LAPACK  3.10.1 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 Hermitian
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 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).``` [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.```

Definition at line 105 of file cpotrf2.f.

106 *
107 * -- LAPACK computational routine --
108 * -- LAPACK is a software package provided by Univ. of Tennessee, --
109 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110 *
111 * .. Scalar Arguments ..
112  CHARACTER UPLO
113  INTEGER INFO, LDA, N
114 * ..
115 * .. Array Arguments ..
116  COMPLEX A( LDA, * )
117 * ..
118 *
119 * =====================================================================
120 *
121 * .. Parameters ..
122  REAL ONE, ZERO
123  parameter( one = 1.0e+0, zero = 0.0e+0 )
124  COMPLEX CONE
125  parameter( cone = (1.0e+0, 0.0e+0) )
126 * ..
127 * .. Local Scalars ..
128  LOGICAL UPPER
129  INTEGER N1, N2, IINFO
130  REAL AJJ
131 * ..
132 * .. External Functions ..
133  LOGICAL LSAME, SISNAN
134  EXTERNAL lsame, sisnan
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL cherk, ctrsm, xerbla
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC max, real, sqrt
141 * ..
142 * .. Executable Statements ..
143 *
144 * Test the input parameters
145 *
146  info = 0
147  upper = lsame( uplo, 'U' )
148  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
149  info = -1
150  ELSE IF( n.LT.0 ) THEN
151  info = -2
152  ELSE IF( lda.LT.max( 1, n ) ) THEN
153  info = -4
154  END IF
155  IF( info.NE.0 ) THEN
156  CALL xerbla( 'CPOTRF2', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( n.EQ.0 )
163  \$ RETURN
164 *
165 * N=1 case
166 *
167  IF( n.EQ.1 ) THEN
168 *
169 * Test for non-positive-definiteness
170 *
171  ajj = real( a( 1, 1 ) )
172  IF( ajj.LE.zero.OR.sisnan( ajj ) ) THEN
173  info = 1
174  RETURN
175  END IF
176 *
177 * Factor
178 *
179  a( 1, 1 ) = sqrt( ajj )
180 *
181 * Use recursive code
182 *
183  ELSE
184  n1 = n/2
185  n2 = n-n1
186 *
187 * Factor A11
188 *
189  CALL cpotrf2( uplo, n1, a( 1, 1 ), lda, iinfo )
190  IF ( iinfo.NE.0 ) THEN
191  info = iinfo
192  RETURN
193  END IF
194 *
195 * Compute the Cholesky factorization A = U**H*U
196 *
197  IF( upper ) THEN
198 *
199 * Update and scale A12
200 *
201  CALL ctrsm( 'L', 'U', 'C', 'N', n1, n2, cone,
202  \$ a( 1, 1 ), lda, a( 1, n1+1 ), lda )
203 *
204 * Update and factor A22
205 *
206  CALL cherk( uplo, 'C', n2, n1, -one, a( 1, n1+1 ), lda,
207  \$ one, a( n1+1, n1+1 ), lda )
208 *
209  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
210 *
211  IF ( iinfo.NE.0 ) THEN
212  info = iinfo + n1
213  RETURN
214  END IF
215 *
216 * Compute the Cholesky factorization A = L*L**H
217 *
218  ELSE
219 *
220 * Update and scale A21
221 *
222  CALL ctrsm( 'R', 'L', 'C', 'N', n2, n1, cone,
223  \$ a( 1, 1 ), lda, a( n1+1, 1 ), lda )
224 *
225 * Update and factor A22
226 *
227  CALL cherk( uplo, 'N', n2, n1, -one, a( n1+1, 1 ), lda,
228  \$ one, a( n1+1, n1+1 ), lda )
229 *
230  CALL cpotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
231 *
232  IF ( iinfo.NE.0 ) THEN
233  info = iinfo + n1
234  RETURN
235  END IF
236 *
237  END IF
238  END IF
239  RETURN
240 *
241 * End of CPOTRF2
242 *
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
recursive subroutine cpotrf2(UPLO, N, A, LDA, INFO)
CPOTRF2
Definition: cpotrf2.f:106
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