TESTING/MATGEN/dlatm3.f(3)

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💅 TESTING/MATGEN/dlatm3.f(3) — Library Functions Manual 💅

okay so bestie, welcome to TESTING/MATGEN/dlatm3.f(3) from the Library Functions Manual — yes, the filename is literally the whole vibe here, no cap 💖

👑 NAME 👑

TESTING/MATGEN/dlatm3.f — that's the name, that's the whole name, periodt ✨

🌸 SYNOPSIS 🌸

🌈 Functions/Subroutines 🌈

double precision function dlatm3 (m, n, i, j, isub, jsub, kl, ku, idist,
    iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)

and the subroutine's name is DLATM3 💫

🧚 Function/Subroutine Documentation 🧚

double precision function dlatm3 (integer m, integer n, integer i, integer
    j, integer isub, integer jsub, integer kl, integer ku, integer idist,
    integer, dimension( 4 ) iseed, double precision, dimension( * ) d,
    integer igrade, double precision, dimension( * ) dl, double precision,
    dimension( * ) dr, integer ipvtng, integer, dimension( * ) iwork, double
    precision sparse)

DLATM3 ✨

🎯 Purpose 🎯

okay so DLATM3 returns the (ISUB,JSUB) entry of a random matrix of dimension (M, N) described by the other parameters. (ISUB,JSUB) is the final position of the (I,J) entry after pivoting according to IPVTNG and IWORK. DLATM3 is called by the DLATMR 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 DLATMR which has already checked the parameters 💅

Use of DLATM3 differs from SLATM2 in the order in which the random number generator is called to fill in random matrix entries. With DLATM2, the generator is called to fill in the pivoted matrix columnwise. With DLATM3, the generator is called to fill in the matrix columnwise, after which it is pivoted. Thus, DLATM3 can be used to construct random matrices which differ only in their order of rows and/or columns. DLATM2 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.

🎀 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 unpivoted entry to be returned. Not modified.
  • J — J is INTEGER — Column of unpivoted entry to be returned. Not modified.
  • ISUB — ISUB is INTEGER — Row of pivoted entry to be returned. Changed on exit.
  • JSUB — JSUB is INTEGER — Column of pivoted entry to be returned. Changed on exit.
  • 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.
  • D — D is DOUBLE PRECISION 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 DOUBLE PRECISION array ( I or J, as appropriate ) — Left scale factors for grading matrix. Not modified.
  • DR — DR is DOUBLE PRECISION 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) originally in position K is in position IWORK( K ) after pivoting. This differs from IWORK for DLATM2. Not modified.
  • SPARSE — SPARSE is DOUBLE PRECISION 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 223 of file dlatm3.f.

👑 Author 👑

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