spbtf2 (3p)

Name

spbtf2 - tive definite band matrix A

Synopsis

SUBROUTINE SPBTF2(UPLO, N, KD, AB, LDAB, INFO)

CHARACTER*1 UPLO
INTEGER N, KD, LDAB, INFO
REAL AB(LDAB,*)

SUBROUTINE SPBTF2_64(UPLO, N, KD, AB, LDAB, INFO)

CHARACTER*1 UPLO
INTEGER*8 N, KD, LDAB, INFO
REAL AB(LDAB,*)




F95 INTERFACE
SUBROUTINE PBTF2(UPLO, N, KD, AB, LDAB, INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER :: N, KD, LDAB, INFO
REAL, DIMENSION(:,:) :: AB

SUBROUTINE PBTF2_64(UPLO, N, KD, AB, LDAB, INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, KD, LDAB, INFO
REAL, DIMENSION(:,:) :: AB




C INTERFACE
#include <sunperf.h>

void spbtf2(char uplo, int n, int kd, float *ab, int ldab, int *info);

void spbtf2_64(char uplo, long n, long kd, float *ab, long  ldab,  long
*info);

Description

Oracle Solaris Studio Performance Library                           spbtf2(3P)



NAME
       spbtf2  -  compute the Cholesky factorization of a real symmetric posi-
       tive definite band matrix A


SYNOPSIS
       SUBROUTINE SPBTF2(UPLO, N, KD, AB, LDAB, INFO)

       CHARACTER*1 UPLO
       INTEGER N, KD, LDAB, INFO
       REAL AB(LDAB,*)

       SUBROUTINE SPBTF2_64(UPLO, N, KD, AB, LDAB, INFO)

       CHARACTER*1 UPLO
       INTEGER*8 N, KD, LDAB, INFO
       REAL AB(LDAB,*)




   F95 INTERFACE
       SUBROUTINE PBTF2(UPLO, N, KD, AB, LDAB, INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, KD, LDAB, INFO
       REAL, DIMENSION(:,:) :: AB

       SUBROUTINE PBTF2_64(UPLO, N, KD, AB, LDAB, INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, KD, LDAB, INFO
       REAL, DIMENSION(:,:) :: AB




   C INTERFACE
       #include <sunperf.h>

       void spbtf2(char uplo, int n, int kd, float *ab, int ldab, int *info);

       void spbtf2_64(char uplo, long n, long kd, float *ab, long  ldab,  long
                 *info);



PURPOSE
       spbtf2 computes the Cholesky factorization of a real symmetric 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 transpose of U, and  L
       is lower triangular.

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


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


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


       KD (input)
                 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)
                 On  entry,  the upper or lower triangle of the symmetric 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.


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


       INFO (output)
                 = 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  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':

       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.




                                  7 Nov 2015                        spbtf2(3P)