TESTING/MATGEN/zlatm2.f(3)

TESTING/MATGEN/zlatm2.f

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NAME

TESTING/MATGEN/zlatm2.f

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SYNOPSIS

Functions/Subroutines

The lineup is literally this function/subroutine, no cap:

complex *16 function zlatm2 (m, n, i, j, kl, ku, idist, iseed, d,
           igrade, dl, dr, ipvtng, iwork, sparse)
           ZLATM2

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Function/Subroutine Documentation

Here's the full signature, bestie — every type and every space matters:

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.

⚠️ Caveat cutie: No error checking on parameters is done, because this routine is called in a tight loop by ZLATMR which has already checked the parameters. Keep that in mind, bestie.

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 — and yes, the source sentence trails off right there 😭).

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 — 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. Not modified.
  • 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 )
• ISEED — ISEED is INTEGER array of dimension ( 4 ). Seed for random number generator. Changed on exit.
• 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. Not modified.
  • 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 )
• 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. Not modified.
  • 0 => none.
  • 1 => row pivoting.
  • 2 => column pivoting.
  • 3 => full pivoting, i.e., on both sides.
• 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.
• 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 209 of file zlatm2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💖 that's the whole page, bestie. Source/version energy: LAPACK, Version 3.12.0, for TESTING/MATGEN/zlatm2.f(3). Now go be the main character of random test matrices. 🌈👑