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SUBROUTINE <a name="DPBTF2.1"></a><a href="dpbtf2.f.html#DPBTF2.1">DPBTF2</a>( UPLO, N, KD, AB, LDAB, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER UPLO
INTEGER INFO, KD, LDAB, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION AB( LDAB, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DPBTF2.18"></a><a href="dpbtf2.f.html#DPBTF2.1">DPBTF2</a> computes the Cholesky factorization of a real symmetric
</span><span class="comment">*</span><span class="comment"> positive definite band matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The factorization has the form
</span><span class="comment">*</span><span class="comment"> A = U' * U , if UPLO = 'U', or
</span><span class="comment">*</span><span class="comment"> A = L * L', if UPLO = 'L',
</span><span class="comment">*</span><span class="comment"> where U is an upper triangular matrix, U' is the transpose of U, and
</span><span class="comment">*</span><span class="comment"> L is lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This is the unblocked version of the algorithm, calling Level 2 BLAS.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment"> symmetric matrix A is stored:
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KD (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of super-diagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the symmetric band
</span><span class="comment">*</span><span class="comment"> matrix A, stored in the first KD+1 rows of the array. The
</span><span class="comment">*</span><span class="comment"> j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, the triangular factor U or L from the
</span><span class="comment">*</span><span class="comment"> Cholesky factorization A = U'*U or A = L*L' of the band
</span><span class="comment">*</span><span class="comment"> matrix A, in the same storage format as A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KD+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -k, the k-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = k, the leading minor of order k is not
</span><span class="comment">*</span><span class="comment"> positive definite, and the factorization could not be
</span><span class="comment">*</span><span class="comment"> completed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The band storage scheme is illustrated by the following example, when
</span><span class="comment">*</span><span class="comment"> N = 6, KD = 2, and UPLO = 'U':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On entry: On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> * * a13 a24 a35 a46 * * u13 u24 u35 u46
</span><span class="comment">*</span><span class="comment"> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
</span><span class="comment">*</span><span class="comment"> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Similarly, if UPLO = 'L' the format of A is as follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On entry: On exit:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
</span><span class="comment">*</span><span class="comment"> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
</span><span class="comment">*</span><span class="comment"> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Array elements marked * are not used by the routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
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