# cbdt03.f - Man Page

TESTING/EIG/cbdt03.f

## Synopsis

### Functions/Subroutines

subroutine **cbdt03** (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)**CBDT03**

## Function/Subroutine Documentation

### subroutine cbdt03 (character uplo, integer n, integer kd, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldu, * ) u, integer ldu, real, dimension( * ) s, complex, dimension( ldvt, * ) vt, integer ldvt, complex, dimension( * ) work, real resid)

**CBDT03**

**Purpose:**

CBDT03 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 REAL array, dimension (N) The n diagonal elements of the bidiagonal matrix B.

*E*E is REAL 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 COMPLEX 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 REAL array, dimension (N) The singular values from the SVD of B, sorted in decreasing order.

*VT*VT is COMPLEX 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 COMPLEX array, dimension (2*N)

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

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **133** of file **cbdt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cbdt03(3) is an alias of cbdt03.f(3).

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