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---
:name: dsyequb
:md5sum: e64c1e10d53f2652cb55a29099f76c13
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- s:
:type: doublereal
:intent: output
:dims:
- n
- scond:
:type: doublereal
:intent: output
- amax:
:type: doublereal
:intent: output
- work:
:type: doublereal
:intent: workspace
:dims:
- 3*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DSYEQUB computes row and column scalings intended to equilibrate a\n\
* symmetric matrix A and reduce its condition number\n\
* (with respect to the two-norm). S contains the scale factors,\n\
* S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with\n\
* elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This\n\
* choice of S puts the condition number of B within a factor N of the\n\
* smallest possible condition number over all possible diagonal\n\
* scalings.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* Specifies whether the details of the factorization are stored\n\
* as an upper or lower triangular matrix.\n\
* = 'U': Upper triangular, form is A = U*D*U**T;\n\
* = 'L': Lower triangular, form is A = L*D*L**T.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input) DOUBLE PRECISION array, dimension (LDA,N)\n\
* The N-by-N symmetric matrix whose scaling\n\
* factors are to be computed. Only the diagonal elements of A\n\
* are referenced.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* S (output) DOUBLE PRECISION array, dimension (N)\n\
* If INFO = 0, S contains the scale factors for A.\n\
*\n\
* SCOND (output) DOUBLE PRECISION\n\
* If INFO = 0, S contains the ratio of the smallest S(i) to\n\
* the largest S(i). If SCOND >= 0.1 and AMAX is neither too\n\
* large nor too small, it is not worth scaling by S.\n\
*\n\
* AMAX (output) DOUBLE PRECISION\n\
* Absolute value of largest matrix element. If AMAX is very\n\
* close to overflow or very close to underflow, the matrix\n\
* should be scaled.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (3*N)\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 i-th diagonal element is nonpositive.\n\
*\n\n\
* Further Details\n\
* ======= =======\n\
*\n\
* Reference: Livne, O.E. and Golub, G.H., \"Scaling by Binormalization\",\n\
* Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.\n\
* DOI 10.1023/B:NUMA.0000016606.32820.69\n\
* Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf\n\
*\n\
* =====================================================================\n\
*\n"
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