Man page - gbbrd(3)

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Manual

gbbrd

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) d, real, dimension( * ) e, complex, dimension(ldq, * ) q, integer ldq, complex, dimension( ldpt, * ) pt, integerldpt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension(* ) work, real, dimension( * ) rwork, integer info)
subroutine dgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, double precision, dimension( ldab, * ) ab,integer ldab, double precision, dimension( * ) d, double precision,dimension( * ) e, double precision, dimension( ldq, * ) q, integer ldq,double precision, dimension( ldpt, * ) pt, integer ldpt, doubleprecision, dimension( ldc, * ) c, integer ldc, double precision,dimension( * ) work, integer info)
subroutine sgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldq, *) q, integer ldq, real, dimension( ldpt, * ) pt, integer ldpt, real,dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integerinfo)
subroutine zgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integerldab, double precision, dimension( * ) d, double precision, dimension(* ) e, complex*16, dimension( ldq, * ) q, integer ldq, complex*16,dimension( ldpt, * ) pt, integer ldpt, complex*16, dimension( ldc, * )c, integer ldc, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)
Author

NAME

gbbrd - gbbrd: band to bidiagonal

SYNOPSIS

Functions

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

Detailed Description

Function Documentation

subroutine cgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) d, real, dimension( * ) e, complex, dimension(ldq, * ) q, integer ldq, complex, dimension( ldpt, * ) pt, integerldpt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension(* ) work, real, dimension( * ) rwork, integer info)

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.

subroutine dgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, double precision, dimension( ldab, * ) ab,integer ldab, double precision, dimension( * ) d, double precision,dimension( * ) e, double precision, dimension( ldq, * ) q, integer ldq,double precision, dimension( ldpt, * ) pt, integer ldpt, doubleprecision, dimension( ldc, * ) c, integer ldc, double precision,dimension( * ) work, integer info)

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.

subroutine sgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldq, *) q, integer ldq, real, dimension( ldpt, * ) pt, integer ldpt, real,dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integerinfo)

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.

subroutine zgbbrd (character vect, integer m, integer n, integer ncc,integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integerldab, double precision, dimension( * ) d, double precision, dimension(* ) e, complex*16, dimension( ldq, * ) q, integer ldq, complex*16,dimension( ldpt, * ) pt, integer ldpt, complex*16, dimension( ldc, * )c, integer ldc, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)

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.

Author

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