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---
:name: cgbtrf
:md5sum: cb767c902d74f024a5a58dad38d41372
: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: complex
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: output
:dims:
- MIN(m,n)
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CGBTRF computes an LU factorization of a complex m-by-n band matrix A\n\
* using partial pivoting with row interchanges.\n\
*\n\
* This is the blocked version of the algorithm, calling Level 3 BLAS.\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/output) COMPLEX array, dimension (LDAB,N)\n\
* On entry, the matrix A in band storage, in rows KL+1 to\n\
* 2*KL+KU+1; rows 1 to KL of the array need not be set.\n\
* The j-th column of A is stored in the j-th column of the\n\
* array AB as follows:\n\
* AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)\n\
*\n\
* On exit, details of the factorization: U is stored as an\n\
* upper triangular band matrix with KL+KU superdiagonals in\n\
* rows 1 to KL+KU+1, and the multipliers used during the\n\
* factorization are stored in rows KL+KU+2 to 2*KL+KU+1.\n\
* See below for further details.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= 2*KL+KU+1.\n\
*\n\
* IPIV (output) INTEGER array, dimension (min(M,N))\n\
* The pivot indices; for 1 <= i <= min(M,N), row i of the\n\
* matrix was interchanged with row IPIV(i).\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, U(i,i) is exactly zero. The factorization\n\
* has been completed, but the factor U is exactly\n\
* singular, and division by zero will occur if it is used\n\
* to solve a system of equations.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The band storage scheme is illustrated by the following example, when\n\
* M = N = 6, KL = 2, KU = 1:\n\
*\n\
* On entry: On exit:\n\
*\n\
* * * * + + + * * * u14 u25 u36\n\
* * * + + + + * * u13 u24 u35 u46\n\
* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56\n\
* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66\n\
* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *\n\
* a31 a42 a53 a64 * * m31 m42 m53 m64 * *\n\
*\n\
* Array elements marked * are not used by the routine; elements marked\n\
* + need not be set on entry, but are required by the routine to store\n\
* elements of U because of fill-in resulting from the row interchanges.\n\
*\n\
* =====================================================================\n\
*\n"
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