Annotation of rpl/lapack/lapack/dtpcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTPCON( NORM, UPLO, DIAG, N, AP, 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 DIAG, NORM, UPLO
! 13: INTEGER INFO, N
! 14: DOUBLE PRECISION RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: INTEGER IWORK( * )
! 18: DOUBLE PRECISION AP( * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * DTPCON estimates the reciprocal of the condition number of a packed
! 25: * triangular matrix A, in either the 1-norm or the infinity-norm.
! 26: *
! 27: * The norm of A is computed and an estimate is obtained for
! 28: * norm(inv(A)), then the reciprocal of the condition number is
! 29: * computed as
! 30: * RCOND = 1 / ( norm(A) * norm(inv(A)) ).
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * NORM (input) CHARACTER*1
! 36: * Specifies whether the 1-norm condition number or the
! 37: * infinity-norm condition number is required:
! 38: * = '1' or 'O': 1-norm;
! 39: * = 'I': Infinity-norm.
! 40: *
! 41: * UPLO (input) CHARACTER*1
! 42: * = 'U': A is upper triangular;
! 43: * = 'L': A is lower triangular.
! 44: *
! 45: * DIAG (input) CHARACTER*1
! 46: * = 'N': A is non-unit triangular;
! 47: * = 'U': A is unit triangular.
! 48: *
! 49: * N (input) INTEGER
! 50: * The order of the matrix A. N >= 0.
! 51: *
! 52: * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 53: * The upper or lower triangular matrix A, packed columnwise in
! 54: * a linear array. The j-th column of A is stored in the array
! 55: * AP as follows:
! 56: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 57: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 58: * If DIAG = 'U', the diagonal elements of A are not referenced
! 59: * and are assumed to be 1.
! 60: *
! 61: * RCOND (output) DOUBLE PRECISION
! 62: * The reciprocal of the condition number of the matrix A,
! 63: * computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 64: *
! 65: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
! 66: *
! 67: * IWORK (workspace) INTEGER array, dimension (N)
! 68: *
! 69: * INFO (output) INTEGER
! 70: * = 0: successful exit
! 71: * < 0: if INFO = -i, the i-th argument had an illegal value
! 72: *
! 73: * =====================================================================
! 74: *
! 75: * .. Parameters ..
! 76: DOUBLE PRECISION ONE, ZERO
! 77: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 78: * ..
! 79: * .. Local Scalars ..
! 80: LOGICAL NOUNIT, ONENRM, UPPER
! 81: CHARACTER NORMIN
! 82: INTEGER IX, KASE, KASE1
! 83: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
! 84: * ..
! 85: * .. Local Arrays ..
! 86: INTEGER ISAVE( 3 )
! 87: * ..
! 88: * .. External Functions ..
! 89: LOGICAL LSAME
! 90: INTEGER IDAMAX
! 91: DOUBLE PRECISION DLAMCH, DLANTP
! 92: EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTP
! 93: * ..
! 94: * .. External Subroutines ..
! 95: EXTERNAL DLACN2, DLATPS, DRSCL, XERBLA
! 96: * ..
! 97: * .. Intrinsic Functions ..
! 98: INTRINSIC ABS, DBLE, MAX
! 99: * ..
! 100: * .. Executable Statements ..
! 101: *
! 102: * Test the input parameters.
! 103: *
! 104: INFO = 0
! 105: UPPER = LSAME( UPLO, 'U' )
! 106: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
! 107: NOUNIT = LSAME( DIAG, 'N' )
! 108: *
! 109: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
! 110: INFO = -1
! 111: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 112: INFO = -2
! 113: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
! 114: INFO = -3
! 115: ELSE IF( N.LT.0 ) THEN
! 116: INFO = -4
! 117: END IF
! 118: IF( INFO.NE.0 ) THEN
! 119: CALL XERBLA( 'DTPCON', -INFO )
! 120: RETURN
! 121: END IF
! 122: *
! 123: * Quick return if possible
! 124: *
! 125: IF( N.EQ.0 ) THEN
! 126: RCOND = ONE
! 127: RETURN
! 128: END IF
! 129: *
! 130: RCOND = ZERO
! 131: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
! 132: *
! 133: * Compute the norm of the triangular matrix A.
! 134: *
! 135: ANORM = DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
! 136: *
! 137: * Continue only if ANORM > 0.
! 138: *
! 139: IF( ANORM.GT.ZERO ) THEN
! 140: *
! 141: * Estimate the norm of the inverse of A.
! 142: *
! 143: AINVNM = ZERO
! 144: NORMIN = 'N'
! 145: IF( ONENRM ) THEN
! 146: KASE1 = 1
! 147: ELSE
! 148: KASE1 = 2
! 149: END IF
! 150: KASE = 0
! 151: 10 CONTINUE
! 152: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 153: IF( KASE.NE.0 ) THEN
! 154: IF( KASE.EQ.KASE1 ) THEN
! 155: *
! 156: * Multiply by inv(A).
! 157: *
! 158: CALL DLATPS( UPLO, 'No transpose', DIAG, NORMIN, N, AP,
! 159: $ WORK, SCALE, WORK( 2*N+1 ), INFO )
! 160: ELSE
! 161: *
! 162: * Multiply by inv(A').
! 163: *
! 164: CALL DLATPS( UPLO, 'Transpose', DIAG, NORMIN, N, AP,
! 165: $ WORK, SCALE, WORK( 2*N+1 ), INFO )
! 166: END IF
! 167: NORMIN = 'Y'
! 168: *
! 169: * Multiply by 1/SCALE if doing so will not cause overflow.
! 170: *
! 171: IF( SCALE.NE.ONE ) THEN
! 172: IX = IDAMAX( N, WORK, 1 )
! 173: XNORM = ABS( WORK( IX ) )
! 174: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
! 175: $ GO TO 20
! 176: CALL DRSCL( N, SCALE, WORK, 1 )
! 177: END IF
! 178: GO TO 10
! 179: END IF
! 180: *
! 181: * Compute the estimate of the reciprocal condition number.
! 182: *
! 183: IF( AINVNM.NE.ZERO )
! 184: $ RCOND = ( ONE / ANORM ) / AINVNM
! 185: END IF
! 186: *
! 187: 20 CONTINUE
! 188: RETURN
! 189: *
! 190: * End of DTPCON
! 191: *
! 192: END
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