TESTING/MATGEN/clatme.f(3)

🌸 NAME 🌸

okay bestie, this is the manual page for TESTING/MATGEN/clatme.f(3) from the Library Functions Manual ✨ and it's all about CLATME, no cap 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines:

   Functions/Subroutines
       subroutine clatme (n, dist, iseed, d, mode, cond, dmax, rsign, upper,
           sim, ds, modes, conds, kl, ku, anorm, a, lda, work, info)
           CLATME

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💖 Function/Subroutine Documentation 💖

subroutine clatme (integer n, character dist, integer, dimension( 4 ) iseed,
     complex, dimension( * ) d, integer mode, real cond, complex dmax,
     character rsign, character upper, character sim, real, dimension( * )
     ds, integer modes, real conds, integer kl, integer ku, real anorm,
     complex, dimension( lda, * ) a, integer lda, complex, dimension( * )
     work, integer info)
CLATME

🌸 Purpose 🌸

CLATME generates random non-symmetric square matrices with specified eigenvalues for testing LAPACK programs 🔥

Here's the whole glow-up sequence, in order:

1. Set the diagonal to D, where D may be input or computed according to MODE, COND, DMAX, and RSIGN as described below.
2. If UPPER='T', the upper triangle of A is set to random values out of distribution DIST.
3. If SIM='T', A is multiplied on the left by a random matrix X, whose singular values are specified by DS, MODES, and CONDS, and on the right by X inverse.
4. If KL < N-1, the lower bandwidth is reduced to KL using Householder transformations. If KU < N-1, the upper bandwidth is reduced to KU.
5. If ANORM is not negative, the matrix is scaled to have maximum-element-norm ANORM.

(Note: since the matrix cannot be reduced beyond Hessenberg form, no packing options are available.)

🎀 Parameters 🎀

• N — N is INTEGER. The number of columns (or rows) of A. Not modified.
• DIST — DIST is CHARACTER*1. On entry, DIST specifies the type of distribution to be used to generate the random eigen-/singular values, and on the upper triangle (see UPPER).
  • 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform )
  • 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric )
  • 'N' => NORMAL( 0, 1 ) ( 'N' for normal )
  • 'D' => uniform on the complex disc |z| < 1. Not modified.
• ISEED — ISEED is INTEGER array, dimension ( 4 ). On entry ISEED specifies the seed of the random number generator. They should lie between 0 and 4095 inclusive, and ISEED(4) should be odd. The random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to CLATME to continue the same random number sequence. Changed on exit.
• D — D is COMPLEX array, dimension ( N ). This array is used to specify the eigenvalues of A. If MODE=0, then D is assumed to contain the eigenvalues otherwise they will be computed according to MODE, COND, DMAX, and RSIGN and placed in D. Modified if MODE is nonzero.
• MODE — MODE is INTEGER. On entry this describes how the eigenvalues are to be specified:
  • MODE = 0 means use D as input
  • MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
  • MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
  • MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
  • MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
  • MODE = 5 sets D to random numbers in the range ( 1/COND , 1 ) such that their logarithms are uniformly distributed.
  • MODE = 6 set D to random numbers from same distribution as the rest of the matrix.
  • MODE < 0 has the same meaning as ABS(MODE), except that the order of the elements of D is reversed. Thus if MODE is between 1 and 4, D has entries ranging from 1 to 1/COND, if between -1 and -4, D has entries ranging from 1/COND to 1, Not modified.
• COND — COND is REAL. On entry, this is used as described under MODE above. If used, it must be >= 1. Not modified.
• DMAX — DMAX is COMPLEX. If MODE is neither -6, 0 nor 6, the contents of D, as computed according to MODE and COND, will be scaled by DMAX / max(abs(D(i))). Note that DMAX need not be positive or real: if DMAX is negative or complex (or zero), D will be scaled by a negative or complex number (or zero). If RSIGN='F' then the largest (absolute) eigenvalue will be equal to DMAX. Not modified.
• RSIGN — RSIGN is CHARACTER*1. If MODE is not 0, 6, or -6, and RSIGN='T', then the elements of D, as computed according to MODE and COND, will be multiplied by a random complex number from the unit circle |z| = 1. If RSIGN='F', they will not be. RSIGN may only have the values 'T' or 'F'. Not modified.
• UPPER — UPPER is CHARACTER*1. If UPPER='T', then the elements of A above the diagonal will be set to random numbers out of DIST. If UPPER='F', they will not. UPPER may only have the values 'T' or 'F'. Not modified.
• SIM — SIM is CHARACTER*1. If SIM='T', then A will be operated on by a , i.e., multiplied on the left by a matrix X and on the right by X inverse. X = U S V, where U and V are random unitary matrices and S is a (diagonal) matrix of singular values specified by DS, MODES, and CONDS. If SIM='F', then A will not be transformed. Not modified.
• DS — DS is REAL array, dimension ( N ). This array is used to specify the singular values of X, in the same way that D specifies the eigenvalues of A. If MODE=0, the DS contains the singular values, which may not be zero. Modified if MODE is nonzero.
• MODES — MODES is INTEGER.
• CONDS — CONDS is REAL. Similar to MODE and COND, but for specifying the diagonal of S. MODES=-6 and +6 are not allowed (since they would result in randomly ill-conditioned eigenvalues.)
• KL — KL is INTEGER. This specifies the lower bandwidth of the matrix. KL=1 specifies upper Hessenberg form. If KL is at least N-1, then A will have full lower bandwidth. Not modified.
• KU — KU is INTEGER. This specifies the upper bandwidth of the matrix. KU=1 specifies lower Hessenberg form. If KU is at least N-1, then A will have full upper bandwidth; if KU and KL are both at least N-1, then A will be dense. Only one of KU and KL may be less than N-1. Not modified.
• ANORM — ANORM is REAL. If ANORM is not negative, then A will be scaled by a non-negative real number to make the maximum-element-norm of A to be ANORM. Not modified.
• A — A is COMPLEX array, dimension ( LDA, N ). On exit A is the desired test matrix. Modified.
• LDA — LDA is INTEGER. LDA specifies the first dimension of A as declared in the calling program. LDA must be at least M. Not modified.
• WORK — WORK is COMPLEX array, dimension ( 3*N ). Workspace. Modified.
• INFO — INFO is INTEGER. Error code. On exit, INFO will be set to one of the following values:

 0 => normal return
-1 => N negative
-2 => DIST illegal string
-5 => MODE not in range -6 to 6
-6 => COND less than 1.0, and MODE neither -6, 0 nor 6
-9 => RSIGN is not 'T' or 'F'
-10 => UPPER is not 'T' or 'F'
-11 => SIM   is not 'T' or 'F'
-12 => MODES=0 and DS has a zero singular value.
-13 => MODES is not in the range -5 to 5.
-14 => MODES is nonzero and CONDS is less than 1.
-15 => KL is less than 1.
-16 => KU is less than 1, or KL and KU are both less than
       N-1.
-19 => LDA is less than M.
 1  => Error return from CLATM1 (computing D)
 2  => Cannot scale to DMAX (max. eigenvalue is 0)
 3  => Error return from SLATM1 (computing DS)
 4  => Error return from CLARGE
 5  => Zero singular value from SLATM1.

👑 Author 👑

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

Definition at line 296 of file clatme.f.

💻 Author (generated) 💻

Generated automatically by Doxygen for LAPACK from the source code.

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