Annotation of rpl/lapack/lapack/zla_gercond_c.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF,
! 2: $ LDAF, IPIV, C, CAPPLY,
! 3: $ INFO, 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 Aguments ..
! 16: CHARACTER TRANS
! 17: LOGICAL CAPPLY
! 18: INTEGER N, LDA, LDAF, INFO
! 19: * ..
! 20: * .. Array Arguments ..
! 21: INTEGER IPIV( * )
! 22: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
! 23: DOUBLE PRECISION C( * ), RWORK( * )
! 24: * ..
! 25: *
! 26: * Purpose
! 27: * =======
! 28: *
! 29: * ZLA_GERCOND_C computes the infinity norm condition number of
! 30: * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * TRANS (input) CHARACTER*1
! 36: * Specifies the form of the system of equations:
! 37: * = 'N': A * X = B (No transpose)
! 38: * = 'T': A**T * X = B (Transpose)
! 39: * = 'C': A**H * X = B (Conjugate Transpose = Transpose)
! 40: *
! 41: * N (input) INTEGER
! 42: * The number of linear equations, i.e., the order of the
! 43: * matrix A. N >= 0.
! 44: *
! 45: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 46: * On entry, the N-by-N matrix A
! 47: *
! 48: * LDA (input) INTEGER
! 49: * The leading dimension of the array A. LDA >= max(1,N).
! 50: *
! 51: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
! 52: * The factors L and U from the factorization
! 53: * A = P*L*U as computed by ZGETRF.
! 54: *
! 55: * LDAF (input) INTEGER
! 56: * The leading dimension of the array AF. LDAF >= max(1,N).
! 57: *
! 58: * IPIV (input) INTEGER array, dimension (N)
! 59: * The pivot indices from the factorization A = P*L*U
! 60: * as computed by ZGETRF; row i of the matrix was interchanged
! 61: * with row IPIV(i).
! 62: *
! 63: * C (input) DOUBLE PRECISION array, dimension (N)
! 64: * The vector C in the formula op(A) * inv(diag(C)).
! 65: *
! 66: * CAPPLY (input) LOGICAL
! 67: * If .TRUE. then access the vector C in the formula above.
! 68: *
! 69: * INFO (output) INTEGER
! 70: * = 0: Successful exit.
! 71: * i > 0: The ith argument is invalid.
! 72: *
! 73: * WORK (input) COMPLEX*16 array, dimension (2*N).
! 74: * Workspace.
! 75: *
! 76: * RWORK (input) DOUBLE PRECISION array, dimension (N).
! 77: * Workspace.
! 78: *
! 79: * =====================================================================
! 80: *
! 81: * .. Local Scalars ..
! 82: LOGICAL NOTRANS
! 83: INTEGER KASE, I, J
! 84: DOUBLE PRECISION AINVNM, ANORM, TMP
! 85: COMPLEX*16 ZDUM
! 86: * ..
! 87: * .. Local Arrays ..
! 88: INTEGER ISAVE( 3 )
! 89: * ..
! 90: * .. External Functions ..
! 91: LOGICAL LSAME
! 92: EXTERNAL LSAME
! 93: * ..
! 94: * .. External Subroutines ..
! 95: EXTERNAL ZLACN2, ZGETRS, XERBLA
! 96: * ..
! 97: * .. Intrinsic Functions ..
! 98: INTRINSIC ABS, MAX, REAL, DIMAG
! 99: * ..
! 100: * .. Statement Functions ..
! 101: DOUBLE PRECISION CABS1
! 102: * ..
! 103: * .. Statement Function Definitions ..
! 104: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 105: * ..
! 106: * .. Executable Statements ..
