ZDRVBD(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME

okay so bestie, welcome to zdrvbd.f(3) — straight outta the Library Functions Manual, and it’s giving “SVD test driver main character energy” fr fr. 💅

The file itself is:

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

No cap, that path is a whole journey. 🛤️

bestie, this is part 1 of a long page. Buckle up — the parameters are literally coming.

📜 SYNOPSIS

🛠️ Functions/Subroutines

       subroutine ZDRVBD (nsizes, mm, nn, ntypes, dotype, iseed, thresh, a,
           lda, u, ldu, vt, ldvt, asav, usav, vtsav, s, ssav, e, work, lwork,
           rwork, iwork, nounit, info)
           ZDRVBD

📚 Function/Subroutine Documentation

Here’s the full signature, bestie — every type, every dimension, all of it:

   subroutine ZDRVBD (integer nsizes, integer, dimension( * ) mm, integer,
       dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype,
       integer, dimension( 4 ) iseed, double precision thresh, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( ldu, * ) u,
       integer ldu, complex*16, dimension( ldvt, * ) vt, integer ldvt,
       complex*16, dimension( lda, * ) asav, complex*16, dimension( ldu, * )
       usav, complex*16, dimension( ldvt, * ) vtsav, double precision,
       dimension( * ) s, double precision, dimension( * ) ssav, double
       precision, dimension( * ) e, complex*16, dimension( * ) work, integer
       lwork, double precision, dimension( * ) rwork, integer, dimension( * )
       iwork, integer nounit, integer info)
       ZDRVBD

That’s our icon: ZDRVBD. 👑

🎯 Purpose

okay so ZDRVBD checks the singular value decomposition (SVD) driver ZGESVD, ZGESDD, ZGESVJ, ZGEJSV, ZGESVDX, and ZGESVDQ. It is lowkey the vibe-check queen for these routines. ✨

ZGESVD and ZGESDD factor A = U diag(S) VT, where U and VT are unitary and diag(S) is diagonal with the entries of the array S on its diagonal. The entries of S are the singular values, nonnegative and stored in decreasing order. U and VT can be optionally not computed, overwritten on A, or computed partially. Periodt.

A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN. U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.

When ZDRVBD is called, a number of matrix sizes (M’s and N’s) and a number of matrix types are specified. For each size (M,N) and each type of matrix, and for the minimal workspace as well as workspace adequate to permit blocking, an M x N matrix will be generated and used to test the SVD routines. For each matrix, A will be factored as A = U diag(S) VT and the following 12 tests computed:

  • Test for ZGESVD:
    • (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    • (2) | I - U'U | / ( M ulp )
    • (3) | I - VT VT' | / ( N ulp )
    • (4) S contains MNMIN nonnegative values in decreasing order. (Return 0 if true, 1/ULP if false.)
    • (5) | U - Upartial | / ( M ulp ) where Upartial is a partially computed U.
    • (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially computed VT.
    • (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the vector of singular values from the partial SVD
  • Test for ZGESDD:
    • (8) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    • (9) | I - U'U | / ( M ulp )
    • (10) | I - VT VT' | / ( N ulp )
    • (11) S contains MNMIN nonnegative values in decreasing order. (Return 0 if true, 1/ULP if false.)
    • (12) | U - Upartial | / ( M ulp ) where Upartial is a partially computed U.
    • (13) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially computed VT.
    • (14) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the vector of singular values from the partial SVD
  • Test for ZGESVDQ:
    • (36) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    • (37) | I - U'U | / ( M ulp )
    • (38) | I - VT VT' | / ( N ulp )
    • (39) S contains MNMIN nonnegative values in decreasing order. (Return 0 if true, 1/ULP if false.)
  • Test for ZGESVJ:
    • (15) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    • (16) | I - U'U | / ( M ulp )
    • (17) | I - VT VT' | / ( N ulp )
    • (18) S contains MNMIN nonnegative values in decreasing order. (Return 0 if true, 1/ULP if false.)
  • Test for ZGEJSV:
    • (19) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    • (20) | I - U'U | / ( M ulp )
    • (21) | I - VT VT' | / ( N ulp )
    • (22) S contains MNMIN nonnegative values in decreasing order. (Return 0 if true, 1/ULP if false.)
  • Test for ZGESVDX( 'V', 'V', 'A' )/ZGESVDX( 'N', 'N', 'A' ):
    • (23) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
    • (24) | I - U'U | / ( M ulp )
    • (25) | I - VT VT' | / ( N ulp )
    • (26) S contains MNMIN nonnegative values in decreasing order. (Return 0 if true, 1/ULP if false.)
    • (27) | U - Upartial | / ( M ulp ) where Upartial is a partially computed U.
    • (28) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially computed VT.
    • (29) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the vector of singular values from the partial SVD
  • Test for ZGESVDX( 'V', 'V', 'I' ):
    • (30) | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
    • (31) | I - U'U | / ( M ulp )
    • (32) | I - VT VT' | / ( N ulp )
  • Test for ZGESVDX( 'V', 'V', 'V' ):
    • (33) | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
    • (34) | I - U'U | / ( M ulp )
    • (35) | I - VT VT' | / ( N ulp )

