The purpose of the module is to solve an eigenvalue problem for a complex general matrix. Subroutines are imported from EISPACK (https://netlib.org/eispack/) with minor modifications for compatibility. More...

Functions/Subroutines
subroutine, public	cg (nm, nl, ar, ai, wr, wi, zr, zi, fv1, fv2, fv3, ierr)
	This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (eispack) to find the eigenvalues and eigenvectors (if desired) of a complex general matrix.

subroutine, public	cbal (nm, nl, ar, ai, low, igh, scale)
	This subroutine is a translation of the algol procedure cbalance, which is a complex version of balance, num. math. 13, 293-304(1969) by parlett and reinsch. handbook for auto. comp., vol.ii-linear algebra, 315-326(1971). This subroutine balances a complex matrix and isolates eigenvalues whenever possible.

subroutine, public	corth (nm, nl, low, igh, ar, ai, ortr, orti)
	This subroutine is a translation of a complex analogue of the algol procedure orthes, num. math. 12, 349-368(1968) by martin and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 339-358(1971). Given a complex general matrix, this subroutine reduces a submatrix situated in rows and columns low through igh to upper hessenberg form by unitary similarity transformations.

subroutine, public	comqr2 (nm, nl, low, igh, ortr, orti, hr, hi, wr, wi, zr, zi, ierr)
	This subroutine is a translation of a unitary analogue of the algol procedure comlr2, num. math. 16, 181-204(1970) by peters and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 372-395(1971). The unitary analogue substitutes the qr algorithm of francis (comp. jour. 4, 332-345(1962)) for the lr algorithm. This subroutine finds the eigenvalues and eigenvectors of a complex upper hessenberg matrix by the qr method. The eigenvectors of a complex general matrix can also be found if corth has been used to reduce this general matrix to hessenberg form.

subroutine	cbabk2 (nm, nl, low, igh, scale, ml, zr, zi)
	This subroutine is a translation of the algol procedure cbabk2, which is a complex version of balbak, num. math. 13, 293-304(1969) by parlett and reinsch. handbook for auto. comp., vol.ii-linear algebra, 315-326(1971). This subroutine forms the eigenvectors of a complex general matrix by back transforming those of the correspondingbalanced matrix determined by cbal.

subroutine, public	csroot (xr, xi, yr, yi)

subroutine, public	cdiv (ar, ai, br, bi, cr, ci)

subroutine, public	pythag (a, b, c)

Detailed Description

The purpose of the module is to solve an eigenvalue problem for a complex general matrix. Subroutines are imported from EISPACK (https://netlib.org/eispack/) with minor modifications for compatibility.

Function/Subroutine Documentation

◆ cbabk2()

subroutine m_eigen_solver::cbabk2	(	integer, intent(in)	nm,
		integer, intent(in)	nl,
		integer, intent(in)	low,
		integer, intent(in)	igh,
		real(wp), dimension(nl), intent(in)	scale,
		integer, intent(in)	ml,
		real(wp), dimension(nm, ml), intent(inout)	zr,
		real(wp), dimension(nm, ml), intent(inout)	zi )

This subroutine is a translation of the algol procedure cbabk2, which is a complex version of balbak, num. math. 13, 293-304(1969) by parlett and reinsch. handbook for auto. comp., vol.ii-linear algebra, 315-326(1971). This subroutine forms the eigenvectors of a complex general matrix by back transforming those of the correspondingbalanced matrix determined by cbal.

Parameters

nm	the row dimension of the two-dimensional array parameters
nl	the order of the matrix
ar	the real part of the complex matrix to be balanced
ai	the imaginary part of the complex matrix to be balanced
low	an integer determined by the balancing subroutine cbal
igh	an integer determined by the balancing subroutine cbal
scale	the information determining the permutations and scaling factors used.
ml	the number of eigenvectors to be back transformed
zr	the real part of the eigenvectors to be back transformed in their first ml columns
zi	the imaginary part of the eigenvectors to be back transformed in their first ml columns

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◆ cbal()

subroutine, public m_eigen_solver::cbal	(	integer, intent(in)	nm,
		integer, intent(in)	nl,
		real(wp), dimension(nm, nl), intent(inout)	ar,
		real(wp), dimension(nm, nl), intent(inout)	ai,
		integer, intent(out)	low,
		integer, intent(out)	igh,
		real(wp), dimension(nl), intent(out)	scale )

This subroutine is a translation of the algol procedure cbalance, which is a complex version of balance, num. math. 13, 293-304(1969) by parlett and reinsch. handbook for auto. comp., vol.ii-linear algebra, 315-326(1971). This subroutine balances a complex matrix and isolates eigenvalues whenever possible.

Parameters

nm	the row dimension of the two-dimensional array parameters
nl	the order of the matrix
ar	the real part of the complex matrix to be balanced
ai	the imaginary part of the complex matrix to be balanced
low	one of two integers such that ar(i,j) and ai(i,j) are equal to zero if (1) i is greater than j and (2) j=1, ,low-1 or i=igh+1, ,nl.
igh	one of two integers such that ar(i,j) and ai(i,j) are equal to zero if (1) i is greater than j and (2) j=1, ,low-1 or i=igh+1, ,nl.
scale	the information determining the permutations and scaling factors used.

