# 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

Univ. of Colorado Denver

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