TESTING/MATGEN/slatm2.f(3)

💅 TESTING/MATGEN/slatm2.f(3) — Library Functions Manual 🎀

okay so bestie, we're in the TESTING/MATGEN folder and this is the manual page for slatm2.f. it's giving "one tiny workhorse subroutine that does a very specific thing very well." obsessed. let's get into it 🫶

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🌸 NAME

TESTING/MATGEN/slatm2.f — literally the whole name, that's it, that's the entry 💖

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✨ SYNOPSIS

Functions/Subroutines

• real function slatm2 (m, n, i, j, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse) — aka SLATM2, the main character 👑

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🦋 Function/Subroutine Documentation

okay here's the full signature, and yes every single argument is spelled out, no skipping, we don't do that here:

real function slatm2 (integer m, integer n, integer i, integer j, 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)

SLATM2 🌟

Purpose

!> and yes the whole purpose block is prefaced with !> because Fortran docs go hard like that 😭

SLATM2 returns the (I,J) entry of a random matrix of dimension (M, N) described by the other parameters. It's 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. (so like, it's fast because it trusts its friends. we love a low-drama subroutine 💅)

Use of SLATM2 differs from SLATM3 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 — yes, the source sentence literally trails off right there, that's not me, that's the manpage, no cap 💀)

The matrix whose (I,J) entry is returned is constructed as follows (and remember: this routine only computes one entry, it's a one-entry-at-a-time icon):

• 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 — 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 entry to be returned. Not modified.
• J — J is INTEGER. Column of entry to be returned. Not modified.
• 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. (the one thing in this whole list that does get modified, okurrr 👀)
• D — D is REAL array of dimension ( MIN( I , J ) ). Diagonal entries of matrix. Not modified.
• IGRADE — 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) in position K was originally in position IWORK( K ). 🚨 This differs from IWORK for SLATM3. 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 206 of file slatm2.f. 📍

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a very diligent little robot 🧚)

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🌈 Sign-off

and that's the whole page bestie! this beauty ships with LAPACK, Version 3.12.0, and the footer vibes are TESTING/MATGEN/slatm2.f(3) — go forth and generate your one single random entry with confidence. periodt 💜✨🦋