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zpbstf.f(3) LAPACK zpbstf.f(3)

zpbstf.f -

subroutine zpbstf (UPLO, N, KD, AB, LDAB, INFO)

 ZPBSTF computes a split Cholesky factorization of a complex
 Hermitian positive definite band matrix A.
This routine is designed to be used in conjunction with ZHBGST.
The factorization has the form A = S**H*S where S is a band matrix of the same bandwidth as A and the following structure:
S = ( U ) ( M L )
where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m.
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
          N is INTEGER
          The order of the matrix A.  N >= 0.
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
          AB is COMPLEX*16 array, dimension (LDAB,N)
          On entry, the upper or lower triangle of the Hermitian band
          matrix A, stored in the first kd+1 rows of the array.  The
          j-th column of A is stored in the j-th column of the array AB
          as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
On exit, if INFO = 0, the factor S from the split Cholesky factorization A = S**H*S. See Further Details.
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          > 0: if INFO = i, the factorization could not be completed,
               because the updated element a(i,i) was negative; the
               matrix A is not positive definite.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011
Further Details:
  The band storage scheme is illustrated by the following example, when
  N = 7, KD = 2:
S = ( s11 s12 s13 ) ( s22 s23 s24 ) ( s33 s34 ) ( s44 ) ( s53 s54 s55 ) ( s64 s65 s66 ) ( s75 s76 s77 )
If UPLO = 'U', the array AB holds:
on entry: on exit:
* * a13 a24 a35 a46 a57 * * s13 s24 s53**H s64**H s75**H * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54**H s65**H s76**H a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77
If UPLO = 'L', the array AB holds:
on entry: on exit:
a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 a21 a32 a43 a54 a65 a76 * s12**H s23**H s34**H s54 s65 s76 * a31 a42 a53 a64 a64 * * s13**H s24**H s53 s64 s75 * *
Array elements marked * are not used by the routine; s12**H denotes conjg(s12); the diagonal elements of S are real.
Definition at line 154 of file zpbstf.f.

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