SUBROUTINE CPOTF2( UPLO, N, A, LDA, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. COMPLEX A( LDA, * ) * .. * * Purpose * ======= * * CPOTF2 computes the Cholesky factorization of a complex 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 unblocked version of the algorithm, calling Level 2 BLAS. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * Hermitian matrix A is stored. * = 'U': Upper triangular * = 'L': Lower triangular * * 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 = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order k is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) COMPLEX CONE PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J REAL AJJ * .. * .. External Functions .. LOGICAL LSAME, SISNAN COMPLEX CDOTC EXTERNAL LSAME, CDOTC, SISNAN * .. * .. External Subroutines .. EXTERNAL CGEMV, CLACGV, CSSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, REAL, SQRT * .. * .. 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( 'CPOTF2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Compute the Cholesky factorization A = U**H *U. * DO 10 J = 1, N * * Compute U(J,J) and test for non-positive-definiteness. * AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( 1, J ), 1, $ A( 1, J ), 1 ) IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN A( J, J ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) A( J, J ) = AJJ * * Compute elements J+1:N of row J. * IF( J.LT.N ) THEN CALL CLACGV( J-1, A( 1, J ), 1 ) CALL CGEMV( 'Transpose', J-1, N-J, -CONE, A( 1, J+1 ), $ LDA, A( 1, J ), 1, CONE, A( J, J+1 ), LDA ) CALL CLACGV( J-1, A( 1, J ), 1 ) CALL CSSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA ) END IF 10 CONTINUE ELSE * * Compute the Cholesky factorization A = L*L**H. * DO 20 J = 1, N * * Compute L(J,J) and test for non-positive-definiteness. * AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( J, 1 ), LDA, $ A( J, 1 ), LDA ) IF( AJJ.LE.ZERO.OR.SISNAN( AJJ ) ) THEN A( J, J ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) A( J, J ) = AJJ * * Compute elements J+1:N of column J. * IF( J.LT.N ) THEN CALL CLACGV( J-1, A( J, 1 ), LDA ) CALL CGEMV( 'No transpose', N-J, J-1, -CONE, A( J+1, 1 ), $ LDA, A( J, 1 ), LDA, CONE, A( J+1, J ), 1 ) CALL CLACGV( J-1, A( J, 1 ), LDA ) CALL CSSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 ) END IF 20 CONTINUE END IF GO TO 40 * 30 CONTINUE INFO = J * 40 CONTINUE RETURN * * End of CPOTF2 * END