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---
:name: dggbal
:md5sum: 24ff4f10c5e8790d8d13027b9337a32b
:category: :subroutine
:arguments:
- job:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: doublereal
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- ilo:
:type: integer
:intent: output
- ihi:
:type: integer
:intent: output
- lscale:
:type: doublereal
:intent: output
:dims:
- n
- rscale:
:type: doublereal
:intent: output
:dims:
- n
- work:
:type: doublereal
:intent: workspace
:dims:
- "(lsame_(&job,\"S\")||lsame_(&job,\"B\")) ? MAX(1,6*n) : (lsame_(&job,\"N\")||lsame_(&job,\"P\")) ? 1 : 0"
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DGGBAL balances a pair of general real matrices (A,B). This\n\
* involves, first, permuting A and B by similarity transformations to\n\
* isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N\n\
* elements on the diagonal; and second, applying a diagonal similarity\n\
* transformation to rows and columns ILO to IHI to make the rows\n\
* and columns as close in norm as possible. Both steps are optional.\n\
*\n\
* Balancing may reduce the 1-norm of the matrices, and improve the\n\
* accuracy of the computed eigenvalues and/or eigenvectors in the\n\
* generalized eigenvalue problem A*x = lambda*B*x.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOB (input) CHARACTER*1\n\
* Specifies the operations to be performed on A and B:\n\
* = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0\n\
* and RSCALE(I) = 1.0 for i = 1,...,N.\n\
* = 'P': permute only;\n\
* = 'S': scale only;\n\
* = 'B': both permute and scale.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A and B. N >= 0.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
* On entry, the input matrix A.\n\
* On exit, A is overwritten by the balanced matrix.\n\
* If JOB = 'N', A is not referenced.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* B (input/output) DOUBLE PRECISION array, dimension (LDB,N)\n\
* On entry, the input matrix B.\n\
* On exit, B is overwritten by the balanced matrix.\n\
* If JOB = 'N', B is not referenced.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* ILO (output) INTEGER\n\
* IHI (output) INTEGER\n\
* ILO and IHI are set to integers such that on exit\n\
* A(i,j) = 0 and B(i,j) = 0 if i > j and\n\
* j = 1,...,ILO-1 or i = IHI+1,...,N.\n\
* If JOB = 'N' or 'S', ILO = 1 and IHI = N.\n\
*\n\
* LSCALE (output) DOUBLE PRECISION array, dimension (N)\n\
* Details of the permutations and scaling factors applied\n\
* to the left side of A and B. If P(j) is the index of the\n\
* row interchanged with row j, and D(j)\n\
* is the scaling factor applied to row j, then\n\
* LSCALE(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\
* RSCALE (output) DOUBLE PRECISION array, dimension (N)\n\
* Details of the permutations and scaling factors applied\n\
* to the right side of A and B. If P(j) is the index of the\n\
* column interchanged with column j, and D(j)\n\
* is the scaling factor applied to column j, then\n\
* LSCALE(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\
* WORK (workspace) DOUBLE PRECISION array, dimension (lwork)\n\
* lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and\n\
* at least 1 when JOB = 'N' or 'P'.\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"
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