CPBTF2 man page on IRIX

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CPBTF2(3F)							    CPBTF2(3F)

NAME
     CPBTF2 - compute the Cholesky factorization of a complex Hermitian
     positive definite band matrix A

SYNOPSIS
     SUBROUTINE CPBTF2( UPLO, N, KD, AB, LDAB, INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, KD, LDAB, N

	 COMPLEX	AB( LDAB, * )

PURPOSE
     CPBTF2 computes the Cholesky factorization of a complex Hermitian
     positive definite band matrix A.

     The factorization has the form
	A = U' * U ,  if UPLO = 'U', or
	A = L  * L',  if UPLO = 'L',
     where U is an upper triangular matrix, U' is the conjugate transpose of
     U, and L is lower triangular.

     This is the unblocked version of the algorithm, calling Level 2 BLAS.

ARGUMENTS
     UPLO    (input) CHARACTER*1
	     Specifies whether the upper or lower triangular part of the
	     Hermitian matrix A is stored:
	     = 'U':  Upper triangular
	     = 'L':  Lower triangular

     N	     (input) INTEGER
	     The order of the matrix A.	 N >= 0.

     KD	     (input) INTEGER
	     The number of super-diagonals of the matrix A if UPLO = 'U', or
	     the number of sub-diagonals if UPLO = 'L'.	 KD >= 0.

     AB	     (input/output) 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 triangular factor U or L from the
	     Cholesky factorization A = U'*U or A = L*L' of the band matrix A,
	     in the same storage format as A.

									Page 1

CPBTF2(3F)							    CPBTF2(3F)

     LDAB    (input) INTEGER
	     The leading dimension of the array AB.  LDAB >= KD+1.

     INFO    (output) INTEGER
	     = 0: successful exit
	     < 0: if INFO = -k, the k-th argument had an illegal value
	     > 0: if INFO = k, the leading minor of order k is not positive
	     definite, and the factorization could not be completed.

FURTHER DETAILS
     The band storage scheme is illustrated by the following example, when N =
     6, KD = 2, and UPLO = 'U':

     On entry:			     On exit:

	 *    *	  a13  a24  a35	 a46	  *    *   u13	u24  u35  u46
	 *   a12  a23  a34  a45	 a56	  *   u12  u23	u34  u45  u56
	a11  a22  a33  a44  a55	 a66	 u11  u22  u33	u44  u55  u66

     Similarly, if UPLO = 'L' the format of A is as follows:

     On entry:			     On exit:

	a11  a22  a33  a44  a55	 a66	 l11  l22  l33	l44  l55  l66
	a21  a32  a43  a54  a65	  *	 l21  l32  l43	l54  l65   *
	a31  a42  a53  a64   *	  *	 l31  l42  l53	l64   *	   *

     Array elements marked * are not used by the routine.

									Page 2

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