LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zposv()

 subroutine zposv ( character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, integer INFO )

ZPOSV computes the solution to system of linear equations A * X = B for PO matrices

Purpose:
``` ZPOSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix 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] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [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, 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.```

Definition at line 129 of file zposv.f.

130 *
131 * -- LAPACK driver routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  CHARACTER UPLO
137  INTEGER INFO, LDA, LDB, N, NRHS
138 * ..
139 * .. Array Arguments ..
140  COMPLEX*16 A( LDA, * ), B( LDB, * )
141 * ..
142 *
143 * =====================================================================
144 *
145 * .. External Functions ..
146  LOGICAL LSAME
147  EXTERNAL lsame
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL xerbla, zpotrf, zpotrs
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC max
154 * ..
155 * .. Executable Statements ..
156 *
157 * Test the input parameters.
158 *
159  info = 0
160  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
161  info = -1
162  ELSE IF( n.LT.0 ) THEN
163  info = -2
164  ELSE IF( nrhs.LT.0 ) THEN
165  info = -3
166  ELSE IF( lda.LT.max( 1, n ) ) THEN
167  info = -5
168  ELSE IF( ldb.LT.max( 1, n ) ) THEN
169  info = -7
170  END IF
171  IF( info.NE.0 ) THEN
172  CALL xerbla( 'ZPOSV ', -info )
173  RETURN
174  END IF
175 *
176 * Compute the Cholesky factorization A = U**H *U or A = L*L**H.
177 *
178  CALL zpotrf( uplo, n, a, lda, info )
179  IF( info.EQ.0 ) THEN
180 *
181 * Solve the system A*X = B, overwriting B with X.
182 *
183  CALL zpotrs( uplo, n, nrhs, a, lda, b, ldb, info )
184 *
185  END IF
186  RETURN
187 *
188 * End of ZPOSV
189 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
ZPOTRS
Definition: zpotrs.f:110
subroutine zpotrf(UPLO, N, A, LDA, INFO)
ZPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.
Definition: zpotrf.f:102
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