Annotation of rpl/lapack/lapack/zla_hercond_x.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF,
! 2: $ LDAF, IPIV, X, INFO,
! 3: $ WORK, RWORK )
! 4: *
! 5: * -- LAPACK routine (version 3.2.1) --
! 6: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 7: * -- Jason Riedy of Univ. of California Berkeley. --
! 8: * -- April 2009 --
! 9: *
! 10: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 11: * -- Univ. of California Berkeley and NAG Ltd. --
! 12: *
! 13: IMPLICIT NONE
! 14: * ..
! 15: * .. Scalar Arguments ..
! 16: CHARACTER UPLO
! 17: INTEGER N, LDA, LDAF, INFO
! 18: * ..
! 19: * .. Array Arguments ..
! 20: INTEGER IPIV( * )
! 21: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
! 22: DOUBLE PRECISION RWORK( * )
! 23: * ..
! 24: *
! 25: * Purpose
! 26: * =======
! 27: *
! 28: * ZLA_HERCOND_X computes the infinity norm condition number of
! 29: * op(A) * diag(X) where X is a COMPLEX*16 vector.
! 30: *
! 31: * Arguments
! 32: * =========
! 33: *
! 34: * UPLO (input) CHARACTER*1
! 35: * = 'U': Upper triangle of A is stored;
! 36: * = 'L': Lower triangle of A is stored.
! 37: *
! 38: * N (input) INTEGER
! 39: * The number of linear equations, i.e., the order of the
! 40: * matrix A. N >= 0.
! 41: *
! 42: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 43: * On entry, the N-by-N matrix A.
! 44: *
! 45: * LDA (input) INTEGER
! 46: * The leading dimension of the array A. LDA >= max(1,N).
! 47: *
! 48: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
! 49: * The block diagonal matrix D and the multipliers used to
! 50: * obtain the factor U or L as computed by ZHETRF.
! 51: *
! 52: * LDAF (input) INTEGER
! 53: * The leading dimension of the array AF. LDAF >= max(1,N).
! 54: *
! 55: * IPIV (input) INTEGER array, dimension (N)
! 56: * Details of the interchanges and the block structure of D
! 57: * as determined by CHETRF.
! 58: *
! 59: * X (input) COMPLEX*16 array, dimension (N)
! 60: * The vector X in the formula op(A) * diag(X).
! 61: *
! 62: * INFO (output) INTEGER
! 63: * = 0: Successful exit.
! 64: * i > 0: The ith argument is invalid.
! 65: *
! 66: * WORK (input) COMPLEX*16 array, dimension (2*N).
! 67: * Workspace.
! 68: *
! 69: * RWORK (input) DOUBLE PRECISION array, dimension (N).
! 70: * Workspace.
! 71: *
! 72: * =====================================================================
! 73: *
! 74: * .. Local Scalars ..
! 75: INTEGER KASE, I, J
! 76: DOUBLE PRECISION AINVNM, ANORM, TMP
! 77: LOGICAL UP
! 78: COMPLEX*16 ZDUM
! 79: * ..
! 80: * .. Local Arrays ..
! 81: INTEGER ISAVE( 3 )
! 82: * ..
! 83: * .. External Functions ..
! 84: LOGICAL LSAME
! 85: EXTERNAL LSAME
! 86: * ..
! 87: * .. External Subroutines ..
! 88: EXTERNAL ZLACN2, ZHETRS, XERBLA
! 89: * ..
! 90: * .. Intrinsic Functions ..
! 91: INTRINSIC ABS, MAX
! 92: * ..
! 93: * .. Statement Functions ..
! 94: DOUBLE PRECISION CABS1
! 95: * ..
! 96: * .. Statement Function Definitions ..
! 97: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 98: * ..
! 99: * .. Executable Statements ..
! 100: *
! 101: ZLA_HERCOND_X = 0.0D+0
! 102: *
! 103: INFO = 0
! 104: IF( N.LT.0 ) THEN
! 105: INFO = -2
! 106: END IF
! 107: IF( INFO.NE.0 ) THEN
! 108: CALL XERBLA( 'ZLA_HERCOND_X', -INFO )
! 109: RETURN
! 110: END IF
! 111: UP = .FALSE.
! 112: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
! 113: *
! 114: * Compute norm of op(A)*op2(C).
! 115: *
! 116: ANORM = 0.0D+0
! 117: IF ( UP ) THEN
! 118: DO I = 1, N
! 119: TMP = 0.0D+0
! 120: DO J = 1, I
! 121: TMP = TMP + CABS1( A( J, I ) * X( J ) )
! 122: END DO
! 123: DO J = I+1, N
! 124: TMP = TMP + CABS1( A( I, J ) * X( J ) )
! 125: END DO
! 126: RWORK( I ) = TMP
! 127: ANORM = MAX( ANORM, TMP )
! 128: END DO
! 129: ELSE
! 130: DO I = 1, N
! 131: TMP = 0.0D+0
! 132: DO J = 1, I
! 133: TMP = TMP + CABS1( A( I, J ) * X( J ) )
! 134: END DO
! 135: DO J = I+1, N
! 136: TMP = TMP + CABS1( A( J, I ) * X( J ) )
! 137: END DO
! 138: RWORK( I ) = TMP
! 139: ANORM = MAX( ANORM, TMP )
! 140: END DO
! 141: END IF
! 142: *
! 143: * Quick return if possible.
! 144: *
! 145: IF( N.EQ.0 ) THEN
! 146: ZLA_HERCOND_X = 1.0D+0
! 147: RETURN
! 148: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
! 149: RETURN
! 150: END IF
! 151: *
! 152: * Estimate the norm of inv(op(A)).
! 153: *
! 154: AINVNM = 0.0D+0
! 155: *
! 156: KASE = 0
! 157: 10 CONTINUE
! 158: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 159: IF( KASE.NE.0 ) THEN
! 160: IF( KASE.EQ.2 ) THEN
! 161: *
! 162: * Multiply by R.
! 163: *
! 164: DO I = 1, N
! 165: WORK( I ) = WORK( I ) * RWORK( I )
! 166: END DO
! 167: *
! 168: IF ( UP ) THEN
! 169: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
! 170: $ WORK, N, INFO )
! 171: ELSE
! 172: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
! 173: $ WORK, N, INFO )
! 174: ENDIF
! 175: *
! 176: * Multiply by inv(X).
! 177: *
! 178: DO I = 1, N
! 179: WORK( I ) = WORK( I ) / X( I )
! 180: END DO
! 181: ELSE
! 182: *
! 183: * Multiply by inv(X').
! 184: *
! 185: DO I = 1, N
! 186: WORK( I ) = WORK( I ) / X( I )
! 187: END DO
! 188: *
! 189: IF ( UP ) THEN
! 190: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
! 191: $ WORK, N, INFO )
! 192: ELSE
! 193: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
! 194: $ WORK, N, INFO )
! 195: END IF
! 196: *
! 197: * Multiply by R.
! 198: *
! 199: DO I = 1, N
! 200: WORK( I ) = WORK( I ) * RWORK( I )
! 201: END DO
! 202: END IF
! 203: GO TO 10
! 204: END IF
! 205: *
! 206: * Compute the estimate of the reciprocal condition number.
! 207: *
! 208: IF( AINVNM .NE. 0.0D+0 )
! 209: $ ZLA_HERCOND_X = 1.0D+0 / AINVNM
! 210: *
! 211: RETURN
! 212: *
! 213: END
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