! 107: ZLA_GERCOND_C = 0.0D+0
! 108: *
! 109: INFO = 0
! 110: NOTRANS = LSAME( TRANS, 'N' )
! 111: IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
! 112: $ LSAME( TRANS, 'C' ) ) THEN
! 113: ELSE IF( N.LT.0 ) THEN
! 114: INFO = -2
! 115: END IF
! 116: IF( INFO.NE.0 ) THEN
! 117: CALL XERBLA( 'ZLA_GERCOND_C', -INFO )
! 118: RETURN
! 119: END IF
! 120: *
! 121: * Compute norm of op(A)*op2(C).
! 122: *
! 123: ANORM = 0.0D+0
! 124: IF ( NOTRANS ) THEN
! 125: DO I = 1, N
! 126: TMP = 0.0D+0
! 127: IF ( CAPPLY ) THEN
! 128: DO J = 1, N
! 129: TMP = TMP + CABS1( A( I, J ) ) / C( J )
! 130: END DO
! 131: ELSE
! 132: DO J = 1, N
! 133: TMP = TMP + CABS1( A( I, J ) )
! 134: END DO
! 135: END IF
! 136: RWORK( I ) = TMP
! 137: ANORM = MAX( ANORM, TMP )
! 138: END DO
! 139: ELSE
! 140: DO I = 1, N
! 141: TMP = 0.0D+0
! 142: IF ( CAPPLY ) THEN
! 143: DO J = 1, N
! 144: TMP = TMP + CABS1( A( J, I ) ) / C( J )
! 145: END DO
! 146: ELSE
! 147: DO J = 1, N
! 148: TMP = TMP + CABS1( A( J, I ) )
! 149: END DO
! 150: END IF
! 151: RWORK( I ) = TMP
! 152: ANORM = MAX( ANORM, TMP )
! 153: END DO
! 154: END IF
! 155: *
! 156: * Quick return if possible.
! 157: *
! 158: IF( N.EQ.0 ) THEN
! 159: ZLA_GERCOND_C = 1.0D+0
! 160: RETURN
! 161: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
! 162: RETURN
! 163: END IF
! 164: *
! 165: * Estimate the norm of inv(op(A)).
! 166: *
! 167: AINVNM = 0.0D+0
! 168: *
! 169: KASE = 0
! 170: 10 CONTINUE
! 171: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 172: IF( KASE.NE.0 ) THEN
! 173: IF( KASE.EQ.2 ) THEN
! 174: *
! 175: * Multiply by R.
! 176: *
! 177: DO I = 1, N
! 178: WORK( I ) = WORK( I ) * RWORK( I )
! 179: END DO
! 180: *
! 181: IF (NOTRANS) THEN
! 182: CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
! 183: $ WORK, N, INFO )
! 184: ELSE
! 185: CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
! 186: $ WORK, N, INFO )
! 187: ENDIF
! 188: *
! 189: * Multiply by inv(C).
! 190: *
! 191: IF ( CAPPLY ) THEN
! 192: DO I = 1, N
! 193: WORK( I ) = WORK( I ) * C( I )
! 194: END DO
! 195: END IF
! 196: ELSE
! 197: *
! 198: * Multiply by inv(C').
! 199: *
! 200: IF ( CAPPLY ) THEN
! 201: DO I = 1, N
! 202: WORK( I ) = WORK( I ) * C( I )
! 203: END DO
! 204: END IF
! 205: *
! 206: IF ( NOTRANS ) THEN
! 207: CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
! 208: $ WORK, N, INFO )
! 209: ELSE
! 210: CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
! 211: $ WORK, N, INFO )
! 212: END IF
! 213: *
! 214: * Multiply by R.
! 215: *
! 216: DO I = 1, N
! 217: WORK( I ) = WORK( I ) * RWORK( I )
! 218: END DO
! 219: END IF
! 220: GO TO 10
! 221: END IF
! 222: *
! 223: * Compute the estimate of the reciprocal condition number.
! 224: *
! 225: IF( AINVNM .NE. 0.0D+0 )
! 226: $ ZLA_GERCOND_C = 1.0D+0 / AINVNM
! 227: *
! 228: RETURN
! 229: *
! 230: END
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