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eigvalvecsymtri.3
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eigvalvecsymtri.3
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.\" Automatically generated by Pandoc 3.1.3
.\"
.\" Define V font for inline verbatim, using C font in formats
.\" that render this, and otherwise B font.
.ie "\f[CB]x\f[]"x" \{\
. ftr V B
. ftr VI BI
. ftr VB B
. ftr VBI BI
.\}
.el \{\
. ftr V CR
. ftr VI CI
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.\}
.TH "eigvalvecsymtri" "1" "2021-02-15" "Fortran 95" "SHTOOLS 4.11"
.hy
.SH EigValVecSymTri
.PP
Compute the eigenvalues and eigenvectors of a real symmetric tridiagonal
matrix.
.SH Usage
.PP
call EigValVecSymTri (\f[V]ain\f[R], \f[V]n\f[R], \f[V]eval\f[R],
\f[V]evec\f[R], \f[V]ul\f[R], \f[V]exitstatus\f[R])
.SH Parameters
.TP
\f[V]ain\f[R] : input, real(dp), dimension (\f[V]n\f[R], \f[V]n\f[R])
The input real symmetric tridiagonal matrix.
.TP
\f[V]n\f[R] : input, integer(int32)
The rank of the matrix \f[V]ain\f[R].
.TP
\f[V]eval\f[R] : output, real(dp), dimension (\f[V]n\f[R])
The eigenvalues of \f[V]ain\f[R], sorted from largest to smallest.
.TP
\f[V]evec\f[R] : output, real(dp), dimension (\f[V]n\f[R], \f[V]n\f[R])
The eigenvectors of \f[V]ain\f[R], sorted from largest to smallest
eigenvalues.
The sign of the first element of each eigenvector is chosen to be
positive.
.TP
\f[V]ul\f[R] : optional, input, character, default = \f[V]L\f[R]
If \f[V]U\f[R] then the upper portion of the matrix \f[V]ain\f[R] will
be used.
If \f[V]L\f[R] then the lower portion of the matrix \f[V]ain\f[R] will
be used (default).
.TP
\f[V]exitstatus\f[R] : output, optional, integer(int32)
If present, instead of executing a STOP when an error is encountered,
the variable exitstatus will be returned describing the error.
0 = No errors; 1 = Improper dimensions of input array; 2 = Improper
bounds for input variable; 3 = Error allocating memory; 4 = File IO
error.
.SH Description
.PP
\f[V]EigValVecSymTri\f[R] will calculate the eigenvalues and
eigenvectors of a real symmetric tridiagonal matrix.
By default, only the lower portion of the matrix is used, but this can
be changed by the optional argument \f[V]ul\f[R].
The eigenvalues and eigenvectors are sorted from largest to smallest
eigenvalues, and the sign of the first element of each eigenvector is
chosen to be positive.
This routine factors the matrix \f[V]ain\f[R] using the LAPACK routine
\f[V]DSTEGR\f[R].
.SH See also
.PP
eigvalsym, eigvalvecsym