SUBROUTINE CPOTRF ( UPLO, N, A, LDA, INFO ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * March 2008 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. COMPLEX A( LDA, * ) * .. * * Purpose * ======= * * CPOTRF computes the Cholesky factorization of a real 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 right looking 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) 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. * * 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 COMPLEX CONE PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, JB, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL CGEMM, CPOTF2, CHERK, CTRSM, 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( 'CPOTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'CPOTRF', UPLO, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code. * CALL CPOTF2( 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 CPOTF2( 'Upper', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 30 IF( J+JB.LE.N ) THEN * * Updating the trailing submatrix. * CALL CTRSM( 'Left', 'Upper', 'Conjugate Transpose', \$ 'Non-unit', JB, N-J-JB+1, CONE, A( J, J ), \$ LDA, A( J, J+JB ), LDA ) CALL CHERK( 'Upper', 'Conjugate transpose', N-J-JB+1, \$ JB, -ONE, A( J, J+JB ), LDA, \$ ONE, A( J+JB, 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 CPOTF2( 'Lower', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 30 IF( J+JB.LE.N ) THEN * * Updating the trailing submatrix. * CALL CTRSM( 'Right', 'Lower', 'Conjugate Transpose', \$ 'Non-unit', N-J-JB+1, JB, CONE, A( J, J ), \$ LDA, A( J+JB, J ), LDA ) CALL CHERK( 'Lower', 'No Transpose', N-J-JB+1, JB, \$ -ONE, A( J+JB, J ), LDA, \$ ONE, A( J+JB, J+JB ), LDA ) END IF 20 CONTINUE END IF END IF GO TO 40 * 30 CONTINUE INFO = INFO + J - 1 * 40 CONTINUE RETURN * * End of CPOTRF * END