Annotation of rpl/lapack/lapack/dla_porcond.f, revision 1.1
1.1 ! bertrand 1: DOUBLE PRECISION FUNCTION DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
! 2: $ CMODE, C, INFO, WORK,
! 3: $ IWORK )
! 4: *
! 5: * -- LAPACK routine (version 3.2.2) --
! 6: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 7: * -- Jason Riedy of Univ. of California Berkeley. --
! 8: * -- June 2010 --
! 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, CMODE
! 18: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
! 19: $ C( * )
! 20: * ..
! 21: * .. Array Arguments ..
! 22: INTEGER IWORK( * )
! 23: * ..
! 24: *
! 25: * Purpose
! 26: * =======
! 27: *
! 28: * DLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C)
! 29: * where op2 is determined by CMODE as follows
! 30: * CMODE = 1 op2(C) = C
! 31: * CMODE = 0 op2(C) = I
! 32: * CMODE = -1 op2(C) = inv(C)
! 33: * The Skeel condition number cond(A) = norminf( |inv(A)||A| )
! 34: * is computed by computing scaling factors R such that
! 35: * diag(R)*A*op2(C) is row equilibrated and computing the standard
! 36: * infinity-norm condition number.
! 37: *
! 38: * Arguments
! 39: * ==========
! 40: *
! 41: * UPLO (input) CHARACTER*1
! 42: * = 'U': Upper triangle of A is stored;
! 43: * = 'L': Lower triangle of A is stored.
! 44: *
! 45: * N (input) INTEGER
! 46: * The number of linear equations, i.e., the order of the
! 47: * matrix A. N >= 0.
! 48: *
! 49: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
! 50: * On entry, the N-by-N matrix A.
! 51: *
! 52: * LDA (input) INTEGER
! 53: * The leading dimension of the array A. LDA >= max(1,N).
! 54: *
! 55: * AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
! 56: * The triangular factor U or L from the Cholesky factorization
! 57: * A = U**T*U or A = L*L**T, as computed by DPOTRF.
! 58: *
! 59: * LDAF (input) INTEGER
! 60: * The leading dimension of the array AF. LDAF >= max(1,N).
! 61: *
! 62: * CMODE (input) INTEGER
! 63: * Determines op2(C) in the formula op(A) * op2(C) as follows:
! 64: * CMODE = 1 op2(C) = C
! 65: * CMODE = 0 op2(C) = I
! 66: * CMODE = -1 op2(C) = inv(C)
! 67: *
! 68: * C (input) DOUBLE PRECISION array, dimension (N)
! 69: * The vector C in the formula op(A) * op2(C).
! 70: *
! 71: * INFO (output) INTEGER
! 72: * = 0: Successful exit.
! 73: * i > 0: The ith argument is invalid.
! 74: *
! 75: * WORK (input) DOUBLE PRECISION array, dimension (3*N).
! 76: * Workspace.
! 77: *
! 78: * IWORK (input) INTEGER array, dimension (N).
! 79: * Workspace.
! 80: *
! 81: * =====================================================================
! 82: *
! 83: * .. Local Scalars ..
! 84: INTEGER KASE, I, J
! 85: DOUBLE PRECISION AINVNM, TMP
! 86: LOGICAL UP
! 87: * ..
! 88: * .. Array Arguments ..
! 89: INTEGER ISAVE( 3 )
! 90: * ..
! 91: * .. External Functions ..
! 92: LOGICAL LSAME
! 93: INTEGER IDAMAX
! 94: EXTERNAL LSAME, IDAMAX
! 95: * ..
! 96: * .. External Subroutines ..
! 97: EXTERNAL DLACN2, DPOTRS, XERBLA
! 98: * ..
! 99: * .. Intrinsic Functions ..
! 100: INTRINSIC ABS, MAX
! 101: * ..
! 102: * .. Executable Statements ..
! 103: *
! 104: DLA_PORCOND = 0.0D+0
! 105: *
! 106: INFO = 0
! 107: IF( N.LT.0 ) THEN
! 108: INFO = -2
! 109: END IF
! 110: IF( INFO.NE.0 ) THEN
! 111: CALL XERBLA( 'DLA_PORCOND', -INFO )
! 112: RETURN
! 113: END IF
! 114:
! 115: IF( N.EQ.0 ) THEN
! 116: DLA_PORCOND = 1.0D+0
! 117: RETURN
! 118: END IF
! 119: UP = .FALSE.
! 120: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
! 121: *
! 122: * Compute the equilibration matrix R such that
! 123: * inv(R)*A*C has unit 1-norm.
