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template<typename T>
void gbbrd(char *vect, integer *m, integer *n, integer *ncc, integer *kl, integer *ku, T *ab, integer *ldab, T *d, T *e, T *q, integer *ldq, T *pt, integer *ldpt, T *c, integer *ldc, T *work, integer *info)# Reduces a general band matrix to bidiagonal form.
Purpose :
GBBRD 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.
- Parameters:
VECT – [in]
VECT is 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 – [in]
M is INTEGER
The number of rows of the matrix A. M >= 0.
N – [in]
N is INTEGER
The number of columns of the matrix A. N >= 0.
NCC – [in]
NCC is INTEGER
The number of columns of the matrix C. NCC >= 0.
KL – [in]
KL is INTEGER
The number of subdiagonals of the matrix A. KL >= 0.
KU – [in]
KU is INTEGER
The number of superdiagonals of the matrix A. KU >= 0.
AB – [inout]
AB is 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 fla_max(1,j-ku)<=i<=min(m,j+kl). On exit, A is overwritten by values generated during the reduction.LDAB – [in]
LDAB is INTEGER
The leading dimension of the array A. LDAB >= KL+KU+1.
D – [out]
D is REAL array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.
E – [out]
E is REAL array, dimension (min(M,N)-1)
The superdiagonal elements of the bidiagonal matrix B.
Q – [out]
Q is 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 – [in]
LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= fla_max(1,M) if VECT = ‘Q’ or ‘B’; LDQ >= 1 otherwise.PT – [out]
PT is 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 – [in]
LDPT is INTEGER
The leading dimension of the array PT.
LDPT >= fla_max(1,N) if VECT = ‘P’ or ‘B’; LDPT >= 1 otherwise.C – [inout]
C is 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 – [in]
LDC is INTEGER
The leading dimension of the array C.
LDC >= fla_max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.WORK – [out] WORK is COMPLEX array, dimension (fla_max(M,N))
RWORK – [out] RWORK is REAL array, dimension (fla_max(M,N))
INFO – [out]
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.