COMPLEX routines for symmetric or Hermitian positive definite matrix

cpocon

Estimates the reciprocal of the condition number of aHermitian positive definite matrix, using theCholesky factorization computed by CPOTRF. 
USAGE:
  rcond, info = NumRu::Lapack.cpocon( uplo, a, anorm)
    or
  NumRu::Lapack.cpocon  # print help


FORTRAN MANUAL
      SUBROUTINE CPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO )

*  Purpose
*  =======
*
*  CPOCON estimates the reciprocal of the condition number (in the
*  1-norm) of a complex Hermitian positive definite matrix using the
*  Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.
*
*  An estimate is obtained for norm(inv(A)), and the reciprocal of the
*  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,N)
*          The triangular factor U or L from the Cholesky factorization
*          A = U**H*U or A = L*L**H, as computed by CPOTRF.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  ANORM   (input) REAL
*          The 1-norm (or infinity-norm) of the Hermitian matrix A.
*
*  RCOND   (output) REAL
*          The reciprocal of the condition number of the matrix A,
*          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
*          estimate of the 1-norm of inv(A) computed in this routine.
*
*  WORK    (workspace) COMPLEX array, dimension (2*N)
*
*  RWORK   (workspace) REAL array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*
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cpoequ

Computes row and column scalings to equilibrate a Hermitianpositive definite matrix and reduce its condition number. 
USAGE:
  s, scond, amax, info = NumRu::Lapack.cpoequ( a)
    or
  NumRu::Lapack.cpoequ  # print help


FORTRAN MANUAL
      SUBROUTINE CPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )

*  Purpose
*  =======
*
*  CPOEQU computes row and column scalings intended to equilibrate a
*  Hermitian positive definite matrix A and reduce its condition number
*  (with respect to the two-norm).  S contains the scale factors,
*  S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
*  elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
*  choice of S puts the condition number of B within a factor N of the
*  smallest possible condition number over all possible diagonal
*  scalings.
*

*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,N)
*          The N-by-N Hermitian positive definite matrix whose scaling
*          factors are to be computed.  Only the diagonal elements of A
*          are referenced.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  S       (output) REAL array, dimension (N)
*          If INFO = 0, S contains the scale factors for A.
*
*  SCOND   (output) REAL
*          If INFO = 0, S contains the ratio of the smallest S(i) to
*          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
*          large nor too small, it is not worth scaling by S.
*
*  AMAX    (output) REAL
*          Absolute value of largest matrix element.  If AMAX is very
*          close to overflow or very close to underflow, the matrix
*          should be scaled.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
*

*  =====================================================================
*
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cporfs

Improves the computed solution to a Hermitian positivedefinite system of linear equations AX=B, and provides forwardand backward error bounds for the solution. 
USAGE:
  ferr, berr, info, x = NumRu::Lapack.cporfs( uplo, a, af, b, x)
    or
  NumRu::Lapack.cporfs  # print help


FORTRAN MANUAL
      SUBROUTINE CPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

