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---
:name: spbtf2
:md5sum: 60a9f976698f8a9e6d64eb1bc045f8d4
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- ab:
:type: real
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SPBTF2( UPLO, N, KD, AB, LDAB, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SPBTF2 computes the Cholesky factorization of a real symmetric\n\
* positive definite band matrix A.\n\
*\n\
* The factorization has the form\n\
* A = U' * U , if UPLO = 'U', or\n\
* A = L * L', if UPLO = 'L',\n\
* where U is an upper triangular matrix, U' is the transpose of U, and\n\
* L is lower triangular.\n\
*\n\
* This is the unblocked version of the algorithm, calling Level 2 BLAS.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* Specifies whether the upper or lower triangular part of the\n\
* symmetric matrix A is stored:\n\
* = 'U': Upper triangular\n\
* = 'L': Lower triangular\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of super-diagonals of the matrix A if UPLO = 'U',\n\
* or the number of sub-diagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* AB (input/output) REAL array, dimension (LDAB,N)\n\
* On entry, the upper or lower triangle of the symmetric band\n\
* matrix A, stored in the first KD+1 rows of the array. The\n\
* j-th column of A is stored in the j-th column of the array AB\n\
* 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\
* On exit, if INFO = 0, the triangular factor U or L from the\n\
* Cholesky factorization A = U'*U or A = L*L' of the band\n\
* matrix A, in the same storage format as A.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD+1.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -k, the k-th argument had an illegal value\n\
* > 0: if INFO = k, the leading minor of order k is not\n\
* positive definite, and the factorization could not be\n\
* completed.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The band storage scheme is illustrated by the following example, when\n\
* N = 6, KD = 2, and UPLO = 'U':\n\
*\n\
* On entry: On exit:\n\
*\n\
* * * a13 a24 a35 a46 * * 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\
*\n\
* Similarly, if UPLO = 'L' the format of A is as follows:\n\
*\n\
* On entry: On exit:\n\
*\n\
* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66\n\
* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *\n\
* a31 a42 a53 a64 * * l31 l42 l53 l64 * *\n\
*\n\
* Array elements marked * are not used by the routine.\n\
*\n\
* =====================================================================\n\
*\n"
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