ZDRVEV(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 ZDRVEV(3) 💅

Manual name: Library Functions Manual. The source title situation is /home/abui...IG/zdrvev.f(3) — folded in right here, bestie, because we’re doing this cute. ✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zdrvev.f

Okay so that’s the file, no cap. 💖

🦋 SYNOPSIS 🦋

🎀 Functions/Subroutines 🎀

subroutine ZDRVEV (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a,
    lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre, result, work, nwork,
    rwork, iwork, info)
    ZDRVEV

🌸 Function/Subroutine Documentation 🌸

💖 subroutine ZDRVEV 💖

subroutine ZDRVEV (integer nsizes, integer, dimension( * ) nn, integer
    ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed,
    double precision thresh, integer nounit, complex*16, dimension( lda, * )
    a, integer lda, complex*16, dimension( lda, * ) h, complex*16,
    dimension( * ) w, complex*16, dimension( * ) w1, complex*16, dimension(
    ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer
    ldvr, complex*16, dimension( ldlre, * ) lre, integer ldlre, double
    precision, dimension( 7 ) result, complex*16, dimension( * ) work,
    integer nwork, double precision, dimension( * ) rwork, integer,
    dimension( * ) iwork, integer info)
    ZDRVEV

🫶 ZDRVEV 🫶

ZDRVEV — that’s the routine, bestie. Main character energy fr fr. 👑

🌟 Purpose 🌟

ZDRVEV checks the nonsymmetric eigenvalue problem driver ZGEEV. That’s the whole vibe: this routine is the test queen for that driver. 👑

When ZDRVEV is called, a number of matrix () and a number of matrix are specified. For each size () and each type of matrix, one matrix will be generated and used to test the nonsymmetric eigenroutines. For each matrix, 7 tests will be performed:

  • (1) | A * VR - VR * W | / ( n |A| ulp )

Here VR is the matrix of unit right eigenvectors. W is a diagonal matrix with diagonal entries W(j).

  • (2) | A**H * VL - VL * W**H | / ( n |A| ulp )

Here VL is the matrix of unit left eigenvectors, A**H is the conjugate-transpose of A, and W is as above.

  • (3) | |VR(i)| - 1 | / ulp and whether largest component real

VR(i) denotes the i-th column of VR.

  • (4) | |VL(i)| - 1 | / ulp and whether largest component real

VL(i) denotes the i-th column of VL.

  • (5) W(full) = W(partial)

W(full) denotes the eigenvalues computed when both VR and VL are also computed, and W(partial) denotes the eigenvalues computed when only W, only W and VR, or only W and VL are computed.

  • (6) VR(full) = VR(partial)

VR(full) denotes the right eigenvectors computed when both VR and VL are computed, and VR(partial) denotes the result when only VR is computed.

  • (7) VL(full) = VL(partial)

VL(full) denotes the left eigenvectors computed when both VR and VL are also computed, and VL(partial) denotes the result when only VL is computed.

The are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size. The are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type will be generated. Currently, the list of possible types is:

  • (1) The zero matrix.
  • (2) The identity matrix.
  • (3) A (transposed) Jordan block, with 1's on the diagonal.
  • (4) A diagonal matrix with evenly spaced entries 1, ..., ULP and random complex angles. (ULP = (first number larger than 1) - 1 )
  • (5) A diagonal matrix with geometrically spaced entries 1, ..., ULP and random complex angles.
  • (6) A diagonal matrix with entries 1, ULP, ..., ULP and random complex angles.
  • (7) Same as (4), but multiplied by a constant near the overflow threshold
  • (8) Same as (4), but multiplied by a constant near the underflow threshold
  • (9) A matrix of the form U' T U, where U is unitary and T has evenly spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  • (10) A matrix of the form U' T U, where U is unitary and T has geometrically spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  • (11) A matrix of the form U' T U, where U is unitary and T has entries 1, ULP,..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  • (12) A matrix of the form U' T U, where U is unitary and T has complex eigenvalues randomly chosen from ULP < |z| < 1 and random O(1) entries in the upper triangle.
  • (13) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  • (14) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has geometrically spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  • (15) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has entries 1, ULP,..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  • (16) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has complex eigenvalues randomly chosen from ULP < |z| < 1 and random O(1) entries in the upper triangle.
  • (17) Same as (16), but multiplied by a constant near the overflow threshold
  • (18) Same as (16), but multiplied by a constant near the underflow threshold
  • (19) Nonsymmetric matrix with random entries chosen from |z| < 1. If N is at least 4, all entries in first two rows and last row, and first column and last two columns are zero.
  • (20) Same as (19), but multiplied by a constant near the overflow threshold
  • (21) Same as (19), but multiplied by a constant near the underflow threshold

🧚 Parameters 🧚

NSIZES

NSIZES is INTEGER. The number of sizes of matrices to use. If it is zero, ZDRVEV does nothing. It must be at least zero.

