ZDRVSG2STG(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 NAME 🦋

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zdrvsg2stg.f

okay so bestie, the "NAME" here is literally just the whole path to the file — like, that's the entire name section. The header up top goes /home/abui...drvsg2stg.f(3) Library Functions Manual /home/abui...drvsg2stg.f(3), and then the NAME is the full /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zdrvsg2stg.f path. no cap. that's it. that's the name. 💀

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZDRVSG2STG (nsizes, nn, ntypes, dotype, iseed, thresh,
    nounit, a, lda, b, ldb, d, d2, z, ldz, ab, bb, ap, bp, work, nwork,
    rwork, lrwork, iwork, liwork, result, info)

ZDRVSG2STG — that's the whole synopsis, she's right there 💅

🎀 FUNCTION/SUBROUTINE DOCUMENTATION 🎀

subroutine ZDRVSG2STG

here's the full signature so you can see every single argument with her type and dimensions, exactly as written, no shrinkage:

subroutine ZDRVSG2STG (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( ldb, * ) b, integer ldb, double
    precision, dimension( * ) d, double precision, dimension( * ) d2,
    complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension(
    lda, * ) ab, complex*16, dimension( ldb, * ) bb, complex*16, dimension(
    * ) ap, complex*16, dimension( * ) bp, complex*16, dimension( * ) work,
    integer nwork, double precision, dimension( * ) rwork, integer lrwork,
    integer, dimension( * ) iwork, integer liwork, double precision,
    dimension( * ) result, integer info)

ZDRVSG2STG 🌸

✨ Purpose ✨

!> !> ZDRVSG2STG checks the complex Hermitian generalized eigenproblem !> drivers. !>

okay so the whole vibe of this subroutine is: she is the quality-control bestie for the complex Hermitian generalized eigenproblem drivers. she runs them, she checks them, she reports back. main character energy for a test routine, honestly. 🎀

here's her crew, the drivers she's checking on:

!> ZHEGV computes all eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite generalized !> eigenproblem.
!> ZHEGVD computes all eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite generalized !> eigenproblem using a divide and conquer algorithm.
!> ZHEGVX computes selected eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite generalized !> eigenproblem.
!> ZHPGV computes all eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite generalized !> eigenproblem in packed storage.
!> ZHPGVD computes all eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite generalized !> eigenproblem in packed storage using a divide and !> conquer algorithm.
!> ZHPGVX computes selected eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite generalized !> eigenproblem in packed storage.
!> ZHBGV computes all eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite banded !> generalized eigenproblem.
!> ZHBGVD computes all eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite banded !> generalized eigenproblem using a divide and conquer !> algorithm.
!> ZHBGVX computes selected eigenvalues and, optionally, !> eigenvectors of a complex Hermitian-definite banded !> generalized eigenproblem.

slay, that's nine drivers. she keeps track of all of them. 🔥

!> When ZDRVSG2STG is called, a number of matrix () and a !> number of matrix are specified. For each size () !> and each type of matrix, one matrix A of the given type will be !> generated; a random well-conditioned matrix B is also generated !> and the pair (A,B) is used to test the drivers. !>

and yes — the blank spots in a number of matrix () are literally in the original, the roff ate some words and honestly good for her 🙈 i'm not gonna make up what was there, so you get the gaps exactly as they are.

so the deal is: for each size and each type of matrix, one matrix A of that type gets generated, plus a random well-conditioned matrix B, and then the pair (A,B) gets thrown at the drivers. that's the whole setup. 🫶

!> For each pair (A,B), the following tests are performed: !>

okay here comes the checklist, this is the part where she pops off 💅

!> (1) ZHEGV with ITYPE = 1 and UPLO ='U': !> !> | A Z - B Z D | / ( |A| |Z| n ulp ) !> | D - D2 | / ( |D| ulp ) where D is computed by !> ZHEGV and D2 is computed by !> ZHEGV_2STAGE. This test is !> only performed for DSYGV !>

so test (1) is ZHEGV with ITYPE = 1 and UPLO ='U', checking those two residuals:

| A Z - B Z D | / ( |A| |Z| n ulp )
| D - D2 | / ( |D| ulp )   where D is computed by
                           ZHEGV and  D2 is computed by
                           ZHEGV_2STAGE. This test is
                           only performed for DSYGV

