LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zppsv()

subroutine zppsv ( character  UPLO,
integer  N,
integer  NRHS,
complex*16, dimension( * )  AP,
complex*16, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

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

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

Purpose:
 ZPPSV 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*16 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*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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016
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 zppsv.f.

146 *
147 * -- LAPACK driver routine (version 3.7.0) --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 * December 2016
151 *
152 * .. Scalar Arguments ..
153  CHARACTER uplo
154  INTEGER info, ldb, n, nrhs
155 * ..
156 * .. Array Arguments ..
157  COMPLEX*16 ap( * ), b( ldb, * )
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. External Functions ..
163  LOGICAL lsame
164  EXTERNAL lsame
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL xerbla, zpptrf, zpptrs
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( 'ZPPSV ', -info )
188  RETURN
189  END IF
190 *
191 * Compute the Cholesky factorization A = U**H *U or A = L*L**H.
192 *
193  CALL zpptrf( 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 zpptrs( uplo, n, nrhs, ap, b, ldb, info )
199 *
200  END IF
201  RETURN
202 *
203 * End of ZPPSV
204 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zpptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
ZPPTRS
Definition: zpptrs.f:110
subroutine zpptrf(UPLO, N, AP, INFO)
ZPPTRF
Definition: zpptrf.f:121
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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