NAME

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

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

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) triangular 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)

* 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)

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 CHPTRF, stored as a packed triangular matrix in the same storage format as A.

* IPIVOT (output)

Details of the interchanges and the block structure of D, as determined by CHPTRF. If IPIVOT(k) > 0, then rows and columns 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)

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)