DDRVBD(3)

📦 version 3.12.0, in opensuse-leap 16.0

DDRVBD(3) 💅✨

Okay bestie, this page is from the Library Functions Manual, and it is so LAPACK testing coded. We are in DDRVBD(3) territory: SVD drivers, test ratios, and a whole lot of “bestie, trust the math.” 🦋

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ddrvbd.f — that is literally the file, no extra lore. Slay. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

  • subroutine DDRVBD — the icon itself, with the full crew of arguments in the code block below. 👑
subroutine DDRVBD (nsizes, mm, nn, ntypes, dotype, iseed, thresh, a,
    lda, u, ldu, vt, ldvt, asav, usav, vtsav, s, ssav, e, work, lwork,
    iwork, nout, info)
    DDRVBD

💖 Function/Subroutine Documentation 💖

🦋 subroutine DDRVBD 🦋

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

🎯 Purpose 🎯

Okay so DDRVBD checks the singular value decomposition (SVD) drivers DGESVD, DGESDD, DGESVDQ, DGESVJ, DGEJSV, and DGESVDX. It is giving “quality control but make it couture.” 💅

Both DGESVD and DGESDD factor A = U diag(S) VT, where U and VT are orthogonal 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. 🫶

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. Literally the shape lore. 📐

When DDRVBD 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 DGESVD:

  • (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 DGESDD:

  • (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 DGESVDQ:

  • (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 DGESVJ:

  • (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 DGEJSV:

  • (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 DGESVDX( 'V', 'V', 'A' )/DGESVDX( '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 DGESVDX( '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 DGESVDX( '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 orthogonal 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 is the number of matrix sizes (M,N) contained in the vectors MM and NN. Count ‘em, bestie. ✨
  • MM — MM is INTEGER array, dimension (NSIZES). The values of the matrix row dimension M. 🍓
  • NN — NN is INTEGER array, dimension (NSIZES). The values of the matrix column dimension N. 🦋
  • NTYPES — NTYPES is INTEGER. It is the number of elements in DOTYPE. If it is zero, DDRVBD 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.. Keep that exact condition, iykyk. 💀
  • 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, it is 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. On exit, ISEED is changed and can be used in the next call to DDRVBD to continue the same random number sequence. 🔥
  • THRESH — THRESH is DOUBLE PRECISION. It is the threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. The test ratios are scaled to be O(1), so THRESH should be a small multiple of 1, e.g., 10 or 100. To have every test ratio printed, use THRESH = 0. 💅
  • A — A is DOUBLE PRECISION array, dimension (LDA,NMAX), where NMAX is the maximum value of N in NN. 🌈
  • LDA — LDA is INTEGER. It is the leading dimension of the array A. LDA >= max(1,MMAX), where MMAX is the maximum value of M in MM. 👑
  • U — U is DOUBLE PRECISION array, dimension (LDU,MMAX). ⭐
  • LDU — LDU is INTEGER. It is the leading dimension of the array U. LDU >= max(1,MMAX). 🎀
  • VT — VT is DOUBLE PRECISION array, dimension (LDVT,NMAX). 🦋
  • LDVT — LDVT is INTEGER. It is the leading dimension of the array VT. LDVT >= max(1,NMAX). 💖
  • ASAV — ASAV is DOUBLE PRECISION array, dimension (LDA,NMAX). 💜
  • USAV — USAV is DOUBLE PRECISION array, dimension (LDU,MMAX). 🌸
  • VTSAV — VTSAV is DOUBLE PRECISION array, dimension (LDVT,NMAX). ✨
  • S — S is DOUBLE PRECISION array, dimension (max(min(MM,NN))). 🍓
  • SSAV — SSAV is DOUBLE PRECISION array, dimension (max(min(MM,NN))). 🧚
  • E — E is DOUBLE PRECISION array, dimension (max(min(MM,NN))). 🎀
  • WORK — WORK is DOUBLE PRECISION array, dimension (LWORK). 🌈
  • LWORK — this is where part 1 cuts off; the original page ends at LWORK before giving the description. Part 2 has the rest. 🫶

okay so the argument-list queen is still going, and honestly? we love a thorough icon. here’s the rest, with every little detail intact:

  • LWORK — INTEGER. The number of entries in WORK. This must be at least:
max(3*MN+MX,5*MN-4)+2*MN**2

for all pairs pairs (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) )

  • IWORK — INTEGER array, dimension at least 8*min(M,N).
  • NOUT — INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)
  • INFO — INTEGER. If 0, then everything ran OK.
    • -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 DLATMS, or DGESVD returns an error code, the absolute value of it is returned.

👑 Author

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

Definition at line 363 of file ddrvbd.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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