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---
:name: dgebal
:md5sum: 45f9fb3e24750e422000cd2ba1545396
: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
- ilo:
:type: integer
:intent: output
- ihi:
:type: integer
:intent: output
- scale:
:type: doublereal
:intent: output
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DGEBAL balances a general real matrix A. This involves, first,\n\
* permuting A by a similarity transformation to isolate eigenvalues\n\
* in the first 1 to ILO-1 and last IHI+1 to N elements on the\n\
* diagonal; and second, applying a diagonal similarity transformation\n\
* to rows and columns ILO to IHI to make the rows and columns as\n\
* close in norm as possible. Both steps are optional.\n\
*\n\
* Balancing may reduce the 1-norm of the matrix, and improve the\n\
* accuracy of the computed eigenvalues and/or eigenvectors.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOB (input) CHARACTER*1\n\
* Specifies the operations to be performed on A:\n\
* = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0\n\
* 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 matrix A. 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\
* See Further Details.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= 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 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.\n\
* If JOB = 'N' or 'S', ILO = 1 and IHI = N.\n\
*\n\
* SCALE (output) DOUBLE PRECISION array, dimension (N)\n\
* Details of the permutations and scaling factors applied to\n\
* A. If P(j) is the index of the row and column interchanged\n\
* with row and column j and D(j) is the scaling factor\n\
* 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\
* 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\
* The permutations consist of row and column interchanges which put\n\
* the matrix in the form\n\
*\n\
* ( T1 X Y )\n\
* P A P = ( 0 B Z )\n\
* ( 0 0 T2 )\n\
*\n\
* where T1 and T2 are upper triangular matrices whose eigenvalues lie\n\
* along the diagonal. The column indices ILO and IHI mark the starting\n\
* and ending columns of the submatrix B. Balancing consists of applying\n\
* a diagonal similarity transformation inv(D) * B * D to make the\n\
* 1-norms of each row of B and its corresponding column nearly equal.\n\
* The output matrix is\n\
*\n\
* ( T1 X*D Y )\n\
* ( 0 inv(D)*B*D inv(D)*Z ).\n\
* ( 0 0 T2 )\n\
*\n\
* Information about the permutations P and the diagonal matrix D is\n\
* returned in the vector SCALE.\n\
*\n\
* This subroutine is based on the EISPACK routine BALANC.\n\
*\n\
* Modified by Tzu-Yi Chen, Computer Science Division, University of\n\
* California at Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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