# 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

Univ. of Colorado Denver

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