.TH "TESTING/EIG/dsbt21.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/dsbt21.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdsbt21\fP (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, result)"
.br
.RI "\fBDSBT21\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dsbt21 (character uplo, integer n, integer ka, integer ks, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) work, double precision, dimension( 2 ) result)"

.PP
\fBDSBT21\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DSBT21  generally checks a decomposition of the form

         A = U S U**T

 where **T means transpose, A is symmetric banded, U is
 orthogonal, and S is diagonal (if KS=0) or symmetric
 tridiagonal (if KS=1)\&.

 Specifically:

         RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
         RESULT(2) = | I - U U**T | / ( n ulp )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER
          If UPLO='U', the upper triangle of A and V will be used and
          the (strictly) lower triangle will not be referenced\&.
          If UPLO='L', the lower triangle of A and V will be used and
          the (strictly) upper triangle will not be referenced\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The size of the matrix\&.  If it is zero, DSBT21 does nothing\&.
          It must be at least zero\&.
.fi
.PP
.br
\fIKA\fP 
.PP
.nf
          KA is INTEGER
          The bandwidth of the matrix A\&.  It must be at least zero\&.  If
          it is larger than N-1, then max( 0, N-1 ) will be used\&.
.fi
.PP
.br
\fIKS\fP 
.PP
.nf
          KS is INTEGER
          The bandwidth of the matrix S\&.  It may only be zero or one\&.
          If zero, then S is diagonal, and E is not referenced\&.  If
          one, then S is symmetric tri-diagonal\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA, N)
          The original (unfactored) matrix\&.  It is assumed to be
          symmetric, and only the upper (UPLO='U') or only the lower
          (UPLO='L') will be referenced\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of A\&.  It must be at least 1
          and at least min( KA, N-1 )\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal of the (symmetric tri-) diagonal matrix S\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          The off-diagonal of the (symmetric tri-) diagonal matrix S\&.
          E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
          (3,2) element, etc\&.
          Not referenced if KS=0\&.
.fi
.PP
.br
\fIU\fP 
.PP
.nf
          U is DOUBLE PRECISION array, dimension (LDU, N)
          The orthogonal matrix in the decomposition, expressed as a
          dense matrix (i\&.e\&., not as a product of Householder
          transformations, Givens transformations, etc\&.)
.fi
.PP
.br
\fILDU\fP 
.PP
.nf
          LDU is INTEGER
          The leading dimension of U\&.  LDU must be at least N and
          at least 1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (N**2+N)
.fi
.PP
.br
\fIRESULT\fP 
.PP
.nf
          RESULT is DOUBLE PRECISION array, dimension (2)
          The values computed by the two tests described above\&.  The
          values are currently limited to 1/ulp, to avoid overflow\&.
.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

.PP
Definition at line \fB145\fP of file \fBdsbt21\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.