(yes it says DSYGV at the end there even though everything around it is Z-flavoured — that's what the page says and i'm not touching it, iykyk 🌸)

!> (2) as (1) but calling ZHPGV !> (3) as (1) but calling ZHBGV !> (4) as (1) but with UPLO = 'L' !> (5) as (4) but calling ZHPGV !> (6) as (4) but calling ZHBGV !>

okay the next six, rapid fire, all the same energy just different drivers and different UPLO:

  1. (2) as (1) but calling ZHPGV
  2. (3) as (1) but calling ZHBGV
  3. (4) as (1) but with UPLO = 'L'
  4. (5) as (4) but calling ZHPGV
  5. (6) as (4) but calling ZHBGV

wait that's five, let me recount — no, it's (2) through (6), that's five items, (1) was already done above. ok we're fine. moving on 🧚

!> (7) ZHEGV with ITYPE = 2 and UPLO ='U': !> !> | A B Z - Z D | / ( |A| |Z| n ulp ) !> !> (8) as (7) but calling ZHPGV !> (9) as (7) but with UPLO = 'L' !> (10) as (9) but calling ZHPGV !>

(7) is ZHEGV with ITYPE = 2 and UPLO ='U', and the residual is:

| A B Z - Z D | / ( |A| |Z| n ulp )

then (8), (9), (10) are the remixes:

  • (8) as (7) but calling ZHPGV
  • (9) as (7) but with UPLO = 'L'
  • (10) as (9) but calling ZHPGV
!> (11) ZHEGV with ITYPE = 3 and UPLO ='U': !> !> | B A Z - Z D | / ( |A| |Z| n ulp ) !> !> (12) as (11) but calling ZHPGV !> (13) as (11) but with UPLO = 'L' !> (14) as (13) but calling ZHPGV !>

and (11) is ZHEGV with ITYPE = 3 and UPLO ='U', residual:

| B A Z - Z D | / ( |A| |Z| n ulp )

plus:

  • (12) as (11) but calling ZHPGV
  • (13) as (11) but with UPLO = 'L'
  • (14) as (13) but calling ZHPGV

that's the full 14, we ate. 👑

!> ZHEGVD, ZHPGVD and ZHBGVD performed the same 14 tests. !>

the divide and conquer girlies — ZHEGVD, ZHPGVD and ZHBGVD — run the exact same 14 tests. same energy, different algorithm. ✨

!> ZHEGVX, ZHPGVX and ZHBGVX performed the above 14 tests with !> the parameter RANGE = 'A', 'N' and 'I', respectively. !>

and the selective ones — ZHEGVX, ZHPGVX and ZHBGVX — run those same 14 tests above, but with the parameter RANGE = 'A', 'N' and 'I', respectively. 🦋

!> 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. !> This type is used for the matrix A which has half-bandwidth KA. !> B is generated as a well-conditioned positive definite matrix !> with half-bandwidth KB (<= KA). !>

okay so the sizes live in the array NN(1:NSIZES) — each element NN(j) specifies one size. and the types live in the logical array DOTYPE( 1:NTYPES ) — if DOTYPE(j) is .TRUE., then that matrix type gets generated. (more blank spots in the original there, again, not me, the roff was hungry 🙈)

that type is used for the matrix A, which has half-bandwidth KA. B is generated as a well-conditioned positive definite matrix with half-bandwidth KB (<= KA). cute. matching bandwidths, bestie behaviour. 💜

!> Currently, the list of possible types for A is: !>

alright, the type menu. 21 of them. let's go one by one, no skipping, i promised. 🍓

