cpbsv man page on Scientific

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CPBSV(1)	      LAPACK driver routine (version 3.2)	      CPBSV(1)

NAME
       CPBSV  -	 computes 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 equa‐
       tions 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 subdiagonals 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 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).  See below for further details.  On exit, if
	       INFO  =	0, the triangular factor U or L from the Cholesky fac‐
	       torization 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 Simi‐
       larly, 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 driver routine (version 3November 2008			      CPBSV(1)
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