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SUBROUTINE <a name="SPBSTF.1"></a><a href="spbstf.f.html#SPBSTF.1">SPBSTF</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> REAL 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="SPBSTF.18"></a><a href="spbstf.f.html#SPBSTF.1">SPBSTF</a> computes a split Cholesky factorization of a real
</span><span class="comment">*</span><span class="comment"> symmetric positive definite band matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> This routine is designed to be used in conjunction with <a name="SSBGST.21"></a><a href="ssbgst.f.html#SSBGST.1">SSBGST</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The factorization has the form A = S**T*S where S is a band matrix
</span><span class="comment">*</span><span class="comment"> of the same bandwidth as A and the following structure:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> S = ( U )
</span><span class="comment">*</span><span class="comment"> ( M L )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where U is upper triangular of order m = (n+kd)/2, and L is lower
</span><span class="comment">*</span><span class="comment"> triangular of order n-m.
</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"> = 'U': Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangle of A is stored.
</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 superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input/output) REAL 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 factor S from the split Cholesky
</span><span class="comment">*</span><span class="comment"> factorization A = S**T*S. See Further Details.
</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 = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = i, the factorization could not be completed,
</span><span class="comment">*</span><span class="comment"> because the updated element a(i,i) was negative; the
</span><span class="comment">*</span><span class="comment"> matrix A is not positive definite.
</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 = 7, KD = 2:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> S = ( s11 s12 s13 )
</span><span class="comment">*</span><span class="comment"> ( s22 s23 s24 )
</span><span class="comment">*</span><span class="comment"> ( s33 s34 )
</span><span class="comment">*</span><span class="comment"> ( s44 )
</span><span class="comment">*</span><span class="comment"> ( s53 s54 s55 )
</span><span class="comment">*</span><span class="comment"> ( s64 s65 s66 )
</span><span class="comment">*</span><span class="comment"> ( s75 s76 s77 )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If UPLO = 'U', the array AB holds:
</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 a57 * * s13 s24 s53 s64 s75
</span><span class="comment">*</span><span class="comment"> * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54 s65 s76
</span><span class="comment">*</span><span class="comment"> a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If UPLO = 'L', the array AB holds:
</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 a77 s11 s22 s33 s44 s55 s66 s77
</span><span class="comment">*</span><span class="comment"> a21 a32 a43 a54 a65 a76 * s12 s23 s34 s54 s65 s76 *
</span><span class="comment">*</span><span class="comment"> a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * *
</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 ..
</span> REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
INTEGER J, KLD, KM, M
REAL AJJ
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.111"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.112"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL SSCAL, SSYR, <a name="XERBLA.115"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, MIN, SQRT
<span class="comment">*</span><span class="comment"> ..
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