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---
:name: dggbak
:md5sum: b7d43e8ff3f48a5a2749288abaa6a7c0
:category: :subroutine
:arguments:
- job:
:type: char
:intent: input
- side:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ilo:
:type: integer
:intent: input
- ihi:
:type: integer
:intent: input
- lscale:
:type: doublereal
:intent: input
:dims:
- n
- rscale:
:type: doublereal
:intent: input
:dims:
- n
- m:
:type: integer
:intent: input
- v:
:type: doublereal
:intent: input/output
:dims:
- ldv
- m
- ldv:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DGGBAK forms the right or left eigenvectors of a real generalized\n\
* eigenvalue problem A*x = lambda*B*x, by backward transformation on\n\
* the computed eigenvectors of the balanced pair of matrices output by\n\
* DGGBAL.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOB (input) CHARACTER*1\n\
* Specifies the type of backward transformation required:\n\
* = 'N': do nothing, return immediately;\n\
* = 'P': do backward transformation for permutation only;\n\
* = 'S': do backward transformation for scaling only;\n\
* = 'B': do backward transformations for both permutation and\n\
* scaling.\n\
* JOB must be the same as the argument JOB supplied to DGGBAL.\n\
*\n\
* SIDE (input) CHARACTER*1\n\
* = 'R': V contains right eigenvectors;\n\
* = 'L': V contains left eigenvectors.\n\
*\n\
* N (input) INTEGER\n\
* The number of rows of the matrix V. N >= 0.\n\
*\n\
* ILO (input) INTEGER\n\
* IHI (input) INTEGER\n\
* The integers ILO and IHI determined by DGGBAL.\n\
* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.\n\
*\n\
* LSCALE (input) DOUBLE PRECISION array, dimension (N)\n\
* Details of the permutations and/or scaling factors applied\n\
* to the left side of A and B, as returned by DGGBAL.\n\
*\n\
* RSCALE (input) DOUBLE PRECISION array, dimension (N)\n\
* Details of the permutations and/or scaling factors applied\n\
* to the right side of A and B, as returned by DGGBAL.\n\
*\n\
* M (input) INTEGER\n\
* The number of columns of the matrix V. M >= 0.\n\
*\n\
* V (input/output) DOUBLE PRECISION array, dimension (LDV,M)\n\
* On entry, the matrix of right or left eigenvectors to be\n\
* transformed, as returned by DTGEVC.\n\
* On exit, V is overwritten by the transformed eigenvectors.\n\
*\n\
* LDV (input) INTEGER\n\
* The leading dimension of the matrix V. LDV >= max(1,N).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* See R.C. Ward, Balancing the generalized eigenvalue problem,\n\
* SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.\n\
*\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL LEFTV, RIGHTV\n INTEGER I, K\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL DSCAL, DSWAP, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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