gbbrd - Man Page

subroutine cgbbrd (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, rwork, info)
CGBBRD
subroutine dgbbrd (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, info)
DGBBRD
subroutine sgbbrd (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, info)
SGBBRD
subroutine zgbbrd (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, rwork, info)
ZGBBRD

CGBBRD  

Purpose:

 CGBBRD reduces a complex general m-by-n band matrix A to real upper
 bidiagonal form B by a unitary transformation: Q**H * A * P = B.

 The routine computes B, and optionally forms Q or P**H, or computes
 Q**H*C for a given matrix C.

Parameters

VECT

          VECT is CHARACTER*1
          Specifies whether or not the matrices Q and P**H are to be
          formed.
          = 'N': do not form Q or P**H;
          = 'Q': form Q only;
          = 'P': form P**H 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 COMPLEX 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 COMPLEX array, dimension (LDQ,M)
          If VECT = 'Q' or 'B', the m-by-m unitary 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 COMPLEX array, dimension (LDPT,N)
          If VECT = 'P' or 'B', the n-by-n unitary 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 COMPLEX array, dimension (LDC,NCC)
          On entry, an m-by-ncc matrix C.
          On exit, C is overwritten by Q**H*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 COMPLEX array, dimension (max(M,N))

RWORK

          RWORK is REAL array, dimension (max(M,N))

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 191 of file cgbbrd.f.

DGBBRD  

Purpose:

 DGBBRD 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

          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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B.

E

          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B.

Q

          Q is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 185 of file dgbbrd.f.

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.

Parameters

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 185 of file sgbbrd.f.

ZGBBRD  

Purpose:

 ZGBBRD reduces a complex general m-by-n band matrix A to real upper
 bidiagonal form B by a unitary transformation: Q**H * A * P = B.

 The routine computes B, and optionally forms Q or P**H, or computes
 Q**H*C for a given matrix C.

Parameters

VECT

          VECT is CHARACTER*1
          Specifies whether or not the matrices Q and P**H are to be
          formed.
          = 'N': do not form Q or P**H;
          = 'Q': form Q only;
          = 'P': form P**H 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 COMPLEX*16 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 DOUBLE PRECISION array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B.

E

          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B.

Q

          Q is COMPLEX*16 array, dimension (LDQ,M)
          If VECT = 'Q' or 'B', the m-by-m unitary 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 COMPLEX*16 array, dimension (LDPT,N)
          If VECT = 'P' or 'B', the n-by-n unitary 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 COMPLEX*16 array, dimension (LDC,NCC)
          On entry, an m-by-ncc matrix C.
          On exit, C is overwritten by Q**H*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 COMPLEX*16 array, dimension (max(M,N))

RWORK

          RWORK is DOUBLE PRECISION array, dimension (max(M,N))

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 191 of file zgbbrd.f.