SGBBRD
Purpose
SGBBRD reduces a real general m-by-n band matrix A to upper
bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
The routine computes B, and optionally forms Q or P**T, or computes
Q**T*C for a given matrix C.
bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
The routine computes B, and optionally forms Q or P**T, or computes
Q**T*C for a given matrix C.
Arguments
| VECT |
(input) CHARACTER*1
Specifies whether or not the matrices Q and P**T are to be
formed. = 'N': do not form Q or P**T; = 'Q': form Q only; = 'P': form P**T only; = 'B': form both. |
| M |
(input) INTEGER
The number of rows of the matrix A. M >= 0.
|
| N |
(input) INTEGER
The number of columns of the matrix A. N >= 0.
|
| NCC |
(input) INTEGER
The number of columns of the matrix C. NCC >= 0.
|
| KL |
(input) INTEGER
The number of subdiagonals of the matrix A. KL >= 0.
|
| KU |
(input) INTEGER
The number of superdiagonals of the matrix A. KU >= 0.
|
| AB |
(input/output) REAL array, dimension (LDAB,N)
On entry, the m-by-n band matrix A, stored in rows 1 to
KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl). On exit, A is overwritten by values generated during the reduction. |
| LDAB |
(input) INTEGER
The leading dimension of the array A. LDAB >= KL+KU+1.
|
| D |
(output) REAL array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.
|
| E |
(output) REAL array, dimension (min(M,N)-1)
The superdiagonal elements of the bidiagonal matrix B.
|
| Q |
(output) REAL array, dimension (LDQ,M)
If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.
If VECT = 'N' or 'P', the array Q is not referenced. |
| LDQ |
(input) INTEGER
The leading dimension of the array Q.
LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. |
| PT |
(output) REAL array, dimension (LDPT,N)
If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.
If VECT = 'N' or 'Q', the array PT is not referenced. |
| LDPT |
(input) INTEGER
The leading dimension of the array PT.
LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. |
| C |
(input/output) REAL array, dimension (LDC,NCC)
On entry, an m-by-ncc matrix C.
On exit, C is overwritten by Q**T*C. C is not referenced if NCC = 0. |
| LDC |
(input) INTEGER
The leading dimension of the array C.
LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0. |
| WORK |
(workspace) REAL array, dimension (2*max(M,N))
|
| INFO |
(output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value. |