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---
:name: dppequ
:md5sum: 62f6b4c55adfca98e81cfdd929796b64
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ap:
:type: doublereal
:intent: input
:dims:
- ldap
- s:
:type: doublereal
:intent: output
:dims:
- n
- scond:
:type: doublereal
:intent: output
- amax:
:type: doublereal
:intent: output
- info:
:type: integer
:intent: output
:substitutions:
n: ((int)sqrtf(ldap*8+1.0f)-1)/2
:fortran_help: " SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DPPEQU computes row and column scalings intended to equilibrate a\n\
* symmetric positive definite matrix A in packed storage and reduce\n\
* its condition number (with respect to the two-norm). S contains the\n\
* scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix\n\
* B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.\n\
* This choice of S puts the condition number of B within a factor N of\n\
* the smallest possible condition number over all possible diagonal\n\
* scalings.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)\n\
* The upper or lower triangle of the symmetric matrix A, packed\n\
* columnwise in a linear array. The j-th column of A is stored\n\
* in the array AP as follows:\n\
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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\
* 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\
* =====================================================================\n\
*\n"
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