# sdrvbd.f - Man Page

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 (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:

``` SDRVBD checks the singular value decomposition (SVD) drivers
SGESVD, SGESDD, SGESVDQ, SGESVJ, SGEJSV, and DGESVDX.

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 'A' 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 'j'
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
The number of matrix sizes (M,N) contained in the vectors
MM and NN.```

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
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, 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
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
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
The leading dimension of the array U.  LDU >= max(1,MMAX).```

VT

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

LDVT

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

INFO

```          INFO is 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  SLATMS, or SGESVD returns an error code, the
absolute value of it is returned.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 363 of file sdrvbd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sdrvbd(3) is an alias of sdrvbd.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK