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---
:name: sggev
:md5sum: c8f02404add51e664f048466e576c7d2
:category: :subroutine
:arguments:
- jobvl:
:type: char
:intent: input
- jobvr:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: real
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- alphar:
:type: real
:intent: output
:dims:
- n
- alphai:
:type: real
:intent: output
:dims:
- n
- beta:
:type: real
:intent: output
:dims:
- n
- vl:
:type: real
:intent: output
:dims:
- ldvl
- n
- ldvl:
:type: integer
:intent: input
- vr:
:type: real
:intent: output
:dims:
- ldvr
- n
- ldvr:
:type: integer
:intent: input
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: MAX(1,8*n)
- info:
:type: integer
:intent: output
:substitutions:
ldvr: "lsame_(&jobvr,\"V\") ? n : 1"
ldvl: "lsame_(&jobvl,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE SGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)\n\
* the generalized eigenvalues, and optionally, the left and/or right\n\
* generalized eigenvectors.\n\
*\n\
* A generalized eigenvalue for a pair of matrices (A,B) is a scalar\n\
* lambda or a ratio alpha/beta = lambda, such that A - lambda*B is\n\
* singular. It is usually represented as the pair (alpha,beta), as\n\
* there is a reasonable interpretation for beta=0, and even for both\n\
* being zero.\n\
*\n\
* The right eigenvector v(j) corresponding to the eigenvalue lambda(j)\n\
* of (A,B) satisfies\n\
*\n\
* A * v(j) = lambda(j) * B * v(j).\n\
*\n\
* The left eigenvector u(j) corresponding to the eigenvalue lambda(j)\n\
* of (A,B) satisfies\n\
*\n\
* u(j)**H * A = lambda(j) * u(j)**H * B .\n\
*\n\
* where u(j)**H is the conjugate-transpose of u(j).\n\
*\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBVL (input) CHARACTER*1\n\
* = 'N': do not compute the left generalized eigenvectors;\n\
* = 'V': compute the left generalized eigenvectors.\n\
*\n\
* JOBVR (input) CHARACTER*1\n\
* = 'N': do not compute the right generalized eigenvectors;\n\
* = 'V': compute the right generalized eigenvectors.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A, B, VL, and VR. N >= 0.\n\
*\n\
* A (input/output) REAL array, dimension (LDA, N)\n\
* On entry, the matrix A in the pair (A,B).\n\
* On exit, A has been overwritten.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of A. LDA >= max(1,N).\n\
*\n\
* B (input/output) REAL array, dimension (LDB, N)\n\
* On entry, the matrix B in the pair (A,B).\n\
* On exit, B has been overwritten.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of B. LDB >= max(1,N).\n\
*\n\
* ALPHAR (output) REAL array, dimension (N)\n\
* ALPHAI (output) REAL array, dimension (N)\n\
* BETA (output) REAL array, dimension (N)\n\
* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will\n\
* be the generalized eigenvalues. If ALPHAI(j) is zero, then\n\
* the j-th eigenvalue is real; if positive, then the j-th and\n\
* (j+1)-st eigenvalues are a complex conjugate pair, with\n\
* ALPHAI(j+1) negative.\n\
*\n\
* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)\n\
* may easily over- or underflow, and BETA(j) may even be zero.\n\
* Thus, the user should avoid naively computing the ratio\n\
* alpha/beta. However, ALPHAR and ALPHAI will be always less\n\
* than and usually comparable with norm(A) in magnitude, and\n\
* BETA always less than and usually comparable with norm(B).\n\
*\n\
* VL (output) REAL array, dimension (LDVL,N)\n\
* If JOBVL = 'V', the left eigenvectors u(j) are stored one\n\
* after another in the columns of VL, in the same order as\n\
* their eigenvalues. If the j-th eigenvalue is real, then\n\
* u(j) = VL(:,j), the j-th column of VL. If the j-th and\n\
* (j+1)-th eigenvalues form a complex conjugate pair, then\n\
* u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).\n\
* Each eigenvector is scaled so the largest component has\n\
* abs(real part)+abs(imag. part)=1.\n\
* Not referenced if JOBVL = 'N'.\n\
*\n\
* LDVL (input) INTEGER\n\
* The leading dimension of the matrix VL. LDVL >= 1, and\n\
* if JOBVL = 'V', LDVL >= N.\n\
*\n\
* VR (output) REAL array, dimension (LDVR,N)\n\
* If JOBVR = 'V', the right eigenvectors v(j) are stored one\n\
* after another in the columns of VR, in the same order as\n\
* their eigenvalues. If the j-th eigenvalue is real, then\n\
* v(j) = VR(:,j), the j-th column of VR. If the j-th and\n\
* (j+1)-th eigenvalues form a complex conjugate pair, then\n\
* v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).\n\
* Each eigenvector is scaled so the largest component has\n\
* abs(real part)+abs(imag. part)=1.\n\
* Not referenced if JOBVR = 'N'.\n\
*\n\
* LDVR (input) INTEGER\n\
* The leading dimension of the matrix VR. LDVR >= 1, and\n\
* if JOBVR = 'V', LDVR >= N.\n\
*\n\
* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= max(1,8*N).\n\
* For good performance, LWORK must generally be larger.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* = 1,...,N:\n\
* The QZ iteration failed. No eigenvectors have been\n\
* calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)\n\
* should be correct for j=INFO+1,...,N.\n\
* > N: =N+1: other than QZ iteration failed in SHGEQZ.\n\
* =N+2: error return from STGEVC.\n\
*\n\n\
* =====================================================================\n\
*\n"
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