NN

NN is INTEGER array, dimension (NSIZES). An array containing the sizes to be used for the matrices. Zero values will be skipped. The values must be at least zero.

NTYPES

NTYPES is INTEGER. The number of elements in DOTYPE. If it is zero, ZDRVEV does nothing. It must be at least zero. If it is MAXTYP+1 and NSIZES is 1, then an additional type, MAXTYP+1 is defined, which is to use whatever matrix is in A. This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE..

DOTYPE

DOTYPE is LOGICAL array, dimension (NTYPES). If DOTYPE(j) is .TRUE., then for each size in NN a matrix of that size and of type j will be generated. If NTYPES is smaller than the maximum number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP will not be generated. If NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) will be ignored.

ISEED

ISEED is INTEGER array, dimension (4). On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must 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 ZDRVEV to continue the same random number sequence.

THRESH

THRESH is DOUBLE PRECISION. A test will count as if the , computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero.

NOUNIT

NOUNIT is INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)

A

A is COMPLEX*16 array, dimension (LDA, max(NN)). Used to hold the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used.

LDA

LDA is INTEGER. The leading dimension of A, and H. LDA must be at least 1 and at least max(NN).

H

H is COMPLEX*16 array, dimension (LDA, max(NN)). Another copy of the test matrix A, modified by ZGEEV.

W

W is COMPLEX*16 array, dimension (max(NN)). The eigenvalues of A. On exit, W are the eigenvalues of the matrix in A.

W1

🌸 parameter glow-up, continued

  • W1 — W1 is COMPLEX*16 array, dimension (max(NN)). Like W, this array contains the eigenvalues of A, but those computed when ZGEEV only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.
  • VL — VL is COMPLEX*16 array, dimension (LDVL, max(NN)). VL holds the computed left eigenvectors.
  • LDVL — LDVL is INTEGER. Leading dimension of VL. Must be at least max(1,max(NN)).
  • VR — VR is COMPLEX*16 array, dimension (LDVR, max(NN)). VR holds the computed right eigenvectors.
  • LDVR — LDVR is INTEGER. Leading dimension of VR. Must be at least max(1,max(NN)).
  • LRE — LRE is COMPLEX*16 array, dimension (LDLRE, max(NN)). LRE holds the computed right or left eigenvectors.
  • LDLRE — LDLRE is INTEGER. Leading dimension of LRE. Must be at least max(1,max(NN)).
  • RESULT — RESULT is DOUBLE PRECISION array, dimension (7). The values computed by the seven tests described above. The values are currently limited to 1/ulp, to avoid overflow.
  • WORK — WORK is COMPLEX*16 array, dimension (NWORK).
  • NWORK — NWORK is INTEGER. The number of entries in WORK. This must be at least 5*NN(j)+2*NN(j)**2 for all j.
  • RWORK — RWORK is DOUBLE PRECISION array, dimension (2*max(NN)).
  • IWORK — IWORK is INTEGER array, dimension (max(NN)).
  • INFO — INFO is INTEGER. If 0, then everything ran OK.
    • -1: NSIZES < 0
    • -2: Some NN(j) < 0
    • -3: NTYPES < 0
    • -6: THRESH < 0
    • -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    • -14: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ).
    • -16: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ).
    • -18: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ).
    • -21: NWORK too small.
    • If ZLATMR, CLATMS, CLATME or ZGEEV returns an error code, the absolute value of it is returned.

🧚 Some Local Variables and Parameters

  • ZERO, ONE — Real 0 and 1.
  • MAXTYP — The number of types defined.
  • NMAX — Largest value in NN.
  • NERRS — The number of tests which have exceeded THRESH
  • COND, CONDS, IMODE — Values to be passed to the matrix generators.
  • ANORM — Norm of A; passed to matrix generators.
  • OVFL, UNFL — Overflow and underflow thresholds.
  • ULP, ULPINV — Finest relative precision and its inverse.
  • RTULP, RTULPI — Square roots of the previous 4 values.

The following four arrays decode JTYPE:

  • KTYPE(j) — The general type (1-10) for type .
  • KMODE(j) — The MODE value to be passed to the matrix generator for type .
  • KMAGN(j) — The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) )
  • KCONDS(j) — Selectw whether CONDS is to be 1 or 1/sqrt(ulp). (0 means irrelevant.)

👑 Author

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

Definition at line 387 of file zdrvev.f.

🫶 Author

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💅 That’s the whole page, bestie — every parameter, every error code, every local variable, all accounted for. The footer’s source/version info is LAPACK Version 3.12.0 with the path /home/abui...IG/zdrvev.f(3). Go forth and vibe-check those eigenvectors 🦋✨

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