*  Purpose
*  =======
*
*  CPORFS improves the computed solution to a system of linear
*  equations when the coefficient matrix is Hermitian positive definite,
*  and provides error bounds and backward error estimates for the
*  solution.
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrices B and X.  NRHS >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,N)
*          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.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  AF      (input) COMPLEX array, dimension (LDAF,N)
*          The triangular factor U or L from the Cholesky factorization
*          A = U**H*U or A = L*L**H, as computed by CPOTRF.
*
*  LDAF    (input) INTEGER
*          The leading dimension of the array AF.  LDAF >= max(1,N).
*
*  B       (input) COMPLEX array, dimension (LDB,NRHS)
*          The right hand side matrix B.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  X       (input/output) COMPLEX array, dimension (LDX,NRHS)
*          On entry, the solution matrix X, as computed by CPOTRS.
*          On exit, the improved solution matrix X.
*
*  LDX     (input) INTEGER
*          The leading dimension of the array X.  LDX >= max(1,N).
*
*  FERR    (output) REAL array, dimension (NRHS)
*          The estimated forward error bound for each solution vector
*          X(j) (the j-th column of the solution matrix X).
*          If XTRUE is the true solution corresponding to X(j), FERR(j)
*          is an estimated upper bound for the magnitude of the largest
*          element in (X(j) - XTRUE) divided by the magnitude of the
*          largest element in X(j).  The estimate is as reliable as
*          the estimate for RCOND, and is almost always a slight
*          overestimate of the true error.
*
*  BERR    (output) REAL array, dimension (NRHS)
*          The componentwise relative backward error of each solution
*          vector X(j) (i.e., the smallest relative change in
*          any element of A or B that makes X(j) an exact solution).
*
*  WORK    (workspace) COMPLEX array, dimension (2*N)
*
*  RWORK   (workspace) REAL array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  Internal Parameters
*  ===================
*
*  ITMAX is the maximum number of steps of iterative refinement.
*

*  ====================================================================
*
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cposv

Solves a Hermitian positive definite system of linearequations AX=B. 
USAGE:
  info, a, b = NumRu::Lapack.cposv( uplo, a, b)
    or
  NumRu::Lapack.cposv  # print help


FORTRAN MANUAL
      SUBROUTINE CPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )

*  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.
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The number of linear equations, i.e., the order of the
*          matrix A.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrix B.  NRHS >= 0.
*
*  A       (input/output) 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.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  B       (input/output) 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.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  INFO    (output) 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.
*

*  =====================================================================
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CPOTRF, CPOTRS, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
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cposvx

Solves a Hermitian positive definite system of linearequations AX=B, and provides an estimate of the condition numberand error bounds on the solution. 
USAGE:
  x, rcond, ferr, berr, info, a, af, equed, s, b = NumRu::Lapack.cposvx( fact, uplo, a, af, equed, s, b)
    or
  NumRu::Lapack.cposvx  # print help


FORTRAN MANUAL
      SUBROUTINE CPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED, S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )

*  Purpose
*  =======
*
*  CPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
*  compute 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.
*
*  Error bounds on the solution and a condition estimate are also
*  provided.
*
*  Description
*  ===========
*
*  The following steps are performed:
*
*  1. If FACT = 'E', real scaling factors are computed to equilibrate
*     the system:
*        diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
*     Whether or not the system will be equilibrated depends on the
*     scaling of the matrix A, but if equilibration is used, A is
*     overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
*
*  2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
*     factor the matrix A (after equilibration if FACT = 'E') 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.
*
*  3. If the leading i-by-i principal minor is not positive definite,
*     then the routine returns with INFO = i. Otherwise, the factored
*     form of A is used to estimate the condition number of the matrix
*     A.  If the reciprocal of the condition number is less than machine
*     precision, INFO = N+1 is returned as a warning, but the routine
*     still goes on to solve for X and compute error bounds as
*     described below.
*
*  4. The system of equations is solved for X using the factored form
*     of A.
*
*  5. Iterative refinement is applied to improve the computed solution
*     matrix and calculate error bounds and backward error estimates
*     for it.
*
*  6. If equilibration was used, the matrix X is premultiplied by
*     diag(S) so that it solves the original system before
*     equilibration.
*

