# sbdt05.f - Man Page

TESTING/EIG/sbdt05.f

## Synopsis

### Functions/Subroutines

subroutine sbdt05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
SBDT05

## Function/Subroutine Documentation

### subroutine sbdt05 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, integer ns, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, real resid)

SBDT05

Purpose:

``` SBDT05 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

M

```          M is INTEGER
The number of rows of the matrices A and U.```

N

```          N is INTEGER
The number of columns of the matrices A and VT.```

A

```          A is REAL array, dimension (LDA,N)
The m by n matrix A.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).```

S

```          S is REAL 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 REAL 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 REAL 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 REAL array, dimension (M,N)`

RESID

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 125 of file sbdt05.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sbdt05(3) is an alias of sbdt05.f(3).

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