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dppsv(3P)		    Sun Performance Library		     dppsv(3P)

NAME
       dppsv  - compute the solution to a real system of linear equations  A *
       X = B,

SYNOPSIS
       SUBROUTINE DPPSV(UPLO, N, NRHS, A, B, LDB, INFO)

       CHARACTER * 1 UPLO
       INTEGER N, NRHS, LDB, INFO
       DOUBLE PRECISION A(*), B(LDB,*)

       SUBROUTINE DPPSV_64(UPLO, N, NRHS, A, B, LDB, INFO)

       CHARACTER * 1 UPLO
       INTEGER*8 N, NRHS, LDB, INFO
       DOUBLE PRECISION A(*), B(LDB,*)

   F95 INTERFACE
       SUBROUTINE PPSV(UPLO, [N], [NRHS], A, B, [LDB], [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, NRHS, LDB, INFO
       REAL(8), DIMENSION(:) :: A
       REAL(8), DIMENSION(:,:) :: B

       SUBROUTINE PPSV_64(UPLO, [N], [NRHS], A, B, [LDB], [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, NRHS, LDB, INFO
       REAL(8), DIMENSION(:) :: A
       REAL(8), DIMENSION(:,:) :: B

   C INTERFACE
       #include <sunperf.h>

       void dppsv(char uplo, int n, int nrhs, double *a, double *b,  int  ldb,
		 int *info);

       void  dppsv_64(char uplo, long n, long nrhs, double *a, double *b, long
		 ldb, long *info);

PURPOSE
       dppsv computes the solution to a real system of linear equations
	  A * X = B, where A is an N-by-N symmetric positive  definite	matrix
       stored in packed format and X and B are N-by-NRHS matrices.

       The Cholesky decomposition is used to factor A as
	  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 a lower triangular
       matrix.	The factored form of A is then used to	solve  the  system  of
       equations A * X = B.

ARGUMENTS
       UPLO (input)
		 = 'U':	 Upper triangle of A is stored;
		 = 'L':	 Lower triangle of A is stored.

       N (input) The number of linear equations, i.e., the order of the matrix
		 A.  N >= 0.

       NRHS (input)
		 The number of right hand sides, i.e., the number  of  columns
		 of the matrix B.  NRHS >= 0.

       A (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
		 On entry, the upper or lower triangle of the symmetric matrix
		 A, packed columnwise in a linear array.  The j-th column of A
		 is  stored  in	 the  array A as follows: if UPLO = 'U', A(i +
		 (j-1)*j/2) = A(i,j)  for  1<=i<=j;  if	 UPLO  =  'L',	A(i  +
		 (j-1)*(2n-j)/2)  = A(i,j) for j<=i<=n.	 See below for further
		 details.

		 On exit, if INFO = 0, the factor U or	L  from	 the  Cholesky
		 factorization	A  = U**T*U or A = L*L**T, in the same storage
		 format as A.

       B (input/output) DOUBLE PRECISION 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)
		 The leading dimension of the array B.	LDB >= max(1,N).

       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 of A is not
		 positive definite, so the factorization  could	 not  be  com‐
		 pleted, and the solution has not been computed.

FURTHER DETAILS
       The  packed storage scheme is illustrated by the following example when
       N = 4, UPLO = 'U':

       Two-dimensional storage of the symmetric matrix A:

	  a11 a12 a13 a14
	      a22 a23 a24
		  a33 a34     (aij = conjg(aji))
		      a44

       Packed storage of the upper triangle of A:

       A = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

				  6 Mar 2009			     dppsv(3P)
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