*  Arguments
*  =========
*
*  FACT    (input) CHARACTER*1
*          Specifies whether or not the factored form of the matrix A is
*          supplied on entry, and if not, whether the matrix A should be
*          equilibrated before it is factored.
*          = 'F':  On entry, AF contains the factored form of A.
*                  If EQUED = 'Y', the matrix A has been equilibrated
*                  with scaling factors given by S.  A and AF will not
*                  be modified.
*          = 'N':  The matrix A will be copied to AF and factored.
*          = 'E':  The matrix A will be equilibrated if necessary, then
*                  copied to AF and factored.
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The number of linear equations, i.e., the order of the
*          matrix A.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrices B and X.  NRHS >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the Hermitian matrix A, except if FACT = 'F' and
*          EQUED = 'Y', then A must contain the equilibrated matrix
*          diag(S)*A*diag(S).  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.  A is not modified if
*          FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit.
*
*          On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
*          diag(S)*A*diag(S).
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  AF      (input or output) COMPLEX array, dimension (LDAF,N)
*          If FACT = 'F', then AF is an input argument and on entry
*          contains the triangular factor U or L from the Cholesky
*          factorization A = U**H*U or A = L*L**H, in the same storage
*          format as A.  If EQUED .ne. 'N', then AF is the factored form
*          of the equilibrated matrix diag(S)*A*diag(S).
*
*          If FACT = 'N', then AF is an output argument and on exit
*          returns the triangular factor U or L from the Cholesky
*          factorization A = U**H*U or A = L*L**H of the original
*          matrix A.
*
*          If FACT = 'E', then AF is an output argument and on exit
*          returns the triangular factor U or L from the Cholesky
*          factorization A = U**H*U or A = L*L**H of the equilibrated
*          matrix A (see the description of A for the form of the
*          equilibrated matrix).
*
*  LDAF    (input) INTEGER
*          The leading dimension of the array AF.  LDAF >= max(1,N).
*
*  EQUED   (input or output) CHARACTER*1
*          Specifies the form of equilibration that was done.
*          = 'N':  No equilibration (always true if FACT = 'N').
*          = 'Y':  Equilibration was done, i.e., A has been replaced by
*                  diag(S) * A * diag(S).
*          EQUED is an input argument if FACT = 'F'; otherwise, it is an
*          output argument.
*
*  S       (input or output) REAL array, dimension (N)
*          The scale factors for A; not accessed if EQUED = 'N'.  S is
*          an input argument if FACT = 'F'; otherwise, S is an output
*          argument.  If FACT = 'F' and EQUED = 'Y', each element of S
*          must be positive.
*
*  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
*          On entry, the N-by-NRHS righthand side matrix B.
*          On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y',
*          B is overwritten by diag(S) * B.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  X       (output) COMPLEX array, dimension (LDX,NRHS)
*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to
*          the original system of equations.  Note that if EQUED = 'Y',
*          A and B are modified on exit, and the solution to the
*          equilibrated system is inv(diag(S))*X.
*
*  LDX     (input) INTEGER
*          The leading dimension of the array X.  LDX >= max(1,N).
*
*  RCOND   (output) REAL
*          The estimate of the reciprocal condition number of the matrix
*          A after equilibration (if done).  If RCOND is less than the
*          machine precision (in particular, if RCOND = 0), the matrix
*          is singular to working precision.  This condition is
*          indicated by a return code of INFO > 0.
*
*  FERR    (output) REAL array, dimension (NRHS)
*          The estimated forward error bound for each solution vector
*          X(j) (the j-th column of the solution matrix X).
*          If XTRUE is the true solution corresponding to X(j), FERR(j)
*          is an estimated upper bound for the magnitude of the largest
*          element in (X(j) - XTRUE) divided by the magnitude of the
*          largest element in X(j).  The estimate is as reliable as
*          the estimate for RCOND, and is almost always a slight
*          overestimate of the true error.
*
*  BERR    (output) REAL array, dimension (NRHS)
*          The componentwise relative backward error of each solution
*          vector X(j) (i.e., the smallest relative change in
*          any element of A or B that makes X(j) an exact solution).
*
*  WORK    (workspace) COMPLEX array, dimension (2*N)
*
*  RWORK   (workspace) REAL array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*          > 0: if INFO = i, and i is
*                <= N:  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. RCOND = 0 is returned.
*                = N+1: U is nonsingular, but RCOND is less than machine
*                       precision, meaning that the matrix is singular
*                       to working precision.  Nevertheless, the
*                       solution and error bounds are computed because
*                       there are a number of situations where the
*                       computed solution can be more accurate than the
*                       value of RCOND would suggest.
*

