.TH "dsbtrd.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
dsbtrd.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdsbtrd\fP (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)"
.br
.RI "\fI\fBDSBTRD\fP \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dsbtrd (characterVECT, characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( ldq, * )Q, integerLDQ, double precision, dimension( * )WORK, integerINFO)"

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

.PP
.nf
 DSBTRD reduces a real symmetric band matrix A to symmetric
 tridiagonal form T by an orthogonal similarity transformation:
 Q**T * A * Q = T.
.fi
.PP
 
.RE
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\fBParameters:\fP
.RS 4
\fIVECT\fP 
.PP
.nf
          VECT is CHARACTER*1
          = 'N':  do not form Q;
          = 'V':  form Q;
          = 'U':  update a matrix X, by forming X*Q.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
.fi
.PP
.br
\fIN\fP 
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.nf
          N is INTEGER
          The order of the matrix A.  N >= 0.
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          On entry, the upper or lower triangle of the symmetric band
          matrix A, stored in the first KD+1 rows of the array.  The
          j-th column of A is stored in the j-th column of the array AB
          as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
          On exit, the diagonal elements of AB are overwritten by the
          diagonal elements of the tridiagonal matrix T; if KD > 0, the
          elements on the first superdiagonal (if UPLO = 'U') or the
          first subdiagonal (if UPLO = 'L') are overwritten by the
          off-diagonal elements of T; the rest of AB is overwritten by
          values generated during the reduction.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of the tridiagonal matrix T.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          The off-diagonal elements of the tridiagonal matrix T:
          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is DOUBLE PRECISION array, dimension (LDQ,N)
          On entry, if VECT = 'U', then Q must contain an N-by-N
          matrix X; if VECT = 'N' or 'V', then Q need not be set.

          On exit:
          if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;
          if VECT = 'U', Q contains the product X*Q;
          if VECT = 'N', the array Q is not referenced.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q.
          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (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
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\fBDate:\fP
.RS 4
November 2011 
.RE
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\fBFurther Details: \fP
.RS 4

.PP
.nf
  Modified by Linda Kaufman, Bell Labs.
.fi
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.RE
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Definition at line 163 of file dsbtrd\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.