.TH "disna" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
disna \- disna: eig condition numbers
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBddisna\fP (job, m, n, d, sep, info)"
.br
.RI "\fBDDISNA\fP "
.ti -1c
.RI "subroutine \fBsdisna\fP (job, m, n, d, sep, info)"
.br
.RI "\fBSDISNA\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine ddisna (character job, integer m, integer n, double precision, dimension( * ) d, double precision, dimension( * ) sep, integer info)"

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

.PP
.nf
 DDISNA computes the reciprocal condition numbers for the eigenvectors
 of a real symmetric or complex Hermitian matrix or for the left or
 right singular vectors of a general m-by-n matrix\&. The reciprocal
 condition number is the 'gap' between the corresponding eigenvalue or
 singular value and the nearest other one\&.

 The bound on the error, measured by angle in radians, in the I-th
 computed vector is given by

        DLAMCH( 'E' ) * ( ANORM / SEP( I ) )

 where ANORM = 2-norm(A) = max( abs( D(j) ) )\&.  SEP(I) is not allowed
 to be smaller than DLAMCH( 'E' )*ANORM in order to limit the size of
 the error bound\&.

 DDISNA may also be used to compute error bounds for eigenvectors of
 the generalized symmetric definite eigenproblem\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOB\fP 
.PP
.nf
          JOB is CHARACTER*1
          Specifies for which problem the reciprocal condition numbers
          should be computed:
          = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
          = 'L':  the left singular vectors of a general matrix;
          = 'R':  the right singular vectors of a general matrix\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix\&. M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          If JOB = 'L' or 'R', the number of columns of the matrix,
          in which case N >= 0\&. Ignored if JOB = 'E'\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (M) if JOB = 'E'
                              dimension (min(M,N)) if JOB = 'L' or 'R'
          The eigenvalues (if JOB = 'E') or singular values (if JOB =
          'L' or 'R') of the matrix, in either increasing or decreasing
          order\&. If singular values, they must be non-negative\&.
.fi
.PP
.br
\fISEP\fP 
.PP
.nf
          SEP is DOUBLE PRECISION array, dimension (M) if JOB = 'E'
                               dimension (min(M,N)) if JOB = 'L' or 'R'
          The reciprocal condition numbers of the vectors\&.
.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 sdisna (character job, integer m, integer n, real, dimension( * ) d, real, dimension( * ) sep, integer info)"

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

.PP
.nf
 SDISNA computes the reciprocal condition numbers for the eigenvectors
 of a real symmetric or complex Hermitian matrix or for the left or
 right singular vectors of a general m-by-n matrix\&. The reciprocal
 condition number is the 'gap' between the corresponding eigenvalue or
 singular value and the nearest other one\&.

 The bound on the error, measured by angle in radians, in the I-th
 computed vector is given by

        SLAMCH( 'E' ) * ( ANORM / SEP( I ) )

 where ANORM = 2-norm(A) = max( abs( D(j) ) )\&.  SEP(I) is not allowed
 to be smaller than SLAMCH( 'E' )*ANORM in order to limit the size of
 the error bound\&.

 SDISNA may also be used to compute error bounds for eigenvectors of
 the generalized symmetric definite eigenproblem\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOB\fP 
.PP
.nf
          JOB is CHARACTER*1
          Specifies for which problem the reciprocal condition numbers
          should be computed:
          = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
          = 'L':  the left singular vectors of a general matrix;
          = 'R':  the right singular vectors of a general matrix\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix\&. M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          If JOB = 'L' or 'R', the number of columns of the matrix,
          in which case N >= 0\&. Ignored if JOB = 'E'\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (M) if JOB = 'E'
                              dimension (min(M,N)) if JOB = 'L' or 'R'
          The eigenvalues (if JOB = 'E') or singular values (if JOB =
          'L' or 'R') of the matrix, in either increasing or decreasing
          order\&. If singular values, they must be non-negative\&.
.fi
.PP
.br
\fISEP\fP 
.PP
.nf
          SEP is REAL array, dimension (M) if JOB = 'E'
                               dimension (min(M,N)) if JOB = 'L' or 'R'
          The reciprocal condition numbers of the vectors\&.
.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\&.