/home/abui...N/slatm2.f(3)

🎀 slatm2.f(3) — Library Functions Manual 🎀

Okay bestie, welcome to the slatm2.f(3) page from the Library Functions Manual. It's a LAPACK source-file page for SLATM2, and it's lowkey serving “internal helper that knows exactly what it's doing” energy. ✨

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/slatm2.f

That's the whole name, no cap. Periodt. 💅

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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)
           SLATM2

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💖 Function/Subroutine Documentation 💖

   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

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. And ngl, there is no error checking on parameters done here, because this routine is called in a tight loop by SLATMR, which has already checked the parameters. So it's giving “trust me bestie, the grown-up already did the vibe check.” 😌

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 🫠

The matrix whose (I,J) entry is returned is constructed as follows — and yes, 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.

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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 => 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 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.

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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.

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Source/version sign-off: LAPACK Version 3.12.0, footer path /home/abui...N/slatm2.f(3) — the date isn't sitting in this footer, so I'm not inventing one, bestie. Mwah 💋✨