LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cpotrf2()

recursive subroutine cpotrf2 ( character  UPLO,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
integer  INFO 
)

CPOTRF2

Purpose:
 CPOTRF2 computes the Cholesky factorization of a real symmetric
 positive definite matrix A using the recursive algorithm.

 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 recursive version of the algorithm. It divides
 the matrix into four submatrices:

        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
    A = [ -----|----- ]  with n1 = n/2
        [  A21 | A22  ]       n2 = n-n1

 The subroutine calls itself to factor A11. Update and scale A21
 or A12, update A22 then calls itself to factor A22.
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 order of the matrix A.  N >= 0.
[in,out]A
          A is COMPLEX 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**H*U or A = L*L**H.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= 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 is not
                positive definite, and the factorization could not be
                completed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
June 2016

Definition at line 108 of file cpotrf2.f.

108 *
109 * -- LAPACK computational routine (version 3.7.0) --
110 * -- LAPACK is a software package provided by Univ. of Tennessee, --
111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112 * June 2016
113 *
114 * .. Scalar Arguments ..
115  CHARACTER uplo
116  INTEGER info, lda, n
117 * ..
118 * .. Array Arguments ..
119  COMPLEX a( lda, * )
120 * ..
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125  REAL one, zero
126  parameter( one = 1.0e+0, zero = 0.0e+0 )
127  COMPLEX cone
128  parameter( cone = (1.0e+0, 0.0e+0) )
129 * ..
130 * .. Local Scalars ..
131  LOGICAL upper
132  INTEGER n1, n2, iinfo
133  REAL ajj
134 * ..
135 * .. External Functions ..
136  LOGICAL lsame, sisnan
137  EXTERNAL lsame, sisnan
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL cherk, ctrsm, xerbla
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC max, REAL, sqrt
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input parameters
148 *
149  info = 0
150  upper = lsame( uplo, 'U' )
151  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
152  info = -1
153  ELSE IF( n.LT.0 ) THEN
154  info = -2
155  ELSE IF( lda.LT.max( 1, n ) ) THEN
156  info = -4
157  END IF
158  IF( info.NE.0 ) THEN
159  CALL xerbla( 'CPOTRF2', -info )
160  RETURN
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( n.EQ.0 )
166  $ RETURN
167 *
168 * N=1 case
169 *
170  IF( n.EQ.1 ) THEN
171 *
172 * Test for non-positive-definiteness
173 *
174  ajj = REAL( A( 1, 1 ) )
175  IF( ajj.LE.zero.OR.sisnan( ajj ) ) THEN
176  info = 1
177  RETURN
178  END IF
179 *
180 * Factor
181 *
182  a( 1, 1 ) = sqrt( ajj )
183 *
184 * Use recursive code
185 *
186  ELSE
187  n1 = n/2
188  n2 = n-n1
189 *
190 * Factor A11
191 *
192  CALL cpotrf2( uplo, n1, a( 1, 1 ), lda, iinfo )
193  IF ( iinfo.NE.0 ) THEN
194  info = iinfo
195  RETURN
196  END IF
197 *
198 * Compute the Cholesky factorization A = U**H*U
199 *
200  IF( upper ) THEN
201 *
202 * Update and scale A12
203 *
204  CALL ctrsm( 'L', 'U', 'C', 'N', n1, n2, cone,
205  $ a( 1, 1 ), lda, a( 1, n1+1 ), lda )
206 *
207 * Update and factor A22
208 *
209  CALL cherk( uplo, 'C', n2, n1, -one, a( 1, n1+1 ), lda,
210  $ one, a( n1+1, n1+1 ), lda )
211 *
212  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
213 *
214  IF ( iinfo.NE.0 ) THEN
215  info = iinfo + n1
216  RETURN
217  END IF
218 *
219 * Compute the Cholesky factorization A = L*L**H
220 *
221  ELSE
222 *
223 * Update and scale A21
224 *
225  CALL ctrsm( 'R', 'L', 'C', 'N', n2, n1, cone,
226  $ a( 1, 1 ), lda, a( n1+1, 1 ), lda )
227 *
228 * Update and factor A22
229 *
230  CALL cherk( uplo, 'N', n2, n1, -one, a( n1+1, 1 ), lda,
231  $ one, a( n1+1, n1+1 ), lda )
232 *
233  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
234 *
235  IF ( iinfo.NE.0 ) THEN
236  info = iinfo + n1
237  RETURN
238  END IF
239 *
240  END IF
241  END IF
242  RETURN
243 *
244 * End of CPOTRF2
245 *
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:175
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:182
recursive subroutine cpotrf2(UPLO, N, A, LDA, INFO)
CPOTRF2
Definition: cpotrf2.f:108
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:61
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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