Annotation of rpl/lapack/lapack/zla_syrcond_x.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION ZLA_SYRCOND_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_SYRCOND_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 ZSYTRF.
! 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 ZSYTRF.
! 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
! 76: DOUBLE PRECISION AINVNM, ANORM, TMP
! 77: INTEGER I, J
! 78: LOGICAL UP
! 79: COMPLEX*16 ZDUM
! 80: * ..
! 81: * .. Local Arrays ..
! 82: INTEGER ISAVE( 3 )
! 83: * ..
! 84: * .. External Functions ..
! 85: LOGICAL LSAME
! 86: EXTERNAL LSAME
! 87: * ..
! 88: * .. External Subroutines ..
! 89: EXTERNAL ZLACN2, ZSYTRS, XERBLA
! 90: * ..
! 91: * .. Intrinsic Functions ..
! 92: INTRINSIC ABS, MAX
! 93: * ..
! 94: * .. Statement Functions ..
! 95: DOUBLE PRECISION CABS1
! 96: * ..
! 97: * .. Statement Function Definitions ..
! 98: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 99: * ..
! 100: * .. Executable Statements ..
! 101: *
! 102: ZLA_SYRCOND_X = 0.0D+0
! 103: *
! 104: INFO = 0
! 105: IF( N.LT.0 ) THEN
! 106: INFO = -2
! 107: END IF
! 108: IF( INFO.NE.0 ) THEN
! 109: CALL XERBLA( 'ZLA_SYRCOND_X', -INFO )
! 110: RETURN
! 111: END IF
! 112: UP = .FALSE.
! 113: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
! 114: *
! 115: * Compute norm of op(A)*op2(C).
! 116: *
! 117: ANORM = 0.0D+0
! 118: IF ( UP ) THEN
! 119: DO I = 1, N
! 120: TMP = 0.0D+0
! 121: DO J = 1, I
! 122: TMP = TMP + CABS1( A( J, I ) * X( J ) )
! 123: END DO
! 124: DO J = I+1, N
! 125: TMP = TMP + CABS1( A( I, J ) * X( J ) )
! 126: END DO
! 127: RWORK( I ) = TMP
! 128: ANORM = MAX( ANORM, TMP )
! 129: END DO
! 130: ELSE
! 131: DO I = 1, N
! 132: TMP = 0.0D+0
! 133: DO J = 1, I
! 134: TMP = TMP + CABS1( A( I, J ) * X( J ) )
! 135: END DO
! 136: DO J = I+1, N
! 137: TMP = TMP + CABS1( A( J, I ) * X( J ) )
! 138: END DO
! 139: RWORK( I ) = TMP
! 140: ANORM = MAX( ANORM, TMP )
! 141: END DO
! 142: END IF
! 143: *
! 144: * Quick return if possible.
! 145: *
! 146: IF( N.EQ.0 ) THEN
! 147: ZLA_SYRCOND_X = 1.0D+0
! 148: RETURN
! 149: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
! 150: RETURN
! 151: END IF
! 152: *
! 153: * Estimate the norm of inv(op(A)).
! 154: *
! 155: AINVNM = 0.0D+0
! 156: *
! 157: KASE = 0
! 158: 10 CONTINUE
! 159: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 160: IF( KASE.NE.0 ) THEN
! 161: IF( KASE.EQ.2 ) THEN
! 162: *
! 163: * Multiply by R.
! 164: *
! 165: DO I = 1, N
! 166: WORK( I ) = WORK( I ) * RWORK( I )
! 167: END DO
! 168: *
! 169: IF ( UP ) THEN
! 170: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
! 171: $ WORK, N, INFO )
! 172: ELSE
! 173: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
! 174: $ WORK, N, INFO )
! 175: ENDIF
! 176: *
! 177: * Multiply by inv(X).
! 178: *
! 179: DO I = 1, N
! 180: WORK( I ) = WORK( I ) / X( I )
! 181: END DO
! 182: ELSE
! 183: *
! 184: * Multiply by inv(X').
! 185: *
! 186: DO I = 1, N
! 187: WORK( I ) = WORK( I ) / X( I )
! 188: END DO
! 189: *
! 190: IF ( UP ) THEN
! 191: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
! 192: $ WORK, N, INFO )
! 193: ELSE
! 194: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
! 195: $ WORK, N, INFO )
! 196: END IF
! 197: *
! 198: * Multiply by R.
! 199: *
! 200: DO I = 1, N
! 201: WORK( I ) = WORK( I ) * RWORK( I )
! 202: END DO
! 203: END IF
! 204: GO TO 10
! 205: END IF
! 206: *
! 207: * Compute the estimate of the reciprocal condition number.
! 208: *
! 209: IF( AINVNM .NE. 0.0D+0 )
! 210: $ ZLA_SYRCOND_X = 1.0D+0 / AINVNM
! 211: *
! 212: RETURN
! 213: *
! 214: END
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