LAPACK  3.9.0 LAPACK: Linear Algebra PACKage

## ◆ cposv()

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

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

Purpose:
``` CPOSV 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 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 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
December 2016

Definition at line 132 of file cposv.f.

132 *
133 * -- LAPACK driver routine (version 3.7.0) --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 * December 2016
137 *
138 * .. Scalar Arguments ..
139  CHARACTER UPLO
140  INTEGER INFO, LDA, LDB, N, NRHS
141 * ..
142 * .. Array Arguments ..
143  COMPLEX A( LDA, * ), B( LDB, * )
144 * ..
145 *
146 * =====================================================================
147 *
148 * .. External Functions ..
149  LOGICAL LSAME
150  EXTERNAL lsame
151 * ..
152 * .. External Subroutines ..
153  EXTERNAL cpotrf, cpotrs, xerbla
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC max
157 * ..
158 * .. Executable Statements ..
159 *
160 * Test the input parameters.
161 *
162  info = 0
163  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
164  info = -1
165  ELSE IF( n.LT.0 ) THEN
166  info = -2
167  ELSE IF( nrhs.LT.0 ) THEN
168  info = -3
169  ELSE IF( lda.LT.max( 1, n ) ) THEN
170  info = -5
171  ELSE IF( ldb.LT.max( 1, n ) ) THEN
172  info = -7
173  END IF
174  IF( info.NE.0 ) THEN
175  CALL xerbla( 'CPOSV ', -info )
176  RETURN
177  END IF
178 *
179 * Compute the Cholesky factorization A = U**H*U or A = L*L**H.
180 *
181  CALL cpotrf( uplo, n, a, lda, info )
182  IF( info.EQ.0 ) THEN
183 *
184 * Solve the system A*X = B, overwriting B with X.
185 *
186  CALL cpotrs( uplo, n, nrhs, a, lda, b, ldb, info )
187 *
188  END IF
189  RETURN
190 *
191 * End of CPOSV
192 *
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cpotrs
subroutine cpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
CPOTRS
Definition: cpotrs.f:112
cpotrf
subroutine cpotrf(UPLO, N, A, LDA, INFO)
CPOTRF
Definition: cpotrf.f:109
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55