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21 * SUBROUTINE CSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
23 * .. Scalar Arguments ..
28 * .. Array Arguments ..
30 * COMPLEX AP( * ), WORK( * )
39 *> CSPCON estimates the reciprocal of the condition number (in the
40 *> 1-norm) of a complex symmetric packed matrix A using the
41 *> factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF.
43 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
44 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
52 *> UPLO is CHARACTER*1
53 *> Specifies whether the details of the factorization are stored
54 *> as an upper or lower triangular matrix.
55 *> = 'U': Upper triangular, form is A = U*D*U**T;
56 *> = 'L': Lower triangular, form is A = L*D*L**T.
62 *> The order of the matrix A. N >= 0.
67 *> AP is COMPLEX array, dimension (N*(N+1)/2)
68 *> The block diagonal matrix D and the multipliers used to
69 *> obtain the factor U or L as computed by CSPTRF, stored as a
70 *> packed triangular matrix.
75 *> IPIV is INTEGER array, dimension (N)
76 *> Details of the interchanges and the block structure of D
77 *> as determined by CSPTRF.
83 *> The 1-norm of the original matrix A.
89 *> The reciprocal of the condition number of the matrix A,
90 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
91 *> estimate of the 1-norm of inv(A) computed in this routine.
96 *> WORK is COMPLEX array, dimension (2*N)
102 *> = 0: successful exit
103 *> < 0: if INFO = -i, the i-th argument had an illegal value
109 *> \author Univ. of Tennessee
110 *> \author Univ. of California Berkeley
111 *> \author Univ. of Colorado Denver
114 *> \date November 2011
116 *> \ingroup complexOTHERcomputational
118 * =====================================================================
119 SUBROUTINE CSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
121 * -- LAPACK computational routine (version 3.4.0) --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 * .. Scalar Arguments ..
131 * .. Array Arguments ..
133 COMPLEX AP( * ), WORK( * )
136 * =====================================================================
140 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
142 * .. Local Scalars ..
150 * .. External Functions ..
154 * .. External Subroutines ..
155 EXTERNAL CLACN2, CSPTRS, XERBLA
157 * .. Executable Statements ..
159 * Test the input parameters.
162 UPPER = LSAME( UPLO, 'U' )
163 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
165 ELSE IF( N.LT.0 ) THEN
167 ELSE IF( ANORM.LT.ZERO ) THEN
171 CALL XERBLA( 'CSPCON', -INFO )
175 * Quick return if possible
181 ELSE IF( ANORM.LE.ZERO ) THEN
185 * Check that the diagonal matrix D is nonsingular.
189 * Upper triangular storage: examine D from bottom to top
193 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
199 * Lower triangular storage: examine D from top to bottom.
203 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
209 * Estimate the 1-norm of the inverse.
213 CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
216 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
218 CALL CSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
222 * Compute the estimate of the reciprocal condition number.
225 $ RCOND = ( ONE / AINVNM ) / ANORM