!> (1) The zero matrix. !> (2) The identity matrix.
  • (1) — The zero matrix. (nothing. empty. void. she contains multitudes of zero 💀)
  • (2) — The identity matrix.
!> (3) A diagonal matrix with evenly spaced entries !> 1, ..., ULP and random signs. !> (ULP = (first number larger than 1) - 1 ) !> (4) A diagonal matrix with geometrically spaced entries !> 1, ..., ULP and random signs. !> (5) A diagonal matrix with entries 1, ULP, ..., ULP !> and random signs.
  • (3) — A diagonal matrix with evenly spaced entries 1, ..., ULP and random signs. And yes, (ULP = (first number larger than 1) - 1 ) — that's the definition, keep it.
  • (4) — A diagonal matrix with geometrically spaced entries 1, ..., ULP and random signs.
  • (5) — A diagonal matrix with entries 1, ULP, ..., ULP and random signs. (there's a doubled space in the original right before entries, live with it, i do 🫶)
!> (6) Same as (4), but multiplied by SQRT( overflow threshold ) !> (7) Same as (4), but multiplied by SQRT( underflow threshold )
  • (6) — Same as (4), but multiplied by SQRT( overflow threshold ) 🔥
  • (7) — Same as (4), but multiplied by SQRT( underflow threshold ) 🌊
!> (8) A matrix of the form U* D U, where U is unitary and !> D has evenly spaced entries 1, ..., ULP with random signs !> on the diagonal.
  • (8) — A matrix of the form U* D U, where U is unitary and D has evenly spaced entries 1, ..., ULP with random signs on the diagonal.
!> (9) A matrix of the form U* D U, where U is unitary and !> D has geometrically spaced entries 1, ..., ULP with random !> signs on the diagonal.
  • (9) — A matrix of the form U* D U, where U is unitary and D has geometrically spaced entries 1, ..., ULP with random signs on the diagonal.
!> (10) A matrix of the form U* D U, where U is unitary and !> D has entries 1, ULP,..., ULP with random !> signs on the diagonal.
  • (10) — A matrix of the form U* D U, where U is unitary and D has entries 1, ULP,..., ULP with random signs on the diagonal.
!> (11) Same as (8), but multiplied by SQRT( overflow threshold ) !> (12) Same as (8), but multiplied by SQRT( underflow threshold )
  • (11) — Same as (8), but multiplied by SQRT( overflow threshold )
  • (12) — Same as (8), but multiplied by SQRT( underflow threshold )
!> (13) Hermitian matrix with random entries chosen from (-1,1). !> (14) Same as (13), but multiplied by SQRT( overflow threshold ) !> (15) Same as (13), but multiplied by SQRT( underflow threshold )
  • (13) — Hermitian matrix with random entries chosen from (-1,1).
  • (14) — Same as (13), but multiplied by SQRT( overflow threshold )
  • (15) — Same as (13), but multiplied by SQRT( underflow threshold )
!> (16) Same as (8), but with KA = 1 and KB = 1 !> (17) Same as (8), but with KA = 2 and KB = 1 !> (18) Same as (8), but with KA = 2 and KB = 2 !> (19) Same as (8), but with KA = 3 and KB = 1 !> (20) Same as (8), but with KA = 3 and KB = 2 !> (21) Same as (8), but with KA = 3 and KB = 3

and the bandwidth remixes, all "Same as (8)" just with different KA / KB:

