cpbstf-f(3)

cpbstf.f –

Synopsis

Functions/Subroutines

subroutine cpbstf (UPLO, N, KD, AB, LDAB, INFO)
CPBSTF

Function/Subroutine Documentation

subroutine cpbstf (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, integerINFO)

CPBSTF

Purpose:

 CPBSTF computes a split Cholesky factorization of a complex
 Hermitian positive definite band matrix A.
 This routine is designed to be used in conjunction with CHBGST.
 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.

Parameters:

UPLO

 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 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

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= KD+1.

INFO

 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

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 cpbstf.f.

Author

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