Annotation of rpl/lapack/lapack/dpocon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
! 2: $ INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER UPLO
! 13: INTEGER INFO, LDA, N
! 14: DOUBLE PRECISION ANORM, RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: INTEGER IWORK( * )
! 18: DOUBLE PRECISION A( LDA, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * DPOCON estimates the reciprocal of the condition number (in the
! 25: * 1-norm) of a real symmetric positive definite matrix using the
! 26: * Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
! 27: *
! 28: * An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 29: * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
! 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 order of the matrix A. N >= 0.
! 40: *
! 41: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
! 42: * The triangular factor U or L from the Cholesky factorization
! 43: * A = U**T*U or A = L*L**T, as computed by DPOTRF.
! 44: *
! 45: * LDA (input) INTEGER
! 46: * The leading dimension of the array A. LDA >= max(1,N).
! 47: *
! 48: * ANORM (input) DOUBLE PRECISION
! 49: * The 1-norm (or infinity-norm) of the symmetric matrix A.
! 50: *
! 51: * RCOND (output) DOUBLE PRECISION
! 52: * The reciprocal of the condition number of the matrix A,
! 53: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 54: * estimate of the 1-norm of inv(A) computed in this routine.
! 55: *
! 56: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
! 57: *
! 58: * IWORK (workspace) INTEGER array, dimension (N)
! 59: *
! 60: * INFO (output) INTEGER
! 61: * = 0: successful exit
! 62: * < 0: if INFO = -i, the i-th argument had an illegal value
! 63: *
! 64: * =====================================================================
! 65: *
! 66: * .. Parameters ..
! 67: DOUBLE PRECISION ONE, ZERO
! 68: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 69: * ..
! 70: * .. Local Scalars ..
! 71: LOGICAL UPPER
! 72: CHARACTER NORMIN
! 73: INTEGER IX, KASE
! 74: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
! 75: * ..
! 76: * .. Local Arrays ..
! 77: INTEGER ISAVE( 3 )
! 78: * ..
! 79: * .. External Functions ..
! 80: LOGICAL LSAME
! 81: INTEGER IDAMAX
! 82: DOUBLE PRECISION DLAMCH
! 83: EXTERNAL LSAME, IDAMAX, DLAMCH
! 84: * ..
! 85: * .. External Subroutines ..
! 86: EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA
! 87: * ..
! 88: * .. Intrinsic Functions ..
! 89: INTRINSIC ABS, MAX
! 90: * ..
! 91: * .. Executable Statements ..
! 92: *
! 93: * Test the input parameters.
! 94: *
! 95: INFO = 0
! 96: UPPER = LSAME( UPLO, 'U' )
! 97: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 98: INFO = -1
! 99: ELSE IF( N.LT.0 ) THEN
! 100: INFO = -2
! 101: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 102: INFO = -4
! 103: ELSE IF( ANORM.LT.ZERO ) THEN
! 104: INFO = -5
! 105: END IF
! 106: IF( INFO.NE.0 ) THEN
! 107: CALL XERBLA( 'DPOCON', -INFO )
! 108: RETURN
! 109: END IF
! 110: *
! 111: * Quick return if possible
! 112: *
! 113: RCOND = ZERO
! 114: IF( N.EQ.0 ) THEN
! 115: RCOND = ONE
! 116: RETURN
! 117: ELSE IF( ANORM.EQ.ZERO ) THEN
! 118: RETURN
! 119: END IF
! 120: *
! 121: SMLNUM = DLAMCH( 'Safe minimum' )
! 122: *
! 123: * Estimate the 1-norm of inv(A).
! 124: *
! 125: KASE = 0
! 126: NORMIN = 'N'
! 127: 10 CONTINUE
! 128: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 129: IF( KASE.NE.0 ) THEN
! 130: IF( UPPER ) THEN
! 131: *
! 132: * Multiply by inv(U').
! 133: *
! 134: CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
! 135: $ LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
! 136: NORMIN = 'Y'
! 137: *
! 138: * Multiply by inv(U).
! 139: *
! 140: CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
! 141: $ A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
! 142: ELSE
! 143: *
! 144: * Multiply by inv(L).
! 145: *
! 146: CALL DLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
! 147: $ A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
! 148: NORMIN = 'Y'
! 149: *
! 150: * Multiply by inv(L').
! 151: *
! 152: CALL DLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A,
! 153: $ LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
! 154: END IF
! 155: *
! 156: * Multiply by 1/SCALE if doing so will not cause overflow.
! 157: *
! 158: SCALE = SCALEL*SCALEU
! 159: IF( SCALE.NE.ONE ) THEN
! 160: IX = IDAMAX( N, WORK, 1 )
! 161: IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
! 162: $ GO TO 20
! 163: CALL DRSCL( N, SCALE, WORK, 1 )
! 164: END IF
! 165: GO TO 10
! 166: END IF
! 167: *
! 168: * Compute the estimate of the reciprocal condition number.
! 169: *
! 170: IF( AINVNM.NE.ZERO )
! 171: $ RCOND = ( ONE / AINVNM ) / ANORM
! 172: *
! 173: 20 CONTINUE
! 174: RETURN
! 175: *
! 176: * End of DPOCON
! 177: *
! 178: END
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