.TH "gbbrd" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
gbbrd \- gbbrd: band to bidiagonal
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcgbbrd\fP (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, rwork, info)"
.br
.RI "\fBCGBBRD\fP "
.ti -1c
.RI "subroutine \fBdgbbrd\fP (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, info)"
.br
.RI "\fBDGBBRD\fP "
.ti -1c
.RI "subroutine \fBsgbbrd\fP (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, info)"
.br
.RI "\fBSGBBRD\fP "
.ti -1c
.RI "subroutine \fBzgbbrd\fP (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, rwork, info)"
.br
.RI "\fBZGBBRD\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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, integer ldpt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)"

.PP
\fBCGBBRD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIVECT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fINCC\fP 
.PP
.nf
          NCC is INTEGER
          The number of columns of the matrix C\&.  NCC >= 0\&.
.fi
.PP
.br
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals of the matrix A\&. KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals of the matrix A\&. KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array A\&. LDAB >= KL+KU+1\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&.
          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise\&.
.fi
.PP
.br
\fIPT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDPT\fP 
.PP
.nf
          LDPT is INTEGER
          The leading dimension of the array PT\&.
          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.
          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (max(M,N))
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (max(M,N))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit\&.
          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)"

.PP
\fBDGBBRD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIVECT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fINCC\fP 
.PP
.nf
          NCC is INTEGER
          The number of columns of the matrix C\&.  NCC >= 0\&.
.fi
.PP
.br
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals of the matrix A\&. KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals of the matrix A\&. KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array A\&. LDAB >= KL+KU+1\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&.
          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise\&.
.fi
.PP
.br
\fIPT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDPT\fP 
.PP
.nf
          LDPT is INTEGER
          The leading dimension of the array PT\&.
          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.
          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (2*max(M,N))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit\&.
          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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, integer info)"

.PP
\fBSGBBRD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIVECT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fINCC\fP 
.PP
.nf
          NCC is INTEGER
          The number of columns of the matrix C\&.  NCC >= 0\&.
.fi
.PP
.br
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals of the matrix A\&. KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals of the matrix A\&. KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array A\&. LDAB >= KL+KU+1\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&.
          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise\&.
.fi
.PP
.br
\fIPT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDPT\fP 
.PP
.nf
          LDPT is INTEGER
          The leading dimension of the array PT\&.
          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.
          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (2*max(M,N))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit\&.
          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "subroutine zgbbrd (character vect, integer m, integer n, integer ncc, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, 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)"

.PP
\fBZGBBRD\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIVECT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fINCC\fP 
.PP
.nf
          NCC is INTEGER
          The number of columns of the matrix C\&.  NCC >= 0\&.
.fi
.PP
.br
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals of the matrix A\&. KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals of the matrix A\&. KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array A\&. LDAB >= KL+KU+1\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&.
          LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise\&.
.fi
.PP
.br
\fIPT\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDPT\fP 
.PP
.nf
          LDPT is INTEGER
          The leading dimension of the array PT\&.
          LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&.
          LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (max(M,N))
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION array, dimension (max(M,N))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit\&.
          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.