/home/abui...N/zlatm2.f(3)

🦋 ZLATM2 — the "gimme ONE entry of this random matrix" queen 💅

Okay bestie, so like... this is ZLATM2 from the LAPACK crew, living at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/zlatm2.f. It's a complex *16 function and honestly? She's a whole vibe. Let me tell you everything 💖

✨ SYNOPSIS ✨

🌸 Functions/Subroutines

complex *16 function ZLATM2 (m, n, i, j, kl, ku, idist, iseed, d,
    igrade, dl, dr, ipvtng, iwork, sparse)

Like, that's the whole signature, no cap. Also ZLATM2 (yes the name again, she's iconic like that).

🎀 Function/Subroutine Documentation 🎀

complex*16 function ZLATM2 (integer m, integer n, integer i, integer j,
    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)

ZLATM2

🌈 Purpose

!> !> ZLATM2 returns the (I,J) entry of a random matrix of dimension !> (M, N) described by the other parameters. It 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. !> !> Use of ZLATM2 differs from CLATM3 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 !> !> 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. !>

Bestie, real talk: she computes literally just one entry of the matrix, not the whole thing. Lowkey genius. She does the whole build-the-matrix ritual in her head and hands you back the one little number you asked for. Slay. 🫶

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🌟 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 => 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. !>

Okay so pick your random-flavor, bestie — 1 for UNIFORM( 0, 1 ) on both parts, 2 for UNIFORM( -1, 1 ), 3 for NORMAL( 0, 1 ), 4 for a complex number uniform in DISK( 0 , 1 ). Choose wisely 💅

• ISEED — !> ISEED is INTEGER array of dimension ( 4 ) !> Seed for random number generator. !> Changed on exit. !>

Heads up: she changes on exit. The seed does not survive the encounter 👀

• D — !> D is COMPLEX*16 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( CONJG(DL) ) !> 6 => matrix premultiplied by diag( DL ) and !> postmultiplied by diag( DL ) !> Not modified. !>

The glow-up menu, fr fr: 0 = no grading, 1 = pre by diag( DL ), 2 = post by diag( DR ), 3 = pre by diag( DL ) AND post by diag( DR ), 4 = pre by diag( DL ) and post by inv( diag( DL ) ), 5 = pre by diag( DL ) and post by diag( CONJG(DL) ), 6 = pre by diag( DL ) and post by diag( DL ). Pick your transformation, main character ✨

• DL — !> DL is COMPLEX*16 array ( I or J, as appropriate ) !> Left scale factors for grading matrix. Not modified. !>
• DR — !> DR is COMPLEX*16 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. !>

Perm shuffle options: 0 = none, 1 = row pivoting, 2 = column pivoting, 3 = full pivoting, i.e., on both sides. Werk 💃

• 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 ZLATM3. Not modified. !>

Note the tea: this IWORK differs from IWORK for ZLATM3. Don't mix them up bestie, iykyk 🍓

• 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. !>

So like: a uniform ( 0, 1 ) random number x gets generated and compared to SPARSE. If x is larger, the entry stays; if x is smaller, it gets yeeted to zero. On average a fraction SPARSE of entries get zeroed out. It lives between 0. and 1. — respect the range 🎀

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🦋 Definition at line 209 of file zlatm2.f. 🦋

And that's the whole page, bestie! 💖 Generated automatically by Doxygen for LAPACK from the source code — LAPACK, Version 3.12.0, from /home/abui...N/zlatm2.f(3). Periodt. 🎀✨