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

SPOTRF

Purpose:
``` SPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.

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 block version of the algorithm, calling Level 3 BLAS.```
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 109 of file spotrf.f.

109 *
110 * -- LAPACK computational routine (version 3.6.0) --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 * November 2015
114 *
115 * .. Scalar Arguments ..
116  CHARACTER uplo
117  INTEGER info, lda, n
118 * ..
119 * .. Array Arguments ..
120  REAL a( lda, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  REAL one
127  parameter ( one = 1.0e+0 )
128 * ..
129 * .. Local Scalars ..
130  LOGICAL upper
131  INTEGER j, jb, nb
132 * ..
133 * .. External Functions ..
134  LOGICAL lsame
135  INTEGER ilaenv
136  EXTERNAL lsame, ilaenv
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL sgemm, spotrf2, ssyrk, strsm, xerbla
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max, min
143 * ..
144 * .. Executable Statements ..
145 *
146 * Test the input parameters.
147 *
148  info = 0
149  upper = lsame( uplo, 'U' )
150  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
151  info = -1
152  ELSE IF( n.LT.0 ) THEN
153  info = -2
154  ELSE IF( lda.LT.max( 1, n ) ) THEN
155  info = -4
156  END IF
157  IF( info.NE.0 ) THEN
158  CALL xerbla( 'SPOTRF', -info )
159  RETURN
160  END IF
161 *
162 * Quick return if possible
163 *
164  IF( n.EQ.0 )
165  \$ RETURN
166 *
167 * Determine the block size for this environment.
168 *
169  nb = ilaenv( 1, 'SPOTRF', uplo, n, -1, -1, -1 )
170  IF( nb.LE.1 .OR. nb.GE.n ) THEN
171 *
172 * Use unblocked code.
173 *
174  CALL spotrf2( uplo, n, a, lda, info )
175  ELSE
176 *
177 * Use blocked code.
178 *
179  IF( upper ) THEN
180 *
181 * Compute the Cholesky factorization A = U**T*U.
182 *
183  DO 10 j = 1, n, nb
184 *
185 * Update and factorize the current diagonal block and test
186 * for non-positive-definiteness.
187 *
188  jb = min( nb, n-j+1 )
189  CALL ssyrk( 'Upper', 'Transpose', jb, j-1, -one,
190  \$ a( 1, j ), lda, one, a( j, j ), lda )
191  CALL spotrf2( 'Upper', jb, a( j, j ), lda, info )
192  IF( info.NE.0 )
193  \$ GO TO 30
194  IF( j+jb.LE.n ) THEN
195 *
196 * Compute the current block row.
197 *
198  CALL sgemm( 'Transpose', 'No transpose', jb, n-j-jb+1,
199  \$ j-1, -one, a( 1, j ), lda, a( 1, j+jb ),
200  \$ lda, one, a( j, j+jb ), lda )
201  CALL strsm( 'Left', 'Upper', 'Transpose', 'Non-unit',
202  \$ jb, n-j-jb+1, one, a( j, j ), lda,
203  \$ a( j, j+jb ), lda )
204  END IF
205  10 CONTINUE
206 *
207  ELSE
208 *
209 * Compute the Cholesky factorization A = L*L**T.
210 *
211  DO 20 j = 1, n, nb
212 *
213 * Update and factorize the current diagonal block and test
214 * for non-positive-definiteness.
215 *
216  jb = min( nb, n-j+1 )
217  CALL ssyrk( 'Lower', 'No transpose', jb, j-1, -one,
218  \$ a( j, 1 ), lda, one, a( j, j ), lda )
219  CALL spotrf2( 'Lower', jb, a( j, j ), lda, info )
220  IF( info.NE.0 )
221  \$ GO TO 30
222  IF( j+jb.LE.n ) THEN
223 *
224 * Compute the current block column.
225 *
226  CALL sgemm( 'No transpose', 'Transpose', n-j-jb+1, jb,
227  \$ j-1, -one, a( j+jb, 1 ), lda, a( j, 1 ),
228  \$ lda, one, a( j+jb, j ), lda )
229  CALL strsm( 'Right', 'Lower', 'Transpose', 'Non-unit',
230  \$ n-j-jb+1, jb, one, a( j, j ), lda,
231  \$ a( j+jb, j ), lda )
232  END IF
233  20 CONTINUE
234  END IF
235  END IF
236  GO TO 40
237 *
238  30 CONTINUE
239  info = info + j - 1
240 *
241  40 CONTINUE
242  RETURN
243 *
244 * End of SPOTRF
245 *
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
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
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
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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