*  =====================================================================
*
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cpotf2

USAGE:
  info, a = NumRu::Lapack.cpotf2( uplo, a)
    or
  NumRu::Lapack.cpotf2  # print help


FORTRAN MANUAL
      SUBROUTINE CPOTF2( UPLO, N, A, LDA, INFO )

*  Purpose
*  =======
*
*  CPOTF2 computes the Cholesky factorization of a complex Hermitian
*  positive definite matrix A.
*
*  The factorization has the form
*     A = U' * U ,  if UPLO = 'U', or
*     A = L  * L',  if UPLO = 'L',
*  where U is an upper triangular matrix and L is lower triangular.
*
*  This is the unblocked version of the algorithm, calling Level 2 BLAS.
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          Hermitian matrix A is stored.
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) 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'*U  or A = L*L'.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -k, the k-th argument had an illegal value
*          > 0: if INFO = k, the leading minor of order k is not
*               positive definite, and the factorization could not be
*               completed.
*

*  =====================================================================
*
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cpotrf

Computes the Cholesky factorization of a Hermitianpositive definite matrix. 
USAGE:
  info, a = NumRu::Lapack.cpotrf( uplo, a)
    or
  NumRu::Lapack.cpotrf  # print help


FORTRAN MANUAL
      SUBROUTINE CPOTRF( UPLO, N, A, LDA, INFO )

*  Purpose
*  =======
*
*  CPOTRF computes the Cholesky factorization of a complex Hermitian
*  positive definite matrix A.
*
*  The factorization has the form
*     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 lower triangular.
*
*  This is the block version of the algorithm, calling Level 3 BLAS.
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) 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.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  INFO    (output) 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 is not
*                positive definite, and the factorization could not be
*                completed.
*

*  =====================================================================
*
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cpotri

Computes the inverse of a Hermitian positive definitematrix, using the Cholesky factorization computed by CPOTRF. 
USAGE:
  info, a = NumRu::Lapack.cpotri( uplo, a)
    or
  NumRu::Lapack.cpotri  # print help


FORTRAN MANUAL
      SUBROUTINE CPOTRI( UPLO, N, A, LDA, INFO )

*  Purpose
*  =======
*
*  CPOTRI computes the inverse of a complex Hermitian positive definite
*  matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
*  computed by CPOTRF.
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the triangular factor U or L from the Cholesky
*          factorization A = U**H*U or A = L*L**H, as computed by
*          CPOTRF.
*          On exit, the upper or lower triangle of the (Hermitian)
*          inverse of A, overwriting the input factor U or L.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  if INFO = i, the (i,i) element of the factor U or L is
*                zero, and the inverse could not be computed.
*

*  =====================================================================
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CLAUUM, CTRTRI, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
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cpotrs

Solves a Hermitian positive definite system of linearequations AX=B, using the Cholesky factorization computed byCPOTRF. 
USAGE:
  info, b = NumRu::Lapack.cpotrs( uplo, a, b)
    or
  NumRu::Lapack.cpotrs  # print help


FORTRAN MANUAL
      SUBROUTINE CPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )

*  Purpose
*  =======
*
*  CPOTRS solves a system of linear equations A*X = B with a Hermitian
*  positive definite matrix A using the Cholesky factorization 
*  A = U**H*U or A = L*L**H computed by CPOTRF.
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrix B.  NRHS >= 0.
*
*  A       (input) COMPLEX array, dimension (LDA,N)
*          The triangular factor U or L from the Cholesky factorization
*          A = U**H*U or A = L*L**H, as computed by CPOTRF.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
*          On entry, the right hand side matrix B.
*          On exit, the solution matrix X.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*
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