zpbstf (l) - Linux Man Pages
zpbstf: computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A
NAMEZPBSTF - computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A
- SUBROUTINE ZPBSTF(
- UPLO, N, KD, AB, LDAB, INFO )
- CHARACTER UPLO
- INTEGER INFO, KD, LDAB, N
- COMPLEX*16 AB( LDAB, * )
PURPOSEZPBSTF 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:
where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m.
- UPLO (input) CHARACTER*1
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
- N (input) INTEGER
- The order of the matrix A. N >= 0.
- KD (input) INTEGER
- The number of superdiagonals of the matrix A if UPLO = aqUaq, or the number of subdiagonals if UPLO = aqLaq. KD >= 0.
- AB (input/output) 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 = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = aqLaq, 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 (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1.
- INFO (output) 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.
FURTHER DETAILSThe band storage scheme is illustrated by the following example, when N = 7, KD = 2:
S = ( s11 s12 s13 )
If UPLO = aqUaq, the array AB holds:
on entry: on exit:
on entry: on exit:
a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 a21 a32 a43 a54 a65 a76 * s12aq s23aq s34aq s54 s65 s76 * a31 a42 a53 a64 a64 * * s13aq s24aq s53 s64 s75 * * Array elements marked * are not used by the routine; s12aq denotes conjg(s12); the diagonal elements of S are real.