# dbdt03.f - Man Page

TESTING/EIG/dbdt03.f

## Synopsis

### Functions/Subroutines

subroutine dbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
DBDT03

## Function/Subroutine Documentation

### subroutine dbdt03 (character uplo, integer n, integer kd, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) s, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) work, double precision resid)

DBDT03

Purpose:

``` DBDT03 reconstructs a bidiagonal matrix B from its 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( B - U * S * VT ) / ( 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.```

KD

```          KD is INTEGER
The bandwidth of the bidiagonal matrix B.  If KD = 1, the
matrix B is bidiagonal, and if KD = 0, B is diagonal and E is
not referenced.  If KD is greater than 1, it is assumed to be
1, and if KD is less than 0, it is assumed to be 0.```

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'.```

U

```          U is DOUBLE PRECISION array, dimension (LDU,N)
The n by n orthogonal matrix U in the reduction B = U'*A*P.```

LDU

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

S

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

VT

```          VT is DOUBLE PRECISION array, dimension (LDVT,N)
The n by n orthogonal matrix V' in the reduction
B = U * S * 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(B - U * S * V') / ( n * norm(A) * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 133 of file dbdt03.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dbdt03(3) is an alias of dbdt03.f(3).

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