LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dposv()

subroutine dposv ( character  UPLO,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

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

Download DPOSV + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DPOSV computes the solution to a real system of linear equations
    A * X = B,
 where A is an N-by-N symmetric positive definite matrix and X and B
 are N-by-NRHS matrices.

 The Cholesky decomposition is used to factor A as
    A = U**T* U,  if UPLO = 'U', or
    A = L * L**T,  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 DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the symmetric 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**T*U or A = L*L**T.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 132 of file dposv.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  DOUBLE PRECISION a( lda, * ), b( ldb, * )
144 * ..
145 *
146 * =====================================================================
147 *
148 * .. External Functions ..
149  LOGICAL lsame
150  EXTERNAL lsame
151 * ..
152 * .. External Subroutines ..
153  EXTERNAL dpotrf, dpotrs, 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( 'DPOSV ', -info )
176  RETURN
177  END IF
178 *
179 * Compute the Cholesky factorization A = U**T*U or A = L*L**T.
180 *
181  CALL dpotrf( 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 dpotrs( uplo, n, nrhs, a, lda, b, ldb, info )
187 *
188  END IF
189  RETURN
190 *
191 * End of DPOSV
192 *
subroutine dpotrf(UPLO, N, A, LDA, INFO)
DPOTRF
Definition: dpotrf.f:109
subroutine dpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
DPOTRS
Definition: dpotrs.f:112
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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