TESTING/MATGEN/dlatm2.f(3)

Okay bestie, welcome to the TESTING/MATGEN/dlatm2.f page from the LAPACK Library Functions Manual — the manual name is folded in near the top, just like requested, and this little subroutine is living in it rent-free 💖.

🌸 NAME 🌸

TESTING/MATGEN/dlatm2.f — that’s the file, and dlatm2 is the double precision function doing the work. Periodt.

✨ SYNOPSIS ✨

Functions/Subroutines

double precision function dlatm2 (m, n, i, j, kl, ku, idist, iseed, d,
    igrade, dl, dr, ipvtng, iwork, sparse)
    DLATM2

💅 Function/Subroutine Documentation 💅

Here’s the full signature, bestie — every type, every dimension, every comma exactly where it belongs ✨

double precision function dlatm2 (integer m, integer n, integer i, integer
    j, 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)
    DLATM2

🎀 Purpose 🎀

DLATM2 returns the (I,J) entry of a random matrix of dimension (M, N) described by the other parameters. It 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. No cap 🫶.

Use of DLATM2 differs from SLATM3 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 — yes, the original sentence trails off there, bestie 😭.

The matrix whose (I,J) entry is returned is constructed as follows (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.
  • 1 => UNIFORM( 0, 1 )
  • 2 => UNIFORM( -1, 1 )
  • 3 => NORMAL( 0, 1 ) Not modified.
• ISEED — INTEGER array of dimension ( 4 ). Seed for random number generator. Changed on exit.
• D — DOUBLE PRECISION 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( DL ) Not modified.
• DL — DOUBLE PRECISION array ( I or J, as appropriate ). Left scale factors for grading matrix. Not modified.
• DR — DOUBLE PRECISION 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 DLATM3. Not modified.
• SPARSE — 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 206 of file dlatm2.f.

Author: Generated automatically by Doxygen for LAPACK from the source code.

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