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---
:name: sgeevx
:md5sum: def8c51083d6025e43422c29fe495dfd
:category: :subroutine
:arguments:
- balanc:
:type: char
:intent: input
- jobvl:
:type: char
:intent: input
- jobvr:
:type: char
:intent: input
- sense:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: real
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- wr:
:type: real
:intent: output
:dims:
- n
- wi:
: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
- ilo:
:type: integer
:intent: output
- ihi:
:type: integer
:intent: output
- scale:
:type: real
:intent: output
:dims:
- n
- abnrm:
:type: real
:intent: output
- rconde:
:type: real
:intent: output
:dims:
- n
- rcondv:
:type: real
:intent: output
:dims:
- n
- work:
:type: real
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "(lsame_(&sense,\"N\")||lsame_(&sense,\"E\")) ? 2*n : (lsame_(&jobvl,\"V\")||lsame_(&jobvr,\"V\")) ? 3*n : (lsame_(&sense,\"V\")||lsame_(&sense,\"B\")) ? n*(n+6) : 0"
- iwork:
:type: integer
:intent: workspace
:dims:
- "(lsame_(&sense,\"N\")||lsame_(&sense,\"E\")) ? 0 : 2*n-2"
- info:
:type: integer
:intent: output
:substitutions:
ldvr: "lsame_(&jobvr,\"V\") ? n : 1"
ldvl: "lsame_(&jobvl,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE SGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SGEEVX computes for an N-by-N real nonsymmetric matrix A, the\n\
* eigenvalues and, optionally, the left and/or right eigenvectors.\n\
*\n\
* Optionally also, it computes a balancing transformation to improve\n\
* the conditioning of the eigenvalues and eigenvectors (ILO, IHI,\n\
* SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues\n\
* (RCONDE), and reciprocal condition numbers for the right\n\
* eigenvectors (RCONDV).\n\
*\n\
* The right eigenvector v(j) of A satisfies\n\
* A * v(j) = lambda(j) * v(j)\n\
* where lambda(j) is its eigenvalue.\n\
* The left eigenvector u(j) of A satisfies\n\
* u(j)**H * A = lambda(j) * u(j)**H\n\
* where u(j)**H denotes the conjugate transpose of u(j).\n\
*\n\
* The computed eigenvectors are normalized to have Euclidean norm\n\
* equal to 1 and largest component real.\n\
*\n\
* Balancing a matrix means permuting the rows and columns to make it\n\
* more nearly upper triangular, and applying a diagonal similarity\n\
* transformation D * A * D**(-1), where D is a diagonal matrix, to\n\
* make its rows and columns closer in norm and the condition numbers\n\
* of its eigenvalues and eigenvectors smaller. The computed\n\
* reciprocal condition numbers correspond to the balanced matrix.\n\
* Permuting rows and columns will not change the condition numbers\n\
* (in exact arithmetic) but diagonal scaling will. For further\n\
* explanation of balancing, see section 4.10.2 of the LAPACK\n\
* Users' Guide.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* BALANC (input) CHARACTER*1\n\
* Indicates how the input matrix should be diagonally scaled\n\
* and/or permuted to improve the conditioning of its\n\
* eigenvalues.\n\
* = 'N': Do not diagonally scale or permute;\n\
* = 'P': Perform permutations to make the matrix more nearly\n\
* upper triangular. Do not diagonally scale;\n\
* = 'S': Diagonally scale the matrix, i.e. replace A by\n\
* D*A*D**(-1), where D is a diagonal matrix chosen\n\
* to make the rows and columns of A more equal in\n\
* norm. Do not permute;\n\
* = 'B': Both diagonally scale and permute A.\n\
*\n\
* Computed reciprocal condition numbers will be for the matrix\n\
* after balancing and/or permuting. Permuting does not change\n\
* condition numbers (in exact arithmetic), but balancing does.\n\
*\n\
* JOBVL (input) CHARACTER*1\n\
* = 'N': left eigenvectors of A are not computed;\n\
* = 'V': left eigenvectors of A are computed.\n\
* If SENSE = 'E' or 'B', JOBVL must = 'V'.\n\
*\n\
* JOBVR (input) CHARACTER*1\n\
* = 'N': right eigenvectors of A are not computed;\n\
* = 'V': right eigenvectors of A are computed.\n\
