TESTING/MATGEN/zlatme.f(3)

💅 TESTING/MATGEN/zlatme.f

okay bestie, you're looking at the TESTING/MATGEN/zlatme.f(3) page from the Library Functions Manual, and we are absolutely about to vibe-check a random-matrix generator. No cap: every flag, formula, error code, and author line is still in here. 🫶

🌸 NAME 🌸

TESTING/MATGEN/zlatme.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine zlatme (n, dist, iseed, d, mode, cond, dmax, rsign, upper,
    sim, ds, modes, conds, kl, ku, anorm, a, lda, work, info)
    ZLATME

💖 Function/Subroutine Documentation 💖

subroutine zlatme (integer n, character dist, integer, dimension( 4 ) iseed,
    complex*16, dimension( * ) d, integer mode, double precision cond,
    complex*16 dmax, character rsign, character upper, character sim, double
    precision, dimension( * ) ds, integer modes, double precision conds,
    integer kl, integer ku, double precision anorm, complex*16, dimension(
    lda, * ) a, integer lda, complex*16, dimension( * ) work, integer info)
    ZLATME

🎯 Purpose 🎯

ZLATME generates random non-symmetric square matrices with specified eigenvalues for testing LAPACK programs. Iconic behavior, honestly.

ZLATME operates by applying the following sequence of operations:

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 bestie: since the matrix cannot be reduced beyond Hessenberg form, no packing options are available. That's not me being dramatic, that's just the rule. 💀

🧚 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 ZLATME to continue the same random number sequence. Changed on exit.
• D — D is COMPLEX*16 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 sets D to random numbers from the 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 DOUBLE PRECISION. On entry, this is used as described under MODE above. If used, it must be >= 1. Not modified.
• DMAX — DMAX is COMPLEX*16. 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 DOUBLE PRECISION 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 DOUBLE PRECISION. 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 DOUBLE PRECISION. 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*16 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*16 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 ZLATM1 (computing D)
  • 2 => Cannot scale to DMAX (max. eigenvalue is 0)
  • 3 => Error return from DLATM1 (computing DS)
  • 4 => Error return from ZLARGE
  • 5 => Zero singular value from DLATM1.

👑 Author 👑

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

📍 Definition at line 📍

Definition at line 296 of file zlatme.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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