# dbdt05.f - Man Page

TESTING/EIG/dbdt05.f

## Synopsis

### Functions/Subroutines

subroutine dbdt05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
DBDT05

## Function/Subroutine Documentation

### subroutine dbdt05 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, 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)

DBDT05

Purpose:

DBDT05 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 DOUBLE PRECISION 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 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 (M,N)

RESID

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 125 of file dbdt05.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dbdt05(3) is an alias of dbdt05.f(3).

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