zpbtrf (3p)

Name

zpbtrf - itive definite band matrix A

Synopsis

SUBROUTINE ZPBTRF(UPLO, N, KD, A, LDA, INFO)

CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*)
INTEGER N, KD, LDA, INFO

SUBROUTINE ZPBTRF_64(UPLO, N, KD, A, LDA, INFO)

CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*)
INTEGER*8 N, KD, LDA, INFO




F95 INTERFACE
SUBROUTINE PBTRF(UPLO, N, KD, A, LDA, INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, KD, LDA, INFO

SUBROUTINE PBTRF_64(UPLO, N, KD, A, LDA, INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, KD, LDA, INFO




C INTERFACE
#include <sunperf.h>

void zpbtrf(char uplo, int n, int kd, doublecomplex *a,  int  lda,  int
*info);

void  zpbtrf_64(char uplo, long n, long kd, doublecomplex *a, long lda,
long *info);

Description

Oracle Solaris Studio Performance Library                           zpbtrf(3P)



NAME
       zpbtrf - compute the Cholesky factorization of a complex Hermitian pos-
       itive definite band matrix A


SYNOPSIS
       SUBROUTINE ZPBTRF(UPLO, N, KD, A, LDA, INFO)

       CHARACTER*1 UPLO
       DOUBLE COMPLEX A(LDA,*)
       INTEGER N, KD, LDA, INFO

       SUBROUTINE ZPBTRF_64(UPLO, N, KD, A, LDA, INFO)

       CHARACTER*1 UPLO
       DOUBLE COMPLEX A(LDA,*)
       INTEGER*8 N, KD, LDA, INFO




   F95 INTERFACE
       SUBROUTINE PBTRF(UPLO, N, KD, A, LDA, INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER :: N, KD, LDA, INFO

       SUBROUTINE PBTRF_64(UPLO, N, KD, A, LDA, INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER(8) :: N, KD, LDA, INFO




   C INTERFACE
       #include <sunperf.h>

       void zpbtrf(char uplo, int n, int kd, doublecomplex *a,  int  lda,  int
                 *info);

       void  zpbtrf_64(char uplo, long n, long kd, doublecomplex *a, long lda,
                 long *info);



PURPOSE
       zpbtrf computes the Cholesky factorization of a complex Hermitian posi-
       tive 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)
                 = 'U':  Upper triangle of A is stored;
                 = 'L':  Lower triangle of A is stored.


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


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


       A (input/output)
                 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 A as
                 follows:
                 if UPLO='U', A(kd+1+i-j,j)=A(i,j) for max(1,j-kd)<=i<=j;
                 if UPLO='L', A(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.


       LDA (input)
                 The leading dimension of the array A.
                 LDA >= KD+1.


       INFO (output)
                 = 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 posi-
                 tive 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 : n 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




                                  7 Nov 2015                        zpbtrf(3P)