  • (16) — Same as (8), but with KA = 1 and KB = 1
  • (17) — Same as (8), but with KA = 2 and KB = 1
  • (18) — Same as (8), but with KA = 2 and KB = 2
  • (19) — Same as (8), but with KA = 3 and KB = 1
  • (20) — Same as (8), but with KA = 3 and KB = 2
  • (21) — Same as (8), but with KA = 3 and KB = 3

that's the whole type list, 1 through 21, all accounted for, no stragglers. 🎀

  • NSIZES — INTEGER; the number of sizes of matrices to use. If it is zero, ZDRVSG2STG does nothing. It must be at least zero. Not modified.
  • NN — 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. Not modified.
  • NTYPES — INTEGER; the number of elements in DOTYPE. If it is zero, ZDRVSG2STG 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. . Not modified.
  • DOTYPE — 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. Not modified.
  • ISEED — 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 ZDRVSG2STG to continue the same random number sequence. Modified.
  • THRESH — 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. Not modified.
  • NOUNIT — INTEGER; the FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.) Not modified.
  • A — 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. Modified.
  • LDA — INTEGER; the leading dimension of A. It must be at least 1 and at least max( NN ). Not modified.
  • B — COMPLEX*16 array, dimension (LDB , max(NN)); used to hold the Hermitian positive definite matrix for the generalized problem. On exit, B contains the last matrix actually used. Modified.
  • LDB — INTEGER; the leading dimension of B. It must be at least 1 and at least max( NN ). Not modified.
  • D — DOUBLE PRECISION array, dimension (max(NN)); the eigenvalues of A. On exit, the eigenvalues in D correspond with the matrix in A. Modified.
  • Z — COMPLEX*16 array, dimension (LDZ, max(NN)); the matrix of eigenvectors. Modified.
  • LDZ — INTEGER; the leading dimension of ZZ. It must be at least 1 and at least max( NN ). Not modified.
  • AB — COMPLEX*16 array, dimension (LDA, max(NN)); workspace. Modified.
  • BB — COMPLEX*16 array, dimension (LDB, max(NN)); workspace. Modified.
  • AP — COMPLEX*16 array, dimension (max(NN)**2); workspace. Modified.
  • BP — COMPLEX*16 array, dimension (max(NN)**2); workspace. Modified.
  • WORK — COMPLEX*16 array, dimension (NWORK); workspace. Modified.
  • NWORK — INTEGER; the number of entries in WORK. This must be at least 2*N + N**2 where N = max( NN(j), 2 ). Not modified.
  • RWORK — DOUBLE PRECISION array, dimension (LRWORK); workspace. Modified.
  • LRWORK — INTEGER; the number of entries in RWORK. This must be at least max( 7*N, 1 + 4*N + 2*N*lg(N) + 3*N**2 ) where N = max( NN(j) ) and lg( N ) = smallest integer k such that 2**k >= N . Not modified.
  • IWORK — INTEGER array, dimension (LIWORK)); workspace. Modified.
  • LIWORK — INTEGER; the number of entries in IWORK. This must be at least 2 + 5*max( NN(j) ). Not modified.
  • RESULT — DOUBLE PRECISION array, dimension (70); the values computed by the 70 tests described above. Modified.
  • INFO — INTEGER; if 0, then everything ran OK.
    • -1: NSIZES < 0
    • -2: Some NN(j) < 0
    • -3: NTYPES < 0
    • -5: THRESH < 0
    • -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    • -16: LDZ < 1 or LDZ < NMAX.
    • -21: NWORK too small.
    • -23: LRWORK too small.
    • -25: LIWORK too small. If ZLATMR, CLATMS, ZHEGV, ZHPGV, ZHBGV, CHEGVD, CHPGVD, ZHPGVD, ZHEGVX, CHPGVX, ZHBGVX returns an error code, the absolute value of it is returned. Modified.

Some Local Variables and Parameters: 🧚

  • ZERO, ONE — Real 0 and 1.
  • MAXTYP — The number of types defined.
  • NTEST — The number of tests that have been run on this matrix.
  • NTESTT — The total number of tests for this call.
  • NMAX — Largest value in NN.
  • NMATS — The number of matrices generated so far.
  • NERRS — The number of tests which have exceeded THRESH so far (computed by DLAFTS).
  • COND, 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.
  • RTOVFL, RTUNFL — Square roots of the previous 2 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) )

Author 👑

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

Definition at line 372 of file zdrvsg2stg.f.

Author 💻

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