the other parameters. It gets called by the CLATMR routine 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. Efficiency queen behavior, honestly. 👑

Use of CLATM2 differs from CLATM3 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 — the source line trails off right there, no cap). 😭

The matrix whose (I,J) entry is returned is constructed as follows — and remember, this routine only computes one entry:

  • If I is outside (1..M) or J 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 entry to be returned. Not modified.
  • J — INTEGER. Column of entry to be returned. Not modified.
  • 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. The distribution menu is:
    • 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 — 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:
    • 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 — 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:
    • 0 => none.
    • 1 => row pivoting.
    • 2 => column pivoting.
    • 3 => full pivoting, i.e., on both sides.

Not modified.

  • IWORK — INTEGER array ( I or J, as appropriate ). This array specifies the permutation used. The row (or column) in position K was originally in position IWORK( K ). This differs from IWORK for CLATM3. Not modified.
  • SPARSE — REAL. Value 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 ⭐

210 of file clatm2.f.

💜 Author 💜

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