The sizes are specified by the arrays MM(1:NSIZES) and NN(1:NSIZES); the value of each element pair (MM(j),NN(j)) specifies one size. The types 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 matrix of the form U D V, where U and V are unitary and D has evenly spaced entries 1, ..., ULP with random signs on the diagonal.
  4. Same as (3), but multiplied by the underflow-threshold / ULP.
  5. Same as (3), but multiplied by the overflow-threshold * ULP.

🌸 Parameters

NSIZES

NSIZES is INTEGER. It’s the number of sizes of matrices to use. If it is zero, ZDRVBD does nothing. It must be at least zero.

MM

MM is INTEGER array, dimension (NSIZES). An array containing the matrix sizes to be used. For each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j) will be ignored. The MM(j) values must be at least zero.

NN

NN is INTEGER array, dimension (NSIZES). An array containing the matrix sizes to be used. For each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j) will be ignored. The NN(j) values must be at least zero.

NTYPES

NTYPES is INTEGER. The number of elements in DOTYPE. If it is zero, ZDRVBD 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 matrices are in A and B. 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 (m,n), a matrix 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 ZDRVBD to continue the same random number sequence.

THRESH

THRESH is DOUBLE PRECISION. A test will count as failed if the error, 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.

A

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

LDA

LDA is INTEGER. The leading dimension of A. It must be at least 1 and at least max( MM ).

U

U is COMPLEX*16 array, dimension (LDU,max(MM)). Used to hold the computed matrix of right singular vectors. On exit, U contains the last such vectors actually computed.

LDU

LDU is INTEGER. The leading dimension of U. It must be at least 1 and at least max( MM ).

VT

VT is COMPLEX*16 array, dimension (LDVT,max(NN)). Used to hold the computed matrix of left singular vectors. On exit, VT contains the last such vectors actually computed.

  • LDVT — INTEGER. It's the leading dimension of VT, bestie. Gotta be at least 1 and at least max( NN ). No cap ✨
  • ASAV — COMPLEX*16 array, dimension (LDA,max(NN)). Holds a different copy of the matrix whose singular values are to be computed. On exit, A contains the last matrix actually used. (Yes, A — that's literally what it says 👀)
  • USAV — COMPLEX*16 array, dimension (LDU,max(MM)). Holds a different copy of the computed matrix of right singular vectors. On exit, USAV contains the last such vectors actually computed. 💖
  • VTSAV — COMPLEX*16 array, dimension (LDVT,max(NN)). Holds a different copy of the computed matrix of left singular vectors. On exit, VTSAV contains the last such vectors actually computed. 🦋
  • S — DOUBLE PRECISION array, dimension (max(min(MM,NN))). Contains the computed singular values. Periodt.
  • SSAV — DOUBLE PRECISION array, dimension (max(min(MM,NN))). Contains another copy of the computed singular values. Iconic backup behavior.
  • E — DOUBLE PRECISION array, dimension (max(min(MM,NN))). Workspace for ZGESVD. Slay.
  • WORK — COMPLEX*16 array, dimension (LWORK). The workspace main character.
  • LWORK — INTEGER. The number of entries in WORK. This must be at least MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all pairs (M,N)=(MM(j),NN(j)). That's the whole vibe check, don't skimp 🔥
  • RWORK — DOUBLE PRECISION array, dimension ( 5*max(max(MM,NN)) ). Real ones know.
  • IWORK — INTEGER array, dimension at least 8*min(M,N). Integer energy only 💅
  • NOUNIT — INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.) Note the IINFO, bestie — that's what it says.
  • INFO — INTEGER. If 0, then everything ran OK. But if not, here are the receipts:
    • -1: NSIZES < 0
    • -2: Some MM(j) < 0
    • -3: Some NN(j) < 0
    • -4: NTYPES < 0
    • -7: THRESH < 0
    • -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
    • -12: LDU < 1 or LDU < MMAX.
    • -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ).
    • -21: LWORK too small.

If ZLATMS, or ZGESVD returns an error code, the absolute value of it is returned.

👑 Author

The brain trust, fr fr:

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

Definition at line 397 of file zdrvbd.f. That's where the magic lives ✨

✨ Author

Generated automatically by Doxygen for LAPACK from the source code. So you know it's official 💅

okay that's the whole parameter glow-up, bestie. This page is serving LAPACK Version 3.12.0, straight from /home/abui...IG/zdrvbd.f(3) — catch you in the source, mwah 💋✨

📦 where this page comes from