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---
:name: zgbequb
:md5sum: cb0bd19ed592f0af1af6e5081b15065e
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- ab:
:type: doublereal
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- r:
:type: doublereal
:intent: output
:dims:
- m
- c:
:type: doublereal
:intent: output
:dims:
- n
- rowcnd:
:type: doublereal
:intent: output
- colcnd:
:type: doublereal
:intent: output
- amax:
:type: doublereal
:intent: output
- info:
:type: integer
:intent: output
:substitutions:
m: ldab
:fortran_help: " SUBROUTINE ZGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZGBEQUB computes row and column scalings intended to equilibrate an\n\
* M-by-N matrix A and reduce its condition number. R returns the row\n\
* scale factors and C the column scale factors, chosen to try to make\n\
* the largest element in each row and column of the matrix B with\n\
* elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most\n\
* the radix.\n\
*\n\
* R(i) and C(j) are restricted to be a power of the radix between\n\
* SMLNUM = smallest safe number and BIGNUM = largest safe number. Use\n\
* of these scaling factors is not guaranteed to reduce the condition\n\
* number of A but works well in practice.\n\
*\n\
* This routine differs from ZGEEQU by restricting the scaling factors\n\
* to a power of the radix. Baring over- and underflow, scaling by\n\
* these factors introduces no additional rounding errors. However, the\n\
* scaled entries' magnitured are no longer approximately 1 but lie\n\
* between sqrt(radix) and 1/sqrt(radix).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. N >= 0.\n\
*\n\
* KL (input) INTEGER\n\
* The number of subdiagonals within the band of A. KL >= 0.\n\
*\n\
* KU (input) INTEGER\n\
* The number of superdiagonals within the band of A. KU >= 0.\n\
*\n\
* AB (input) DOUBLE PRECISION array, dimension (LDAB,N)\n\
* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.\n\
* The j-th column of A is stored in the j-th column of the\n\
* array AB as follows:\n\
* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array A. LDAB >= max(1,M).\n\
*\n\
* R (output) DOUBLE PRECISION array, dimension (M)\n\
* If INFO = 0 or INFO > M, R contains the row scale factors\n\
* for A.\n\
*\n\
* C (output) DOUBLE PRECISION array, dimension (N)\n\
* If INFO = 0, C contains the column scale factors for A.\n\
*\n\
* ROWCND (output) DOUBLE PRECISION\n\
* If INFO = 0 or INFO > M, ROWCND contains the ratio of the\n\
* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and\n\
* AMAX is neither too large nor too small, it is not worth\n\
* scaling by R.\n\
*\n\
* COLCND (output) DOUBLE PRECISION\n\
* If INFO = 0, COLCND contains the ratio of the smallest\n\
* C(i) to the largest C(i). If COLCND >= 0.1, it is not\n\
* worth scaling by C.\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, and i is\n\
* <= M: the i-th row of A is exactly zero\n\
* > M: the (i-M)-th column of A is exactly zero\n\
*\n\n\
* =====================================================================\n\
*\n"
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