CBDT01
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
CBDT01 reconstructs a general matrix A from its bidiagonal form
A = Q * B * P'
where Q (m by min(m,n)) and P' (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 * PT ) / ( n * norm(A) * EPS )
where PT = P' and EPS is the machine precision.
A = Q * B * P'
where Q (m by min(m,n)) and P' (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 * PT ) / ( n * norm(A) * EPS )
where PT = P' and EPS is the machine precision.
Arguments
| M |
(input) INTEGER
The number of rows of the matrices A and Q.
|
| N |
(input) INTEGER
The number of columns of the matrices A and P'.
|
| KD |
(input) 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 |
(input) COMPLEX array, dimension (LDA,N)
The m by n matrix A.
|
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
|
| Q |
(input) COMPLEX array, dimension (LDQ,N)
The m by min(m,n) unitary matrix Q in the reduction
A = Q * B * P'. |
| LDQ |
(input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,M).
|
| D |
(input) REAL array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.
|
| E |
(input) 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 |
(input) COMPLEX array, dimension (LDPT,N)
The min(m,n) by n unitary matrix P' in the reduction
A = Q * B * P'. |
| LDPT |
(input) INTEGER
The leading dimension of the array PT.
LDPT >= max(1,min(M,N)). |
| WORK |
(workspace) COMPLEX array, dimension (M+N)
|
| RWORK |
(workspace) REAL array, dimension (M)
|
| RESID |
(output) REAL
The test ratio: norm(A - Q * B * P') / ( n * norm(A) * EPS )
|