! 124: *
! 125: IF ( UP ) THEN
! 126: DO I = 1, N
! 127: TMP = 0.0D+0
! 128: IF ( CMODE .EQ. 1 ) THEN
! 129: DO J = 1, I
! 130: TMP = TMP + ABS( A( J, I ) * C( J ) )
! 131: END DO
! 132: DO J = I+1, N
! 133: TMP = TMP + ABS( A( I, J ) * C( J ) )
! 134: END DO
! 135: ELSE IF ( CMODE .EQ. 0 ) THEN
! 136: DO J = 1, I
! 137: TMP = TMP + ABS( A( J, I ) )
! 138: END DO
! 139: DO J = I+1, N
! 140: TMP = TMP + ABS( A( I, J ) )
! 141: END DO
! 142: ELSE
! 143: DO J = 1, I
! 144: TMP = TMP + ABS( A( J ,I ) / C( J ) )
! 145: END DO
! 146: DO J = I+1, N
! 147: TMP = TMP + ABS( A( I, J ) / C( J ) )
! 148: END DO
! 149: END IF
! 150: WORK( 2*N+I ) = TMP
! 151: END DO
! 152: ELSE
! 153: DO I = 1, N
! 154: TMP = 0.0D+0
! 155: IF ( CMODE .EQ. 1 ) THEN
! 156: DO J = 1, I
! 157: TMP = TMP + ABS( A( I, J ) * C( J ) )
! 158: END DO
! 159: DO J = I+1, N
! 160: TMP = TMP + ABS( A( J, I ) * C( J ) )
! 161: END DO
! 162: ELSE IF ( CMODE .EQ. 0 ) THEN
! 163: DO J = 1, I
! 164: TMP = TMP + ABS( A( I, J ) )
! 165: END DO
! 166: DO J = I+1, N
! 167: TMP = TMP + ABS( A( J, I ) )
! 168: END DO
! 169: ELSE
! 170: DO J = 1, I
! 171: TMP = TMP + ABS( A( I, J ) / C( J ) )
! 172: END DO
! 173: DO J = I+1, N
! 174: TMP = TMP + ABS( A( J, I ) / C( J ) )
! 175: END DO
! 176: END IF
! 177: WORK( 2*N+I ) = TMP
! 178: END DO
! 179: ENDIF
! 180: *
! 181: * Estimate the norm of inv(op(A)).
! 182: *
! 183: AINVNM = 0.0D+0
! 184:
! 185: KASE = 0
! 186: 10 CONTINUE
! 187: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 188: IF( KASE.NE.0 ) THEN
! 189: IF( KASE.EQ.2 ) THEN
! 190: *
! 191: * Multiply by R.
! 192: *
! 193: DO I = 1, N
! 194: WORK( I ) = WORK( I ) * WORK( 2*N+I )
! 195: END DO
! 196:
! 197: IF (UP) THEN
! 198: CALL DPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
! 199: ELSE
! 200: CALL DPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO )
! 201: ENDIF
! 202: *
! 203: * Multiply by inv(C).
! 204: *
! 205: IF ( CMODE .EQ. 1 ) THEN
! 206: DO I = 1, N
! 207: WORK( I ) = WORK( I ) / C( I )
! 208: END DO
! 209: ELSE IF ( CMODE .EQ. -1 ) THEN
! 210: DO I = 1, N
! 211: WORK( I ) = WORK( I ) * C( I )
! 212: END DO
! 213: END IF
! 214: ELSE
! 215: *
! 216: * Multiply by inv(C').
! 217: *
! 218: IF ( CMODE .EQ. 1 ) THEN
! 219: DO I = 1, N
! 220: WORK( I ) = WORK( I ) / C( I )
! 221: END DO
! 222: ELSE IF ( CMODE .EQ. -1 ) THEN
! 223: DO I = 1, N
! 224: WORK( I ) = WORK( I ) * C( I )
! 225: END DO
! 226: END IF
! 227:
! 228: IF ( UP ) THEN
! 229: CALL DPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
! 230: ELSE
! 231: CALL DPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO )
! 232: ENDIF
! 233: *
! 234: * Multiply by R.
! 235: *
! 236: DO I = 1, N
! 237: WORK( I ) = WORK( I ) * WORK( 2*N+I )
! 238: END DO
! 239: END IF
! 240: GO TO 10
! 241: END IF
! 242: *
! 243: * Compute the estimate of the reciprocal condition number.
! 244: *
! 245: IF( AINVNM .NE. 0.0D+0 )
! 246: $ DLA_PORCOND = ( 1.0D+0 / AINVNM )
! 247: *
! 248: RETURN
! 249: *
! 250: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dla_porcond.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack