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

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

Purpose:
``` CPPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian 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**H * U,  if UPLO = 'U', or
A = L * L**H,  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.```
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 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, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A.``` [in,out] B ``` B is COMPLEX 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, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been 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 146 of file cppsv.f.

146 *
147 * -- LAPACK driver routine (version 3.4.0) --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 * November 2011
151 *
152 * .. Scalar Arguments ..
153  CHARACTER uplo
154  INTEGER info, ldb, n, nrhs
155 * ..
156 * .. Array Arguments ..
157  COMPLEX ap( * ), b( ldb, * )
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. External Functions ..
163  LOGICAL lsame
164  EXTERNAL lsame
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL cpptrf, cpptrs, xerbla
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC max
171 * ..
172 * .. Executable Statements ..
173 *
174 * Test the input parameters.
175 *
176  info = 0
177  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
178  info = -1
179  ELSE IF( n.LT.0 ) THEN
180  info = -2
181  ELSE IF( nrhs.LT.0 ) THEN
182  info = -3
183  ELSE IF( ldb.LT.max( 1, n ) ) THEN
184  info = -6
185  END IF
186  IF( info.NE.0 ) THEN
187  CALL xerbla( 'CPPSV ', -info )
188  RETURN
189  END IF
190 *
191 * Compute the Cholesky factorization A = U**H *U or A = L*L**H.
192 *
193  CALL cpptrf( uplo, n, ap, info )
194  IF( info.EQ.0 ) THEN
195 *
196 * Solve the system A*X = B, overwriting B with X.
197 *
198  CALL cpptrs( uplo, n, nrhs, ap, b, ldb, info )
199 *
200  END IF
201  RETURN
202 *
203 * End of CPPSV
204 *
subroutine cpptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
CPPTRS
Definition: cpptrs.f:110
subroutine cpptrf(UPLO, N, AP, INFO)
CPPTRF
Definition: cpptrf.f:121
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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