# dbdt01.f - Man Page

TESTING/EIG/dbdt01.f

## Synopsis

### Functions/Subroutines

subroutine dbdt01 (m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, resid)
DBDT01

## Function/Subroutine Documentation

### subroutine dbdt01 (integer m, integer n, integer kd, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldpt, * ) pt, integer ldpt, double precision, dimension( * ) work, double precision resid)

DBDT01

Purpose:

``` DBDT01 reconstructs a general matrix A from its bidiagonal form
A = Q * B * P**T
where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
matrices and B is bidiagonal.

The test ratio to test the reduction is
RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
where EPS is the machine precision.```
Parameters

M

```          M is INTEGER
The number of rows of the matrices A and Q.```

N

```          N is INTEGER
The number of columns of the matrices A and P**T.```

KD

```          KD is INTEGER
If KD = 0, B is diagonal and the array E is not referenced.
If KD = 1, the reduction was performed by xGEBRD; B is upper
bidiagonal if M >= N, and lower bidiagonal if M < N.
If KD = -1, the reduction was performed by xGBBRD; B is
always upper bidiagonal.```

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).```

Q

```          Q is DOUBLE PRECISION array, dimension (LDQ,N)
The m by min(m,n) orthogonal matrix Q in the reduction
A = Q * B * P**T.```

LDQ

```          LDQ is INTEGER
The leading dimension of the array Q.  LDQ >= max(1,M).```

D

```          D is DOUBLE PRECISION array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.```

E

```          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
The superdiagonal elements of the bidiagonal matrix B if
m >= n, or the subdiagonal elements of B if m < n.```

PT

```          PT is DOUBLE PRECISION array, dimension (LDPT,N)
The min(m,n) by n orthogonal matrix P**T in the reduction
A = Q * B * P**T.```

LDPT

```          LDPT is INTEGER
The leading dimension of the array PT.
LDPT >= max(1,min(M,N)).```

WORK

`          WORK is DOUBLE PRECISION array, dimension (M+N)`

RESID

```          RESID is DOUBLE PRECISION
The test ratio:
norm(A - Q * B * P**T) / ( n * norm(A) * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 139 of file dbdt01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dbdt01(3) is an alias of dbdt01.f(3).

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