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◆ cdiv()

subroutine, public m_eigen_solver::cdiv	(	real(wp), intent(in)	ar,
		real(wp), intent(in)	ai,
		real(wp), intent(in)	br,
		real(wp), intent(in)	bi,
		real(wp), intent(out)	cr,
		real(wp), intent(out)	ci )

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◆ cg()

subroutine, public m_eigen_solver::cg	(	integer, intent(in)	nm,
		integer, intent(in)	nl,
		real(wp), dimension(nm, nl), intent(inout)	ar,
		real(wp), dimension(nm, nl), intent(inout)	ai,
		real(wp), dimension(nl), intent(out)	wr,
		real(wp), dimension(nl), intent(out)	wi,
		real(wp), dimension(nm, nl), intent(out)	zr,
		real(wp), dimension(nm, nl), intent(out)	zi,
		real(wp), dimension(nl), intent(out)	fv1,
		real(wp), dimension(nl), intent(out)	fv2,
		real(wp), dimension(nl), intent(out)	fv3,
		integer, intent(out)	ierr )

This subroutine calls the recommended sequence of subroutines from the eigensystem subroutine package (eispack) to find the eigenvalues and eigenvectors (if desired) of a complex general matrix.

Parameters

nm	the row dimension of the two-dimensional array parameters
nl	the order of the matrix a=(ar,ai)
ar	the real part of the complex general matrix
ai	the imaginary part of the complex general matrix
wr	the real part of the eigenvalues
wi	the imaginary part of the eigenvalues
zr	the real part of the eigenvectors
zi	the imaginary part of the eigenvectors
fv1	temporary storage array
fv2	temporary storage array
fv3	temporary storage array
ierr	an error completion code

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◆ comqr2()

subroutine, public m_eigen_solver::comqr2	(	integer, intent(in)	nm,
		integer, intent(in)	nl,
		integer, intent(in)	low,
		integer, intent(in)	igh,
		real(wp), dimension(igh), intent(inout)	ortr,
		real(wp), dimension(igh), intent(inout)	orti,
		real(wp), dimension(nm, nl), intent(inout)	hr,
		real(wp), dimension(nm, nl), intent(inout)	hi,
		real(wp), dimension(nl), intent(out)	wr,
		real(wp), dimension(nl), intent(out)	wi,
		real(wp), dimension(nm, nl), intent(out)	zr,
		real(wp), dimension(nm, nl), intent(out)	zi,
		integer, intent(out)	ierr )

This subroutine is a translation of a unitary analogue of the algol procedure comlr2, num. math. 16, 181-204(1970) by peters and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 372-395(1971). The unitary analogue substitutes the qr algorithm of francis (comp. jour. 4, 332-345(1962)) for the lr algorithm. This subroutine finds the eigenvalues and eigenvectors of a complex upper hessenberg matrix by the qr method. The eigenvectors of a complex general matrix can also be found if corth has been used to reduce this general matrix to hessenberg form.

Parameters

nm	the row dimension of the two-dimensional array parameters
nl	the order of the matrix
low	an integer determined by the balancing subroutine cbal. if cbal has not been used, set low=1.
igh	an integer determined by the balancing subroutine cbal. if cbal has not been used, set igh=nl.
ortr	information about the unitary transformations used in the reduction by corth
orti	information about the unitary transformations used in the reduction by corth
hr	the real part of the complex upper hessenberg matrix.
hi	the imaginary part of the complex upper hessenberg matrix.
wr	the real part of the eigenvalues
wi	the imaginary part of the eigenvalues
zr	the real part of the eigenvectors
zi	the imaginary part of the eigenvectors
ierr	an error completion code

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◆ corth()

subroutine, public m_eigen_solver::corth	(	integer, intent(in)	nm,
		integer, intent(in)	nl,
		integer, intent(in)	low,
		integer, intent(in)	igh,
		real(wp), dimension(nm, nl), intent(inout)	ar,
		real(wp), dimension(nm, nl), intent(inout)	ai,
		real(wp), dimension(igh), intent(out)	ortr,
		real(wp), dimension(igh), intent(out)	orti )

This subroutine is a translation of a complex analogue of the algol procedure orthes, num. math. 12, 349-368(1968) by martin and wilkinson. handbook for auto. comp., vol.ii-linear algebra, 339-358(1971). Given a complex general matrix, this subroutine reduces a submatrix situated in rows and columns low through igh to upper hessenberg form by unitary similarity transformations.

Parameters

nm	the row dimension of the two-dimensional array parameters
nl	the order of the matrix
ar	the real part of the complex matrix
ai	the imaginary part of the complex matrix
low	an integer determined by the balancing subroutine cbal. if cbal has not been used, set low=1.
igh	an integer determined by the balancing subroutine cbal. if cbal has not been used, set igh=nl.
ortr	further information about the transformations
orti	further information about the transformations

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◆ csroot()

subroutine, public m_eigen_solver::csroot	(	real(wp), intent(in)	xr,
		real(wp), intent(in)	xi,
		real(wp), intent(out)	yr,
		real(wp), intent(out)	yi )

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◆ pythag()

subroutine, public m_eigen_solver::pythag	(	real(wp), intent(in)	a,
		real(wp), intent(in)	b,
		real(wp), intent(out)	c )

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ cbabk2()

◆ cbal()

◆ cdiv()

◆ cg()

◆ comqr2()

◆ corth()

◆ csroot()

◆ pythag()