 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cpotf2()

 subroutine cpotf2 ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer INFO )

CPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).

Purpose:
``` CPOTF2 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 unblocked version of the algorithm, calling Level 2 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular``` [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 = -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.```

Definition at line 108 of file cpotf2.f.

109 *
110 * -- LAPACK computational routine --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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 J
133  REAL AJJ
134 * ..
135 * .. External Functions ..
136  LOGICAL LSAME, SISNAN
137  COMPLEX CDOTC
138  EXTERNAL lsame, cdotc, sisnan
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL cgemv, clacgv, csscal, xerbla
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC max, real, sqrt
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input parameters.
149 *
150  info = 0
151  upper = lsame( uplo, 'U' )
152  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
153  info = -1
154  ELSE IF( n.LT.0 ) THEN
155  info = -2
156  ELSE IF( lda.LT.max( 1, n ) ) THEN
157  info = -4
158  END IF
159  IF( info.NE.0 ) THEN
160  CALL xerbla( 'CPOTF2', -info )
161  RETURN
162  END IF
163 *
164 * Quick return if possible
165 *
166  IF( n.EQ.0 )
167  \$ RETURN
168 *
169  IF( upper ) THEN
170 *
171 * Compute the Cholesky factorization A = U**H *U.
172 *
173  DO 10 j = 1, n
174 *
175 * Compute U(J,J) and test for non-positive-definiteness.
176 *
177  ajj = real( real( a( j, j ) ) - cdotc( j-1, a( 1, j ), 1,
178  \$ a( 1, j ), 1 ) )
179  IF( ajj.LE.zero.OR.sisnan( ajj ) ) THEN
180  a( j, j ) = ajj
181  GO TO 30
182  END IF
183  ajj = sqrt( ajj )
184  a( j, j ) = ajj
185 *
186 * Compute elements J+1:N of row J.
187 *
188  IF( j.LT.n ) THEN
189  CALL clacgv( j-1, a( 1, j ), 1 )
190  CALL cgemv( 'Transpose', j-1, n-j, -cone, a( 1, j+1 ),
191  \$ lda, a( 1, j ), 1, cone, a( j, j+1 ), lda )
192  CALL clacgv( j-1, a( 1, j ), 1 )
193  CALL csscal( n-j, one / ajj, a( j, j+1 ), lda )
194  END IF
195  10 CONTINUE
196  ELSE
197 *
198 * Compute the Cholesky factorization A = L*L**H.
199 *
200  DO 20 j = 1, n
201 *
202 * Compute L(J,J) and test for non-positive-definiteness.
203 *
204  ajj = real( real( a( j, j ) ) - cdotc( j-1, a( j, 1 ), lda,
205  \$ a( j, 1 ), lda ) )
206  IF( ajj.LE.zero.OR.sisnan( ajj ) ) THEN
207  a( j, j ) = ajj
208  GO TO 30
209  END IF
210  ajj = sqrt( ajj )
211  a( j, j ) = ajj
212 *
213 * Compute elements J+1:N of column J.
214 *
215  IF( j.LT.n ) THEN
216  CALL clacgv( j-1, a( j, 1 ), lda )
217  CALL cgemv( 'No transpose', n-j, j-1, -cone, a( j+1, 1 ),
218  \$ lda, a( j, 1 ), lda, cone, a( j+1, j ), 1 )
219  CALL clacgv( j-1, a( j, 1 ), lda )
220  CALL csscal( n-j, one / ajj, a( j+1, j ), 1 )
221  END IF
222  20 CONTINUE
223  END IF
224  GO TO 40
225 *
226  30 CONTINUE
227  info = j
228 *
229  40 CONTINUE
230  RETURN
231 *
232 * End of CPOTF2
233 *
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
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:74
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