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---
:name: cpbequ
:md5sum: 23fe815105e015e77f5f060fae9224b5
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- ab:
:type: complex
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- s:
:type: real
:intent: output
:dims:
- n
- scond:
:type: real
:intent: output
- amax:
:type: real
:intent: output
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CPBEQU computes row and column scalings intended to equilibrate a\n\
* Hermitian positive definite band matrix A and reduce its condition\n\
* number (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\
* = 'U': Upper triangular of A is stored;\n\
* = 'L': Lower triangular of A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* AB (input) COMPLEX array, dimension (LDAB,N)\n\
* The upper or lower triangle of the Hermitian band matrix A,\n\
* stored in the first KD+1 rows of the array. The j-th column\n\
* of A is stored in the j-th column of the array AB as follows:\n\
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array A. LDAB >= KD+1.\n\
*\n\
* S (output) REAL array, dimension (N)\n\
* If INFO = 0, S contains the scale factors for A.\n\
*\n\
* SCOND (output) REAL\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) REAL\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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