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