nwtc_lapack::lapack_ggev Interface Reference

Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B). More...

Public Member Functions
subroutine	lapack_dggev (JOBVL, JOBVR, N, A, B, ALPHAR, ALPHAI, BETA, VL, VR, WORK, LWORK, ErrStat, ErrMsg)
	Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B). More...
subroutine	lapack_sggev (JOBVL, JOBVR, N, A, B, ALPHAR, ALPHAI, BETA, VL, VR, WORK, LWORK, ErrStat, ErrMsg)
	Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B). More...

Detailed Description

Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B).

Member Function/Subroutine Documentation

lapack_dggev()

subroutine nwtc_lapack::lapack_ggev::lapack_dggev	(	character(1), intent(in)	JOBVL,
		character(1), intent(in)	JOBVR,
		integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(inout)	A,
		real(r8ki), dimension( :, : ), intent(inout)	B,
		real(r8ki), dimension( : ), intent(out)	ALPHAR,
		real(r8ki), dimension( : ), intent(out)	ALPHAI,
		real(r8ki), dimension( : ), intent(out)	BETA,
		real(r8ki), dimension( :, : ), intent(out)	VL,
		real(r8ki), dimension( :, : ), intent(out)	VR,
		real(r8ki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B).

use LAPACK_GGEV (nwtc_lapack::lapack_ggev) instead of this specific function.

Parameters

[in]	jobvl	= 'N': do not compute the left generalized eigenvectors; = 'V': compute the left generalized eigenvectors.
[in]	jobvr	= 'N': do not compute the right generalized eigenvectors; = 'V': compute the right generalized eigenvectors.
[in]	n	The order of the matrices A, B, VL, and VR. N >= 0.
[in]	lwork	The dimension of the array WORK. LWORK >= max(1,8*N). For good performance, LWORK must generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[in,out]	a	dimension (LDA, N). On entry, the matrix A in the pair (A,B). On exit, A has been overwritten.
[in,out]	b	dimension (LDB, N). On entry, the matrix B in the pair (A,B). On exit, B has been overwritten.
[out]	alphar	dimension (N). See comments for variable "Beta"
[out]	alphai	dimension (N). See comments for variable "Beta".
[out]	beta	On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the generalized eigenvalues. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) negative.

Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio alpha/beta. However, ALPHAR and ALPHAI will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).

Parameters

[out]	vl	dimension (LDVL,N). If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVL = 'N'.
[out]	vr	dimension (LDVR,N). If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVR = 'N'.
[in,out]	work	dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[out]	errstat	Error level
[out]	errmsg	Message describing error

lapack_sggev()

subroutine nwtc_lapack::lapack_ggev::lapack_sggev	(	character(1), intent(in)	JOBVL,
		character(1), intent(in)	JOBVR,
		integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(inout)	A,
		real(siki), dimension( :, : ), intent(inout)	B,
		real(siki), dimension( : ), intent(out)	ALPHAR,
		real(siki), dimension( : ), intent(out)	ALPHAI,
		real(siki), dimension( : ), intent(out)	BETA,
		real(siki), dimension( :, : ), intent(out)	VL,
		real(siki), dimension( :, : ), intent(out)	VR,
		real(siki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B).

use LAPACK_GGEV (nwtc_lapack::lapack_ggev) instead of this specific function.

Parameters

[in]	jobvl	= 'N': do not compute the left generalized eigenvectors; = 'V': compute the left generalized eigenvectors.
[in]	jobvr	= 'N': do not compute the right generalized eigenvectors; = 'V': compute the right generalized eigenvectors.
[in]	n	The order of the matrices A, B, VL, and VR. N >= 0.
[in]	lwork	The dimension of the array WORK. LWORK >= max(1,8*N). For good performance, LWORK must generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[in,out]	a	dimension (LDA, N). On entry, the matrix A in the pair (A,B). On exit, A has been overwritten.
[in,out]	b	dimension (LDB, N). On entry, the matrix B in the pair (A,B). On exit, B has been overwritten.
[out]	alphar	dimension (N). See comments for variable "Beta"
[out]	alphai	dimension (N). See comments for variable "Beta".
[out]	beta	On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the generalized eigenvalues. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) negative.

Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio alpha/beta. However, ALPHAR and ALPHAI will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).

Parameters

[out]	vl	dimension (LDVL,N). If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVL = 'N'.
[out]	vr	dimension (LDVR,N). If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVR = 'N'.
[in,out]	work	dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[out]	errstat	Error level
[out]	errmsg	Message describing error

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The documentation for this interface was generated from the following file:

• NWTC_LAPACK.f90