spotrf.f

          SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDA, N
    *     ..
    *     .. Array Arguments ..
          REAL               A( LDA, * )
    *     ..
    *
    *  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.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input/output) 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.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  INFO    (output) 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.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE
          PARAMETER          ( ONE = 1.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            J, JB, NB
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           LSAME, ILAENV
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SGEMM, SPOTF2, SSYRK, STRSM, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -4
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SPOTRF', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Determine the block size for this environment.
    *
          NB = ILAENV( 1, 'SPOTRF', UPLO, N, -1, -1, -1 )
          IF( NB.LE.1 .OR. NB.GE.N ) THEN
    *
    *        Use unblocked code.
    *
             CALL SPOTF2( UPLO, N, A, LDA, INFO )
          ELSE
    *
    *        Use blocked code.
    *
             IF( UPPER ) THEN
    *
    *           Compute the Cholesky factorization A = U'*U.
    *
                DO 10 J = 1, N, NB
    *
    *              Update and factorize the current diagonal block and test
    *              for non-positive-definiteness.
    *
                   JB = MIN( NB, N-J+1 )
                   CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE,
         $                     A( 1, J ), LDA, ONE, A( J, J ), LDA )
                   CALL SPOTF2( 'Upper', JB, A( J, J ), LDA, INFO )
                   IF( INFO.NE.0 )
         $            GO TO 30
                   IF( J+JB.LE.N ) THEN
    *
    *                 Compute the current block row.
    *
                      CALL SGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1,
         $                        J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ),
         $                        LDA, ONE, A( J, J+JB ), LDA )
                      CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit',
         $                        JB, N-J-JB+1, ONE, A( J, J ), LDA,
         $                        A( J, J+JB ), LDA )
                   END IF
       10       CONTINUE
    *
             ELSE
    *
    *           Compute the Cholesky factorization A = L*L'.
    *
                DO 20 J = 1, N, NB
    *
    *              Update and factorize the current diagonal block and test
    *              for non-positive-definiteness.
    *
                   JB = MIN( NB, N-J+1 )
                   CALL SSYRK( 'Lower', 'No transpose', JB, J-1, -ONE,
         $                     A( J, 1 ), LDA, ONE, A( J, J ), LDA )
                   CALL SPOTF2( 'Lower', JB, A( J, J ), LDA, INFO )
                   IF( INFO.NE.0 )
         $            GO TO 30
                   IF( J+JB.LE.N ) THEN
    *
    *                 Compute the current block column.
    *
                      CALL SGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
         $                        J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ),
         $                        LDA, ONE, A( J+JB, J ), LDA )
                      CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit',
         $                        N-J-JB+1, JB, ONE, A( J, J ), LDA,
         $                        A( J+JB, J ), LDA )
                   END IF
       20       CONTINUE
             END IF
          END IF
          GO TO 40
    *
       30 CONTINUE
          INFO = INFO + J - 1
    *
       40 CONTINUE
          RETURN
    *
    *     End of SPOTRF
    *
          END