TESTING/EIG/cbdt01.f(3) Library Functions Manual TESTING/EIG/cbdt01.f(3)

# NAME

TESTING/EIG/cbdt01.f

# SYNOPSIS

## Functions/Subroutines

subroutine cbdt01 (m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, rwork, resid)
CBDT01

# Function/Subroutine Documentation

## subroutine cbdt01 (integer m, integer n, integer kd, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldq, * ) q, integer ldq, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldpt, * ) pt, integer ldpt, complex, dimension( * ) work, real, dimension( * ) rwork, real resid)

CBDT01

Purpose:

``` CBDT01 reconstructs a general matrix A from its bidiagonal form
A = Q * B * P**H
where Q (m by min(m,n)) and P**H (min(m,n) by n) are unitary
matrices and B is bidiagonal.
The test ratio to test the reduction is
RESID = norm(A - Q * B * P**H) / ( 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**H.```

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 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).```

Q

```          Q is COMPLEX array, dimension (LDQ,N)
The m by min(m,n) unitary matrix Q in the reduction
A = Q * B * P**H.```

LDQ

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

D

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

E

```          E is REAL 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 COMPLEX array, dimension (LDPT,N)
The min(m,n) by n unitary matrix P**H in the reduction
A = Q * B * P**H.```

LDPT

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

WORK

`          WORK is COMPLEX array, dimension (M+N)`

RWORK

`          RWORK is REAL array, dimension (M)`

RESID

```          RESID is REAL
The test ratio:
norm(A - Q * B * P**H) / ( n * norm(A) * EPS )```

Author

Univ. of Tennessee

Univ. of California Berkeley