LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ spotrf()

 subroutine spotrf ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, integer INFO )

SPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.

SPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

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 right looking 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
December 2016

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 top-looking 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
December 2016

Definition at line 101 of file spotrf.f.

102 *
103 * -- LAPACK computational routine --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 *
107 * .. Scalar Arguments ..
108  CHARACTER UPLO
109  INTEGER INFO, LDA, N
110 * ..
111 * .. Array Arguments ..
112  REAL A( LDA, * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Parameters ..
118  REAL ONE
119  parameter( one = 1.0e+0 )
120 * ..
121 * .. Local Scalars ..
122  LOGICAL UPPER
123  INTEGER J, JB, NB
124 * ..
125 * .. External Functions ..
126  LOGICAL LSAME
127  INTEGER ILAENV
128  EXTERNAL lsame, ilaenv
129 * ..
130 * .. External Subroutines ..
131  EXTERNAL sgemm, spotf2, ssyrk, strsm, xerbla
132 * ..
133 * .. Intrinsic Functions ..
134  INTRINSIC max, min
135 * ..
136 * .. Executable Statements ..
137 *
138 * Test the input parameters.
139 *
140  info = 0
141  upper = lsame( uplo, 'U' )
142  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
143  info = -1
144  ELSE IF( n.LT.0 ) THEN
145  info = -2
146  ELSE IF( lda.LT.max( 1, n ) ) THEN
147  info = -4
148  END IF
149  IF( info.NE.0 ) THEN
150  CALL xerbla( 'SPOTRF', -info )
151  RETURN
152  END IF
153 *
154 * Quick return if possible
155 *
156  IF( n.EQ.0 )
157  \$ RETURN
158 *
159 * Determine the block size for this environment.
160 *
161  nb = ilaenv( 1, 'SPOTRF', uplo, n, -1, -1, -1 )
162  IF( nb.LE.1 .OR. nb.GE.n ) THEN
163 *
164 * Use unblocked code.
165 *
166  CALL spotf2( uplo, n, a, lda, info )
167  ELSE
168 *
169 * Use blocked code.
170 *
171  IF( upper ) THEN
172 *
173 * Compute the Cholesky factorization A = U'*U.
174 *
175  DO 10 j = 1, n, nb
176 *
177 * Update and factorize the current diagonal block and test
178 * for non-positive-definiteness.
179 *
180  jb = min( nb, n-j+1 )
181
182  CALL spotf2( 'Upper', jb, a( j, j ), lda, info )
183
184  IF( info.NE.0 )
185  \$ GO TO 30
186
187  IF( j+jb.LE.n ) THEN
188 *
189 * Updating the trailing submatrix.
190 *
191  CALL strsm( 'Left', 'Upper', 'Transpose', 'Non-unit',
192  \$ jb, n-j-jb+1, one, a( j, j ), lda,
193  \$ a( j, j+jb ), lda )
194  CALL ssyrk( 'Upper', 'Transpose', n-j-jb+1, jb, -one,
195  \$ a( j, j+jb ), lda,
196  \$ one, a( j+jb, j+jb ), lda )
197  END IF
198  10 CONTINUE
199 *
200  ELSE
201 *
202 * Compute the Cholesky factorization A = L*L'.
203 *
204  DO 20 j = 1, n, nb
205 *
206 * Update and factorize the current diagonal block and test
207 * for non-positive-definiteness.
208 *
209  jb = min( nb, n-j+1 )
210
211  CALL spotf2( 'Lower', jb, a( j, j ), lda, info )
212
213  IF( info.NE.0 )
214  \$ GO TO 30
215
216  IF( j+jb.LE.n ) THEN
217 *
218 * Updating the trailing submatrix.
219 *
220  CALL strsm( 'Right', 'Lower', 'Transpose', 'Non-unit',
221  \$ n-j-jb+1, jb, one, a( j, j ), lda,
222  \$ a( j+jb, j ), lda )
223
224  CALL ssyrk( 'Lower', 'No Transpose', n-j-jb+1, jb,
225  \$ -one, a( j+jb, j ), lda,
226  \$ one, a( j+jb, j+jb ), lda )
227  END IF
228  20 CONTINUE
229  END IF
230  END IF
231  GO TO 40
232 *
233  30 CONTINUE
234  info = info + j - 1
235 *
236  40 CONTINUE
237  RETURN
238 *
239 * End of SPOTRF
240 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine spotf2(UPLO, N, A, LDA, INFO)
SPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: spotf2.f:109
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
Here is the call graph for this function: