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DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
$ IPIV, CMODE, C, INFO, WORK,
$ IWORK )
*
* -- LAPACK routine (version 3.2.1) --
* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
* -- Jason Riedy of Univ. of California Berkeley. --
* -- April 2009 --
*
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley and NAG Ltd. --
*
IMPLICIT NONE
* ..
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER N, LDA, LDAF, INFO, CMODE
* ..
* .. Array Arguments
INTEGER IWORK( * ), IPIV( * )
DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
* ..
*
* Purpose
* =======
*
* DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
* where op2 is determined by CMODE as follows
* CMODE = 1 op2(C) = C
* CMODE = 0 op2(C) = I
* CMODE = -1 op2(C) = inv(C)
* The Skeel condition number cond(A) = norminf( |inv(A)||A| )
* is computed by computing scaling factors R such that
* diag(R)*A*op2(C) is row equilibrated and computing the standard
* infinity-norm condition number.
*
* Arguments
* ==========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The number of linear equations, i.e., the order of the
* matrix A. N >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the N-by-N matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
* The block diagonal matrix D and the multipliers used to
* obtain the factor U or L as computed by DSYTRF.
*
* LDAF (input) INTEGER
* The leading dimension of the array AF. LDAF >= max(1,N).
*
* IPIV (input) INTEGER array, dimension (N)
* Details of the interchanges and the block structure of D
* as determined by DSYTRF.
*
* CMODE (input) INTEGER
* Determines op2(C) in the formula op(A) * op2(C) as follows:
* CMODE = 1 op2(C) = C
* CMODE = 0 op2(C) = I
* CMODE = -1 op2(C) = inv(C)
*
* C (input) DOUBLE PRECISION array, dimension (N)
* The vector C in the formula op(A) * op2(C).
*
* INFO (output) INTEGER
* = 0: Successful exit.
* i > 0: The ith argument is invalid.
*
* WORK (input) DOUBLE PRECISION array, dimension (3*N).
* Workspace.
*
* IWORK (input) INTEGER array, dimension (N).
* Workspace.
*
* =====================================================================
*
* .. Local Scalars ..
CHARACTER NORMIN
INTEGER KASE, I, J
DOUBLE PRECISION AINVNM, SMLNUM, TMP
LOGICAL UP
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IDAMAX
DOUBLE PRECISION DLAMCH
EXTERNAL LSAME, IDAMAX, DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA, DSYTRS
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Executable Statements ..
*
DLA_SYRCOND = 0.0D+0
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLA_SYRCOND', -INFO )
RETURN
END IF
IF( N.EQ.0 ) THEN
DLA_SYRCOND = 1.0D+0
RETURN
END IF
UP = .FALSE.
IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
*
* Compute the equilibration matrix R such that
* inv(R)*A*C has unit 1-norm.
*
IF ( UP ) THEN
DO I = 1, N
TMP = 0.0D+0
IF ( CMODE .EQ. 1 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( J, I ) * C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( I, J ) * C( J ) )
END DO
ELSE IF ( CMODE .EQ. 0 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( J, I ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( I, J ) )
END DO
ELSE
DO J = 1, I
TMP = TMP + ABS( A( J, I ) / C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( I, J ) / C( J ) )
END DO
END IF
WORK( 2*N+I ) = TMP
END DO
ELSE
DO I = 1, N
TMP = 0.0D+0
IF ( CMODE .EQ. 1 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( I, J ) * C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( J, I ) * C( J ) )
END DO
ELSE IF ( CMODE .EQ. 0 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( I, J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( J, I ) )
END DO
ELSE
DO J = 1, I
TMP = TMP + ABS( A( I, J) / C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( J, I) / C( J ) )
END DO
END IF
WORK( 2*N+I ) = TMP
END DO
ENDIF
*
* Estimate the norm of inv(op(A)).
*
SMLNUM = DLAMCH( 'Safe minimum' )
AINVNM = 0.0D+0
NORMIN = 'N'
KASE = 0
10 CONTINUE
CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.2 ) THEN
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * WORK( 2*N+I )
END DO
IF ( UP ) THEN
CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
ELSE
CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
ENDIF
*
* Multiply by inv(C).
*
IF ( CMODE .EQ. 1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) / C( I )
END DO
ELSE IF ( CMODE .EQ. -1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
ELSE
*
* Multiply by inv(C**T).
*
IF ( CMODE .EQ. 1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) / C( I )
END DO
ELSE IF ( CMODE .EQ. -1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
IF ( UP ) THEN
CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
ELSE
CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
ENDIF
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * WORK( 2*N+I )
END DO
END IF
*
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM .NE. 0.0D+0 )
$ DLA_SYRCOND = ( 1.0D+0 / AINVNM )
*
RETURN
*
END
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