# dbdt04.f - Man Page

TESTING/EIG/dbdt04.f

## Synopsis

### Functions/Subroutines

subroutine dbdt04 (uplo, n, d, e, s, ns, u, ldu, vt, ldvt, work, resid)
DBDT04

## Function/Subroutine Documentation

### subroutine dbdt04 (character uplo, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) s, integer ns, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) work, double precision resid)

DBDT04

Purpose:

``` DBDT04 reconstructs a bidiagonal matrix B from its (partial) SVD:
S = U' * B * V
where U and V are orthogonal matrices and S is diagonal.

The test ratio to test the singular value decomposition is
RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )
where VT = V' and EPS is the machine precision.```
Parameters

UPLO

```          UPLO is CHARACTER*1
Specifies whether the matrix B is upper or lower bidiagonal.
= 'U':  Upper bidiagonal
= 'L':  Lower bidiagonal```

N

```          N is INTEGER
The order of the matrix B.```

D

```          D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the bidiagonal matrix B.```

E

```          E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) superdiagonal elements of the bidiagonal matrix B
if UPLO = 'U', or the (n-1) subdiagonal elements of B if
UPLO = 'L'.```

S

```          S is DOUBLE PRECISION array, dimension (NS)
The singular values from the (partial) SVD of B, sorted in
decreasing order.```

NS

```          NS is INTEGER
The number of singular values/vectors from the (partial)
SVD of B.```

U

```          U is DOUBLE PRECISION array, dimension (LDU,NS)
The n by ns orthogonal matrix U in S = U' * B * V.```

LDU

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

VT

```          VT is DOUBLE PRECISION array, dimension (LDVT,N)
The n by ns orthogonal matrix V in S = U' * B * V.```

LDVT

```          LDVT is INTEGER
The leading dimension of the array VT.```

WORK

`          WORK is DOUBLE PRECISION array, dimension (2*N)`

RESID

```          RESID is DOUBLE PRECISION
The test ratio:  norm(S - U' * B * V) / ( n * norm(B) * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 129 of file dbdt04.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dbdt04(3) is an alias of dbdt04.f(3).

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