Annotation of rpl/lapack/lapack/zla_gercond_x.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLA_GERCOND_X( TRANS, 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 TRANS
! 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_GERCOND_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: * TRANS (input) CHARACTER*1
! 35: * Specifies the form of the system of equations:
! 36: * = 'N': A * X = B (No transpose)
! 37: * = 'T': A**T * X = B (Transpose)
! 38: * = 'C': A**H * X = B (Conjugate Transpose = Transpose)
! 39: *
! 40: * N (input) INTEGER
! 41: * The number of linear equations, i.e., the order of the
! 42: * matrix A. N >= 0.
! 43: *
! 44: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 45: * On entry, the N-by-N matrix A.
! 46: *
! 47: * LDA (input) INTEGER
! 48: * The leading dimension of the array A. LDA >= max(1,N).
! 49: *
! 50: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
! 51: * The factors L and U from the factorization
! 52: * A = P*L*U as computed by ZGETRF.
! 53: *
! 54: * LDAF (input) INTEGER
! 55: * The leading dimension of the array AF. LDAF >= max(1,N).
! 56: *
! 57: * IPIV (input) INTEGER array, dimension (N)
! 58: * The pivot indices from the factorization A = P*L*U
! 59: * as computed by ZGETRF; row i of the matrix was interchanged
! 60: * with row IPIV(i).
! 61: *
! 62: * X (input) COMPLEX*16 array, dimension (N)
! 63: * The vector X in the formula op(A) * diag(X).
! 64: *
! 65: * INFO (output) INTEGER
! 66: * = 0: Successful exit.
! 67: * i > 0: The ith argument is invalid.
! 68: *
! 69: * WORK (input) COMPLEX*16 array, dimension (2*N).
! 70: * Workspace.
! 71: *
! 72: * RWORK (input) DOUBLE PRECISION array, dimension (N).
! 73: * Workspace.
! 74: *
! 75: * =====================================================================
! 76: *
! 77: * .. Local Scalars ..
! 78: LOGICAL NOTRANS
! 79: INTEGER KASE
! 80: DOUBLE PRECISION AINVNM, ANORM, TMP
! 81: INTEGER I, J
! 82: COMPLEX*16 ZDUM
! 83: * ..
! 84: * .. Local Arrays ..
! 85: INTEGER ISAVE( 3 )
! 86: * ..
! 87: * .. External Functions ..
! 88: LOGICAL LSAME
! 89: EXTERNAL LSAME
! 90: * ..
! 91: * .. External Subroutines ..
! 92: EXTERNAL ZLACN2, ZGETRS, XERBLA
! 93: * ..
! 94: * .. Intrinsic Functions ..
! 95: INTRINSIC ABS, MAX, REAL, DIMAG
! 96: * ..
! 97: * .. Statement Functions ..
! 98: DOUBLE PRECISION CABS1
! 99: * ..
! 100: * .. Statement Function Definitions ..
! 101: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 102: * ..
! 103: * .. Executable Statements ..
! 104: *
! 105: ZLA_GERCOND_X = 0.0D+0
! 106: *
! 107: INFO = 0
! 108: NOTRANS = LSAME( TRANS, 'N' )
! 109: IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
! 110: $ LSAME( TRANS, 'C' ) ) THEN
! 111: INFO = -1
! 112: ELSE IF( N.LT.0 ) THEN
! 113: INFO = -2
! 114: END IF
! 115: IF( INFO.NE.0 ) THEN
! 116: CALL XERBLA( 'ZLA_GERCOND_X', -INFO )
! 117: RETURN
! 118: END IF
! 119: *
! 120: * Compute norm of op(A)*op2(C).
! 121: *
! 122: ANORM = 0.0D+0
! 123: IF ( NOTRANS ) THEN
! 124: DO I = 1, N
! 125: TMP = 0.0D+0
! 126: DO J = 1, N
! 127: TMP = TMP + CABS1( A( I, J ) * X( J ) )
! 128: END DO
! 129: RWORK( I ) = TMP
! 130: ANORM = MAX( ANORM, TMP )
! 131: END DO
! 132: ELSE
! 133: DO I = 1, N
! 134: TMP = 0.0D+0
! 135: DO J = 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_GERCOND_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: * Multiply by R.
! 162: DO I = 1, N
! 163: WORK( I ) = WORK( I ) * RWORK( I )
! 164: END DO
! 165: *
! 166: IF ( NOTRANS ) THEN
! 167: CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
! 168: $ WORK, N, INFO )
! 169: ELSE
! 170: CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
! 171: $ WORK, N, INFO )
! 172: ENDIF
! 173: *
! 174: * Multiply by inv(X).
! 175: *
! 176: DO I = 1, N
! 177: WORK( I ) = WORK( I ) / X( I )
! 178: END DO
! 179: ELSE
! 180: *
! 181: * Multiply by inv(X').
! 182: *
! 183: DO I = 1, N
! 184: WORK( I ) = WORK( I ) / X( I )
! 185: END DO
! 186: *
! 187: IF ( NOTRANS ) THEN
! 188: CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
! 189: $ WORK, N, INFO )
! 190: ELSE
! 191: CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
! 192: $ WORK, N, INFO )
! 193: END IF
! 194: *
! 195: * Multiply by R.
! 196: *
! 197: DO I = 1, N
! 198: WORK( I ) = WORK( I ) * RWORK( I )
! 199: END DO
! 200: END IF
! 201: GO TO 10
! 202: END IF
! 203: *
! 204: * Compute the estimate of the reciprocal condition number.
! 205: *
! 206: IF( AINVNM .NE. 0.0D+0 )
! 207: $ ZLA_GERCOND_X = 1.0D+0 / AINVNM
! 208: *
! 209: RETURN
! 210: *
! 211: END
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