LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 recursive subroutine spotrf2 ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, integer INFO )

SPOTRF2

Purpose:
``` SPOTRF2 computes the Cholesky factorization of a real symmetric
positive definite matrix A using the recursive algorithm.

The factorization has the form
A = U**T * U,  if UPLO = 'U', or
A = L  * L**T,  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 call 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 REAL 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**T*U or A = L*L**T.``` [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.```
Date
November 2015

Definition at line 108 of file spotrf2.f.

108 *
109 * -- LAPACK computational routine (version 3.6.0) --
110 * -- LAPACK is a software package provided by Univ. of Tennessee, --
111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112 * November 2015
113 *
114 * .. Scalar Arguments ..
115  CHARACTER uplo
116  INTEGER info, lda, n
117 * ..
118 * .. Array Arguments ..
119  REAL a( lda, * )
120 * ..
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125  REAL one, zero
126  parameter ( one = 1.0e+0, zero=0.0e+0 )
127 * ..
128 * .. Local Scalars ..
129  LOGICAL upper
130  INTEGER n1, n2, iinfo
131 * ..
132 * .. External Functions ..
133  LOGICAL lsame, sisnan
134  EXTERNAL lsame, sisnan
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL sgemm, ssyrk, xerbla
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC max, 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( 'SPOTRF2', -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  IF( a( 1, 1 ).LE.zero.OR.sisnan( a( 1, 1 ) ) ) THEN
172  info = 1
173  RETURN
174  END IF
175 *
176 * Factor
177 *
178  a( 1, 1 ) = sqrt( a( 1, 1 ) )
179 *
180 * Use recursive code
181 *
182  ELSE
183  n1 = n/2
184  n2 = n-n1
185 *
186 * Factor A11
187 *
188  CALL spotrf2( uplo, n1, a( 1, 1 ), lda, iinfo )
189  IF ( iinfo.NE.0 ) THEN
190  info = iinfo
191  RETURN
192  END IF
193 *
194 * Compute the Cholesky factorization A = U**T*U
195 *
196  IF( upper ) THEN
197 *
198 * Update and scale A12
199 *
200  CALL strsm( 'L', 'U', 'T', 'N', n1, n2, one,
201  \$ a( 1, 1 ), lda, a( 1, n1+1 ), lda )
202 *
203 * Update and factor A22
204 *
205  CALL ssyrk( uplo, 'T', n2, n1, -one, a( 1, n1+1 ), lda,
206  \$ one, a( n1+1, n1+1 ), lda )
207  CALL spotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
208  IF ( iinfo.NE.0 ) THEN
209  info = iinfo + n1
210  RETURN
211  END IF
212 *
213 * Compute the Cholesky factorization A = L*L**T
214 *
215  ELSE
216 *
217 * Update and scale A21
218 *
219  CALL strsm( 'R', 'L', 'T', 'N', n2, n1, one,
220  \$ a( 1, 1 ), lda, a( n1+1, 1 ), lda )
221 *
222 * Update and factor A22
223 *
224  CALL ssyrk( uplo, 'N', n2, n1, -one, a( n1+1, 1 ), lda,
225  \$ one, a( n1+1, n1+1 ), lda )
226  CALL spotrf2( uplo, n2, a( n1+1, n1+1 ), lda, iinfo )
227  IF ( iinfo.NE.0 ) THEN
228  info = iinfo + n1
229  RETURN
230  END IF
231  END IF
232  END IF
233  RETURN
234 *
235 * End of SPOTRF2
236 *
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:171
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:183
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:61
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
recursive subroutine spotrf2(UPLO, N, A, LDA, INFO)
SPOTRF2
Definition: spotrf2.f:108

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