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SUBROUTINE CPBTF2( UPLO, N, KD, AB, LDAB, 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, KD, LDAB, N * .. * .. Array Arguments .. COMPLEX AB( LDAB, * ) * .. * * Purpose * ======= * * CPBTF2 computes the Cholesky factorization of a complex Hermitian * positive definite band 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, U**H is the conjugate transpose * of U, 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. * * KD (input) INTEGER * The number of super-diagonals of the matrix A if UPLO = 'U', * or the number of sub-diagonals if UPLO = 'L'. KD >= 0. * * AB (input/output) COMPLEX array, dimension (LDAB,N) * On entry, the upper or lower triangle of the Hermitian band * matrix A, stored in the first KD+1 rows of the array. The * j-th column of A is stored in the j-th column of the array AB * as follows: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). * * On exit, if INFO = 0, the triangular factor U or L from the * Cholesky factorization A = U**H *U or A = L*L**H of the band * matrix A, in the same storage format as A. * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KD+1. * * 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. * * Further Details * =============== * * The band storage scheme is illustrated by the following example, when * N = 6, KD = 2, and UPLO = 'U': * * On entry: On exit: * * * * a13 a24 a35 a46 * * u13 u24 u35 u46 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 * * Similarly, if UPLO = 'L' the format of A is as follows: * * On entry: On exit: * * a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 * a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * * a31 a42 a53 a64 * * l31 l42 l53 l64 * * * * Array elements marked * are not used by the routine. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, KLD, KN REAL AJJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CHER, CLACGV, CSSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, 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( KD.LT.0 ) THEN INFO = -3 ELSE IF( LDAB.LT.KD+1 ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CPBTF2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * KLD = MAX( 1, LDAB-1 ) * 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( AB( KD+1, J ) ) IF( AJJ.LE.ZERO ) THEN AB( KD+1, J ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) AB( KD+1, J ) = AJJ * * Compute elements J+1:J+KN of row J and update the * trailing submatrix within the band. * KN = MIN( KD, N-J ) IF( KN.GT.0 ) THEN CALL CSSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD ) CALL CLACGV( KN, AB( KD, J+1 ), KLD ) CALL CHER( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD, $ AB( KD+1, J+1 ), KLD ) CALL CLACGV( KN, AB( KD, J+1 ), KLD ) 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( AB( 1, J ) ) IF( AJJ.LE.ZERO ) THEN AB( 1, J ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) AB( 1, J ) = AJJ * * Compute elements J+1:J+KN of column J and update the * trailing submatrix within the band. * KN = MIN( KD, N-J ) IF( KN.GT.0 ) THEN CALL CSSCAL( KN, ONE / AJJ, AB( 2, J ), 1 ) CALL CHER( 'Lower', KN, -ONE, AB( 2, J ), 1, $ AB( 1, J+1 ), KLD ) END IF 20 CONTINUE END IF RETURN * 30 CONTINUE INFO = J RETURN * * End of CPBTF2 * END |