* If SENSE = 'E' or 'B', JOBVR must = 'V'.\n\
*\n\
* SENSE (input) CHARACTER*1\n\
* Determines which reciprocal condition numbers are computed.\n\
* = 'N': None are computed;\n\
* = 'E': Computed for eigenvalues only;\n\
* = 'V': Computed for right eigenvectors only;\n\
* = 'B': Computed for eigenvalues and right eigenvectors.\n\
*\n\
* If SENSE = 'E' or 'B', both left and right eigenvectors\n\
* must also be computed (JOBVL = 'V' and JOBVR = 'V').\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) REAL array, dimension (LDA,N)\n\
* On entry, the N-by-N matrix A.\n\
* On exit, A has been overwritten. If JOBVL = 'V' or\n\
* JOBVR = 'V', A contains the real Schur form of the balanced\n\
* version of the input matrix A.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* WR (output) REAL array, dimension (N)\n\
* WI (output) REAL array, dimension (N)\n\
* WR and WI contain the real and imaginary parts,\n\
* respectively, of the computed eigenvalues. Complex\n\
* conjugate pairs of eigenvalues will appear consecutively\n\
* with the eigenvalue having the positive imaginary part\n\
* first.\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\n\
* as their eigenvalues.\n\
* If JOBVL = 'N', VL is not referenced.\n\
* If the j-th eigenvalue is real, then u(j) = VL(:,j),\n\
* the j-th column of VL.\n\
* If the j-th and (j+1)-st eigenvalues form a complex\n\
* conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and\n\
* u(j+1) = VL(:,j) - i*VL(:,j+1).\n\
*\n\
* LDVL (input) INTEGER\n\
* The leading dimension of the array VL. LDVL >= 1; if\n\
* 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\n\
* as their eigenvalues.\n\
* If JOBVR = 'N', VR is not referenced.\n\
* If the j-th eigenvalue is real, then v(j) = VR(:,j),\n\
* the j-th column of VR.\n\
* If the j-th and (j+1)-st eigenvalues form a complex\n\
* conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and\n\
* v(j+1) = VR(:,j) - i*VR(:,j+1).\n\
*\n\
* LDVR (input) INTEGER\n\
* The leading dimension of the array VR. LDVR >= 1, and if\n\
* JOBVR = 'V', LDVR >= N.\n\
*\n\
* ILO (output) INTEGER\n\
* IHI (output) INTEGER\n\
* ILO and IHI are integer values determined when A was\n\
* balanced. The balanced A(i,j) = 0 if I > J and \n\
* J = 1,...,ILO-1 or I = IHI+1,...,N.\n\
*\n\
* SCALE (output) REAL array, dimension (N)\n\
* Details of the permutations and scaling factors applied\n\
* when balancing A. If P(j) is the index of the row and column\n\
* interchanged with row and column j, and D(j) is the scaling\n\
* factor applied to row and column j, then\n\
* SCALE(J) = P(J), for J = 1,...,ILO-1\n\
* = D(J), for J = ILO,...,IHI\n\
* = P(J) for J = IHI+1,...,N.\n\
* The order in which the interchanges are made is N to IHI+1,\n\
* then 1 to ILO-1.\n\
*\n\
* ABNRM (output) REAL\n\
* The one-norm of the balanced matrix (the maximum\n\
* of the sum of absolute values of elements of any column).\n\
*\n\
* RCONDE (output) REAL array, dimension (N)\n\
* RCONDE(j) is the reciprocal condition number of the j-th\n\
* eigenvalue.\n\
*\n\
* RCONDV (output) REAL array, dimension (N)\n\
* RCONDV(j) is the reciprocal condition number of the j-th\n\
* right eigenvector.\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. If SENSE = 'N' or 'E',\n\
* LWORK >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V',\n\
* LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6).\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\
* IWORK (workspace) INTEGER array, dimension (2*N-2)\n\
* If SENSE = 'N' or 'E', not referenced.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* > 0: if INFO = i, the QR algorithm failed to compute all the\n\
* eigenvalues, and no eigenvectors or condition numbers\n\
* have been computed; elements 1:ILO-1 and i+1:N of WR\n\
* and WI contain eigenvalues which have converged.\n\
*\n\n\
* =====================================================================\n\
*\n"
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