Annotation of rpl/lapack/lapack/ztbcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
! 2: $ RWORK, 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 ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER DIAG, NORM, UPLO
! 13: INTEGER INFO, KD, LDAB, N
! 14: DOUBLE PRECISION RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: DOUBLE PRECISION RWORK( * )
! 18: COMPLEX*16 AB( LDAB, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * ZTBCON estimates the reciprocal of the condition number of a
! 25: * triangular band 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: * KD (input) INTEGER
! 53: * The number of superdiagonals or subdiagonals of the
! 54: * triangular band matrix A. KD >= 0.
! 55: *
! 56: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
! 57: * The upper or lower triangular band matrix A, stored in the
! 58: * first kd+1 rows of the array. The j-th column of A is stored
! 59: * in the j-th column of the array AB as follows:
! 60: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 61: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 62: * If DIAG = 'U', the diagonal elements of A are not referenced
! 63: * and are assumed to be 1.
! 64: *
! 65: * LDAB (input) INTEGER
! 66: * The leading dimension of the array AB. LDAB >= KD+1.
! 67: *
! 68: * RCOND (output) DOUBLE PRECISION
! 69: * The reciprocal of the condition number of the matrix A,
! 70: * computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 71: *
! 72: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 73: *
! 74: * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
! 75: *
! 76: * INFO (output) INTEGER
! 77: * = 0: successful exit
! 78: * < 0: if INFO = -i, the i-th argument had an illegal value
! 79: *
! 80: * =====================================================================
! 81: *
! 82: * .. Parameters ..
! 83: DOUBLE PRECISION ONE, ZERO
! 84: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 85: * ..
! 86: * .. Local Scalars ..
! 87: LOGICAL NOUNIT, ONENRM, UPPER
! 88: CHARACTER NORMIN
! 89: INTEGER IX, KASE, KASE1
! 90: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
! 91: COMPLEX*16 ZDUM
! 92: * ..
! 93: * .. Local Arrays ..
! 94: INTEGER ISAVE( 3 )
! 95: * ..
! 96: * .. External Functions ..
! 97: LOGICAL LSAME
! 98: INTEGER IZAMAX
! 99: DOUBLE PRECISION DLAMCH, ZLANTB
! 100: EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTB
! 101: * ..
! 102: * .. External Subroutines ..
! 103: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS
! 104: * ..
! 105: * .. Intrinsic Functions ..
! 106: INTRINSIC ABS, DBLE, DIMAG, MAX
! 107: * ..
! 108: * .. Statement Functions ..
! 109: DOUBLE PRECISION CABS1
! 110: * ..
! 111: * .. Statement Function definitions ..
! 112: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 113: * ..
! 114: * .. Executable Statements ..
! 115: *
! 116: * Test the input parameters.
! 117: *
! 118: INFO = 0
! 119: UPPER = LSAME( UPLO, 'U' )
! 120: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
! 121: NOUNIT = LSAME( DIAG, 'N' )
! 122: *
! 123: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
! 124: INFO = -1
! 125: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 126: INFO = -2
! 127: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
! 128: INFO = -3
! 129: ELSE IF( N.LT.0 ) THEN
! 130: INFO = -4
! 131: ELSE IF( KD.LT.0 ) THEN
! 132: INFO = -5
! 133: ELSE IF( LDAB.LT.KD+1 ) THEN
! 134: INFO = -7
! 135: END IF
! 136: IF( INFO.NE.0 ) THEN
! 137: CALL XERBLA( 'ZTBCON', -INFO )
! 138: RETURN
! 139: END IF
! 140: *
! 141: * Quick return if possible
! 142: *
! 143: IF( N.EQ.0 ) THEN
! 144: RCOND = ONE
! 145: RETURN
! 146: END IF
! 147: *
! 148: RCOND = ZERO
! 149: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( N, 1 ) )
! 150: *
! 151: * Compute the 1-norm of the triangular matrix A or A'.
! 152: *
! 153: ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK )
! 154: *
! 155: * Continue only if ANORM > 0.
! 156: *
! 157: IF( ANORM.GT.ZERO ) THEN
! 158: *
! 159: * Estimate the 1-norm of the inverse of A.
! 160: *
! 161: AINVNM = ZERO
! 162: NORMIN = 'N'
! 163: IF( ONENRM ) THEN
! 164: KASE1 = 1
! 165: ELSE
! 166: KASE1 = 2
! 167: END IF
! 168: KASE = 0
! 169: 10 CONTINUE
! 170: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 171: IF( KASE.NE.0 ) THEN
! 172: IF( KASE.EQ.KASE1 ) THEN
! 173: *
! 174: * Multiply by inv(A).
! 175: *
! 176: CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
! 177: $ AB, LDAB, WORK, SCALE, RWORK, INFO )
! 178: ELSE
! 179: *
! 180: * Multiply by inv(A').
! 181: *
! 182: CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
! 183: $ N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO )
! 184: END IF
! 185: NORMIN = 'Y'
! 186: *
! 187: * Multiply by 1/SCALE if doing so will not cause overflow.
! 188: *
! 189: IF( SCALE.NE.ONE ) THEN
! 190: IX = IZAMAX( N, WORK, 1 )
! 191: XNORM = CABS1( WORK( IX ) )
! 192: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
! 193: $ GO TO 20
! 194: CALL ZDRSCL( N, SCALE, WORK, 1 )
! 195: END IF
! 196: GO TO 10
! 197: END IF
! 198: *
! 199: * Compute the estimate of the reciprocal condition number.
! 200: *
! 201: IF( AINVNM.NE.ZERO )
! 202: $ RCOND = ( ONE / ANORM ) / AINVNM
! 203: END IF
! 204: *
! 205: 20 CONTINUE
! 206: RETURN
! 207: *
! 208: * End of ZTBCON
! 209: *
! 210: END
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