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.

VECT

          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

          M is INTEGER


          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER


          The number of columns of the matrix A.  N >= 0.

NCC

          NCC is INTEGER


          The number of columns of the matrix C.  NCC >= 0.

KL

          KL is INTEGER


          The number of subdiagonals of the matrix A. KL >= 0.

KU

          KU is INTEGER


          The number of superdiagonals of the matrix A. KU >= 0.

AB

          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 max(1,j-ku)<=i<=min(m,j+kl).


          On exit, A is overwritten by values generated during the


          reduction.

LDAB

          LDAB is INTEGER


          The leading dimension of the array A. LDAB >= KL+KU+1.

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.

Q

          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

          LDQ is INTEGER


          The leading dimension of the array Q.


          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.

PT

          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

          LDPT is INTEGER


          The leading dimension of the array PT.


          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.

C

          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

          LDC is INTEGER


          The leading dimension of the array C.


          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.

WORK

          WORK is REAL array, dimension (2*max(M,N))

INFO

          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011