sppsv - compute 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
SUBROUTINE SPPSV(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER*1 UPLO INTEGER N, NRHS, LDB, INFO REAL A(*), B(LDB,*) SUBROUTINE SPPSV_64(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER*1 UPLO INTEGER*8 N, NRHS, LDB, INFO REAL A(*), B(LDB,*) F95 INTERFACE SUBROUTINE PPSV(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NRHS, LDB, INFO REAL, DIMENSION(:) :: A REAL, DIMENSION(:,:) :: B SUBROUTINE PPSV_64(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NRHS, LDB, INFO REAL, DIMENSION(:) :: A REAL, DIMENSION(:,:) :: B C INTERFACE #include <sunperf.h> void sppsv(char uplo, int n, int nrhs, float *a, float *b, int ldb, int *info); void sppsv_64(char uplo, long n, long nrhs, float *a, float *b, long ldb, long *info);
Oracle Solaris Studio Performance Library sppsv(3P) NAME sppsv - compute 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 SYNOPSIS SUBROUTINE SPPSV(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER*1 UPLO INTEGER N, NRHS, LDB, INFO REAL A(*), B(LDB,*) SUBROUTINE SPPSV_64(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER*1 UPLO INTEGER*8 N, NRHS, LDB, INFO REAL A(*), B(LDB,*) F95 INTERFACE SUBROUTINE PPSV(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NRHS, LDB, INFO REAL, DIMENSION(:) :: A REAL, DIMENSION(:,:) :: B SUBROUTINE PPSV_64(UPLO, N, NRHS, A, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NRHS, LDB, INFO REAL, DIMENSION(:) :: A REAL, DIMENSION(:,:) :: B C INTERFACE #include <sunperf.h> void sppsv(char uplo, int n, int nrhs, float *a, float *b, int ldb, int *info); void sppsv_64(char uplo, long n, long nrhs, float *a, float *b, long ldb, long *info); PURPOSE sppsv 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) REAL 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) REAL 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 ] 7 Nov 2015 sppsv(3P)