SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, $ INFO ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. INTEGER IPIV( * ), IWORK( * ) DOUBLE PRECISION AP( * ), WORK( * ) * .. * * Purpose * ======= * * DSPCON estimates the reciprocal of the condition number (in the * 1-norm) of a real symmetric packed matrix A using the factorization * A = U*D*U**T or A = L*D*L**T computed by DSPTRF. * * 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 * Specifies whether the details of the factorization are stored * as an upper or lower triangular matrix. * = 'U': Upper triangular, form is A = U*D*U**T; * = 'L': Lower triangular, form is A = L*D*L**T. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) * The block diagonal matrix D and the multipliers used to * obtain the factor U or L as computed by DSPTRF, stored as a * packed triangular matrix. * * IPIV (input) INTEGER array, dimension (N) * Details of the interchanges and the block structure of D * as determined by DSPTRF. * * ANORM (input) DOUBLE PRECISION * The 1-norm of the original matrix A. * * RCOND (output) DOUBLE PRECISION * 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) DOUBLE PRECISION array, dimension (2*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 .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, IP, KASE DOUBLE PRECISION AINVNM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLACN2, DSPTRS, XERBLA * .. * .. 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( ANORM.LT.ZERO ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSPCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.LE.ZERO ) THEN RETURN END IF * * Check that the diagonal matrix D is nonsingular. * IF( UPPER ) THEN * * Upper triangular storage: examine D from bottom to top * IP = N*( N+1 ) / 2 DO 10 I = N, 1, -1 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) $ RETURN IP = IP - I 10 CONTINUE ELSE * * Lower triangular storage: examine D from top to bottom. * IP = 1 DO 20 I = 1, N IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) $ RETURN IP = IP + N - I + 1 20 CONTINUE END IF * * Estimate the 1-norm of the inverse. * KASE = 0 30 CONTINUE CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN * * Multiply by inv(L*D*L') or inv(U*D*U'). * CALL DSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO ) GO TO 30 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) $ RCOND = ( ONE / AINVNM ) / ANORM * RETURN * * End of DSPCON * END