TESTING/EIG/sdrvbd.f(3)

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🌸 bestie's guide to TESTING/EIG/sdrvbd.f(3) — Library Functions Manual 🌸

✨ NAME ✨

TESTING/EIG/sdrvbd.f

💅 SYNOPSIS 💅

🧚 Functions/Subroutines 🧚

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

🌈 Function/Subroutine Documentation 🌈

🦋 subroutine sdrvbd ... 🦋

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

🎯 Purpose 🎯

okay so SDRVBD is literally the vibe-checker for the singular value decomposition (SVD) drivers: it checks SGESVD, SGESDD, SGESVDQ, SGESVJ, SGEJSV, and DGESVDX. No cap.

Both SGESVD and SGESDD 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.

When SDRVBD 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 SGESVD:

(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 SGESDD:

(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 SGESVDQ:

(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 SGESVJ:

(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 SGEJSV:

(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 SGESVDX( 'V', 'V', 'A' )/SGESVDX( '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 SGESVDX( '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 SGESVDX( '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's the number of matrix sizes (M,N) contained in the vectors MM and NN.

MM

MM is INTEGER array, dimension (NSIZES). These are the values of the matrix row dimension M.

NN

NN is INTEGER array, dimension (NSIZES). These are the values of the matrix column dimension N.

NTYPES

NTYPES is INTEGER. It's the number of elements in DOTYPE. If it is zero, SDRVBD 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, it's 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 SDRVBD to continue the same random number sequence.

THRESH

THRESH is REAL. It's 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 REAL array, dimension (LDA,NMAX) where NMAX is the maximum value of N in NN.

LDA

LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,MMAX), where MMAX is the maximum value of M in MM.

U

U is REAL array, dimension (LDU,MMAX).

LDU

LDU is INTEGER. It's the leading dimension of the array U. LDU >= max(1,MMAX).

VT

VT is REAL array, dimension (LDVT,NMAX).

LDVT

LDVT is INTEGER. It's the leading dimension of the array VT. LDVT >= max(1,NMAX).

ASAV

ASAV is REAL array, dimension (LDA,NMAX).

USAV

USAV is REAL array, dimension (LDU,MMAX).

VTSAV

VTSAV is REAL array, dimension (LDVT,NMAX).

S

S is REAL array, dimension (max(min(MM,NN))).

SSAV

SSAV is REAL array, dimension (max(min(MM,NN))).

E

E is REAL array, dimension (max(min(MM,NN))).

WORK

WORK is REAL array, dimension (LWORK).

LWORK

LWORK is INTEGER. It's 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

IWORK is INTEGER array, dimension at least 8*min(M,N).

NOUT

  • NOUT — this one’s an INTEGER, bestie: the FORTRAN unit number for printing out error messages (like when a routine returns IINFO not equal to 0). Very “please read the receipts” energy.
  • INFO — also an INTEGER. If it’s 0, then everything ran OK, no cap. Otherwise, the vibe check failed like this:
    • -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 SLATMS, or SGESVD returns an error code, the absolute value of it is returned. So like… the error comes back, but make it positive, periodt. 💅

👑 Author

This iconic little routine is brought to you by:

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

Definition at line 363 of file sdrvbd.f.

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