cpbtrf(l) [redhat man page]

CPBTRF(l)								 )								 CPBTRF(l)

NAME

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

SYNOPSIS

       SUBROUTINE CPBTRF( UPLO, N, KD, AB, LDAB, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   COMPLEX	  AB( LDAB, * )

PURPOSE

       CPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.  The factorization has the form
	  A = U**H * U,  if UPLO = 'U', or
	  A = L  * L**H,  if UPLO = 'L',
       where U is an upper triangular matrix and L is lower triangular.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  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 = 'U', or the number of subdiagonals 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**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.

       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 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.

       Contributed by
       Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

LAPACK version 3.0						   15 June 2000 							 CPBTRF(l)

ZPBTRF(l)								 )								 ZPBTRF(l)

NAME

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

SYNOPSIS

       SUBROUTINE ZPBTRF( UPLO, N, KD, AB, LDAB, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   COMPLEX*16	  AB( LDAB, * )

PURPOSE

       ZPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.  The factorization has the form
	  A = U**H * U,  if UPLO = 'U', or
	  A = L  * L**H,  if UPLO = 'L',
       where U is an upper triangular matrix and L is lower triangular.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  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 = 'U', or the number of subdiagonals if UPLO = 'L'.  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 = '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**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.

       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 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.

       Contributed by
       Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

LAPACK version 3.0						   15 June 2000 							 ZPBTRF(l)