TESTING/MATGEN/zlatm3.f(3)

🌸 NAME 🌸

hey bestie, this is the Library Functions Manual page for TESTING/MATGEN/zlatm3.f(3), and it's all about TESTING/MATGEN/zlatm3.f — specifically the ZLATM3 function, no cap. 💖

✨ SYNOPSIS ✨

Functions/Subroutines

• complex *16 function zlatm3 (...) — ZLATM3

complex *16 function zlatm3 (m, n, i, j, isub, jsub, kl, ku, idist,
    iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
    ZLATM3

🦋 Function/Subroutine Documentation 🦋

ZLATM3

complex*16 function zlatm3 (integer m, integer n, integer i, integer j,
    integer isub, integer jsub, integer kl, integer ku, integer idist,
    integer, dimension( 4 ) iseed, complex*16, dimension( * ) d, integer
    igrade, complex*16, dimension( * ) dl, complex*16, dimension( * ) dr,
    integer ipvtng, integer, dimension( * ) iwork, double precision sparse)
    ZLATM3

Purpose

okay so ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of dimension (M, N) described by the other parameters. The (ISUB,JSUB) position is literally the final position of the (I,J) entry after pivoting according to IPVTNG and IWORK. ZLATM3 is called by the ZLATMR 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 ZLATMR which has already checked the parameters. periodt. 💅

Use of ZLATM3 differs from CLATM2 in the order in which the random number generator is called to fill in random matrix entries. With ZLATM2, the generator is called to fill in the pivoted matrix columnwise. With ZLATM3, the generator is called to fill in the matrix columnwise, after which it is pivoted. Thus, ZLATM3 can be used to construct random matrices which differ only in their order of rows and/or columns. ZLATM2 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 — 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 .
  • 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*16 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*16 array ( I or J, as appropriate ). Left scale factors for grading matrix. Not modified.
• DR — COMPLEX*16 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) originally in position K is in position IWORK( K ) after pivoting. This differs from IWORK for ZLATM2. 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 226 of file zlatm3.f.

Author

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and that's the whole vibe: LAPACK Version 3.12.0, TESTING/MATGEN/zlatm3.f(3) 💜✨