SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, \$ INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH. * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N REAL ANORM, RCOND * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL A( LDA, * ), WORK( * ) * .. * * Purpose * ======= * * SPOCON estimates the reciprocal of the condition number (in the * 1-norm) of a real symmetric positive definite matrix using the * Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF. * * An estimate is obtained for norm(inv(A)), and the reciprocal of the * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). * * 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) REAL array, dimension (LDA,N) * The triangular factor U or L from the Cholesky factorization * A = U**T*U or A = L*L**T, as computed by SPOTRF. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * ANORM (input) REAL * The 1-norm (or infinity-norm) of the symmetric matrix A. * * RCOND (output) REAL * The reciprocal of the condition number of the matrix A, * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an * estimate of the 1-norm of inv(A) computed in this routine. * * WORK (workspace) REAL array, dimension (3*N) * * IWORK (workspace) INTEGER array, dimension (N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER CHARACTER NORMIN INTEGER IX, KASE REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER ISAMAX REAL SLAMCH EXTERNAL LSAME, ISAMAX, SLAMCH * .. * .. External Subroutines .. EXTERNAL SLACN2, SLATRS, SRSCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. 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 ELSE IF( ANORM.LT.ZERO ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SPOCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.EQ.ZERO ) THEN RETURN END IF * SMLNUM = SLAMCH( 'Safe minimum' ) * * Estimate the 1-norm of inv(A). * KASE = 0 NORMIN = 'N' 10 CONTINUE CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( UPPER ) THEN * * Multiply by inv(U'). * CALL SLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A, \$ LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO ) NORMIN = 'Y' * * Multiply by inv(U). * CALL SLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, \$ A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO ) ELSE * * Multiply by inv(L). * CALL SLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N, \$ A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO ) NORMIN = 'Y' * * Multiply by inv(L'). * CALL SLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A, \$ LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO ) END IF * * Multiply by 1/SCALE if doing so will not cause overflow. * SCALE = SCALEL*SCALEU IF( SCALE.NE.ONE ) THEN IX = ISAMAX( N, WORK, 1 ) IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) \$ GO TO 20 CALL SRSCL( N, SCALE, WORK, 1 ) END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) \$ RCOND = ( ONE / AINVNM ) / ANORM * 20 CONTINUE RETURN * * End of SPOCON * END