LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zhpsv ( character UPLO, integer N, integer NRHS, complex*16, dimension( * ) AP, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, integer INFO )

ZHPSV computes the solution to system of linear equations A * X = B for OTHER matrices

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)
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.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.``` [in,out] AP ``` AP is 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 AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(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.``` [out] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by ZHPTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.``` [in,out] B ``` B is 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.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 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.```
Date
November 2011
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:

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

Definition at line 164 of file zhpsv.f.

164 *
165 * -- LAPACK driver routine (version 3.4.0) --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 * November 2011
169 *
170 * .. Scalar Arguments ..
171  CHARACTER uplo
172  INTEGER info, ldb, n, nrhs
173 * ..
174 * .. Array Arguments ..
175  INTEGER ipiv( * )
176  COMPLEX*16 ap( * ), b( ldb, * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. External Functions ..
182  LOGICAL lsame
183  EXTERNAL lsame
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL xerbla, zhptrf, zhptrs
187 * ..
188 * .. Intrinsic Functions ..
189  INTRINSIC max
190 * ..
191 * .. Executable Statements ..
192 *
193 * Test the input parameters.
194 *
195  info = 0
196  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
197  info = -1
198  ELSE IF( n.LT.0 ) THEN
199  info = -2
200  ELSE IF( nrhs.LT.0 ) THEN
201  info = -3
202  ELSE IF( ldb.LT.max( 1, n ) ) THEN
203  info = -7
204  END IF
205  IF( info.NE.0 ) THEN
206  CALL xerbla( 'ZHPSV ', -info )
207  RETURN
208  END IF
209 *
210 * Compute the factorization A = U*D*U**H or A = L*D*L**H.
211 *
212  CALL zhptrf( uplo, n, ap, ipiv, info )
213  IF( info.EQ.0 ) THEN
214 *
215 * Solve the system A*X = B, overwriting B with X.
216 *
217  CALL zhptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
218 *
219  END IF
220  RETURN
221 *
222 * End of ZHPSV
223 *
subroutine zhptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
ZHPTRS
Definition: zhptrs.f:117
subroutine zhptrf(UPLO, N, AP, IPIV, INFO)
ZHPTRF
Definition: zhptrf.f:161
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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