dpbtrf - tive definite band matrix A
SUBROUTINE DPBTRF(UPLO, N, KD, A, LDA, INFO) CHARACTER*1 UPLO INTEGER N, KD, LDA, INFO DOUBLE PRECISION A(LDA,*) SUBROUTINE DPBTRF_64(UPLO, N, KD, A, LDA, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, LDA, INFO DOUBLE PRECISION A(LDA,*) F95 INTERFACE SUBROUTINE PBTRF(UPLO, N, KD, A, LDA, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, LDA, INFO REAL(8), DIMENSION(:,:) :: A SUBROUTINE PBTRF_64(UPLO, N, KD, A, LDA, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, LDA, INFO REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dpbtrf(char uplo, int n, int kd, double *a, int lda, int *info); void dpbtrf_64(char uplo, long n, long kd, double *a, long lda, long *info);
Oracle Solaris Studio Performance Library dpbtrf(3P) NAME dpbtrf - compute the Cholesky factorization of a real symmetric posi- tive definite band matrix A SYNOPSIS SUBROUTINE DPBTRF(UPLO, N, KD, A, LDA, INFO) CHARACTER*1 UPLO INTEGER N, KD, LDA, INFO DOUBLE PRECISION A(LDA,*) SUBROUTINE DPBTRF_64(UPLO, N, KD, A, LDA, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, LDA, INFO DOUBLE PRECISION A(LDA,*) F95 INTERFACE SUBROUTINE PBTRF(UPLO, N, KD, A, LDA, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, LDA, INFO REAL(8), DIMENSION(:,:) :: A SUBROUTINE PBTRF_64(UPLO, N, KD, A, LDA, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, LDA, INFO REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dpbtrf(char uplo, int n, int kd, double *a, int lda, int *info); void dpbtrf_64(char uplo, long n, long kd, double *a, long lda, long *info); PURPOSE dpbtrf computes the Cholesky factorization of a real symmetric positive definite band matrix A. The factorization has the form A = U**T * U, if UPLO = 'U', or A = L * L**T, 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 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 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). ,br On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A=U**T*U or A=L*L**T 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': 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 7 Nov 2015 dpbtrf(3P)