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RedHat 9 (Linux i386) - man page for cpbsv (redhat section l)

CPBSV(l)					)					 CPBSV(l)

NAME
       CPBSV - compute the solution to a complex system of linear equations A * X = B,

SYNOPSIS
       SUBROUTINE CPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

	   CHARACTER	 UPLO

	   INTEGER	 INFO, KD, LDAB, LDB, N, NRHS

	   COMPLEX	 AB( LDAB, * ), B( LDB, * )

PURPOSE
       CPBSV  computes the solution to a complex system of linear equations A * X = B, where A is
       an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS matrices.

       The Cholesky decomposition is used to factor A as
	  A = U**H * U,  if UPLO = 'U', or
	  A = L * L**H,  if UPLO = 'L',
       where U is an upper triangular band matrix, and L is a lower triangular band matrix,  with
       the  same  number  of superdiagonals or subdiagonals as A.  The factored form of A is then
       used to solve the system of equations A * X = B.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The number of linear equations, i.e., the order of the matrix A.  N >= 0.

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

       NRHS    (input) INTEGER
	       The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS
	       >= 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 col-
	       umn 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).
	       See below for further details.

	       On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization
	       A = U**H*U or A = L*L**H of the band matrix A, in the same storage format as A.

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

       B       (input/output) COMPLEX array, dimension (LDB,NRHS)
	       On entry, the N-by-NRHS right hand side matrix B.  On exit, if INFO = 0, the N-by-
	       NRHS solution matrix X.

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= max(1,N).

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

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.

LAPACK version 3.0			   15 June 2000 				 CPBSV(l)


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