TESTING/EIG/cbdt05.f(3) | Library Functions Manual | TESTING/EIG/cbdt05.f(3) |

# NAME

TESTING/EIG/cbdt05.f

# SYNOPSIS

## Functions/Subroutines

subroutine **cbdt05** (m, n, a, lda, s, ns, u, ldu, vt, ldvt,
work, resid)

**CBDT05**

# Function/Subroutine Documentation

## subroutine cbdt05 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, integer ns, complex, dimension( * ) u, integer ldu, complex, dimension( ldvt, * ) vt, integer ldvt, complex, dimension( * ) work, real resid)

**CBDT05**

**Purpose:**

CBDT05 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 **123** of file **cbdt05.f**.

# Author

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