zhpsv - compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices
SUBROUTINE ZHPSV(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*), B(LDB,*) INTEGER N, NRHS, LDB, INFO INTEGER IPIVOT(*) SUBROUTINE ZHPSV_64(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*), B(LDB,*) INTEGER*8 N, NRHS, LDB, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE HPSV(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A COMPLEX(8), DIMENSION(:,:) :: B INTEGER :: N, NRHS, LDB, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE HPSV_64(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A COMPLEX(8), DIMENSION(:,:) :: B INTEGER(8) :: N, NRHS, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zhpsv(char uplo, int n, int nrhs, doublecomplex *a, int *ipivot, doublecomplex *b, int ldb, int *info); void zhpsv_64(char uplo, long n, long nrhs, doublecomplex *a, long *ipivot, doublecomplex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library zhpsv(3P) NAME zhpsv - compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices SYNOPSIS SUBROUTINE ZHPSV(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*), B(LDB,*) INTEGER N, NRHS, LDB, INFO INTEGER IPIVOT(*) SUBROUTINE ZHPSV_64(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(*), B(LDB,*) INTEGER*8 N, NRHS, LDB, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE HPSV(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A COMPLEX(8), DIMENSION(:,:) :: B INTEGER :: N, NRHS, LDB, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE HPSV_64(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: A COMPLEX(8), DIMENSION(:,:) :: B INTEGER(8) :: N, NRHS, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zhpsv(char uplo, int n, int nrhs, doublecomplex *a, int *ipivot, doublecomplex *b, int ldb, int *info); void zhpsv_64(char uplo, long n, long nrhs, doublecomplex *a, long *ipivot, doublecomplex *b, long ldb, long *info); PURPOSE zhpsv computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**H, if UPLO = 'U', or A = L * D * L**H, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) tri- angular matrices, D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 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) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as a packed triangular matrix in the same storage format as A. IPIVOT (output) INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by ZHPTRF. If IPIVOT(k) > 0, then rows and col- umns k and IPIVOT(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIVOT(k) = IPIVOT(k-1) < 0, then rows and columns k-1 and -IPIVOT(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIVOT(k) = IPIVOT(k+1) < 0, then rows and columns k+1 and -IPIVOT(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. B (input/output) COMPLEX*16 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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. FURTHER DETAILS The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U': Two-dimensional storage of the Hermitian 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 zhpsv(3P)