Annotation of rpl/lapack/lapack/ztrcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, 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, LDA, N
! 14: DOUBLE PRECISION RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: DOUBLE PRECISION RWORK( * )
! 18: COMPLEX*16 A( LDA, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * ZTRCON estimates the reciprocal of the condition number of a
! 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: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 53: * The triangular matrix A. If UPLO = 'U', the leading N-by-N
! 54: * upper triangular part of the array A contains the upper
! 55: * triangular matrix, and the strictly lower triangular part of
! 56: * A is not referenced. If UPLO = 'L', the leading N-by-N lower
! 57: * triangular part of the array A contains the lower triangular
! 58: * matrix, and the strictly upper triangular part of A is not
! 59: * referenced. If DIAG = 'U', the diagonal elements of A are
! 60: * also not referenced and are assumed to be 1.
! 61: *
! 62: * LDA (input) INTEGER
! 63: * The leading dimension of the array A. LDA >= max(1,N).
! 64: *
! 65: * RCOND (output) DOUBLE PRECISION
! 66: * The reciprocal of the condition number of the matrix A,
! 67: * computed as RCOND = 1/(norm(A) * norm(inv(A))).
! 68: *
! 69: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 70: *
! 71: * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
! 72: *
! 73: * INFO (output) INTEGER
! 74: * = 0: successful exit
! 75: * < 0: if INFO = -i, the i-th argument had an illegal value
! 76: *
! 77: * =====================================================================
! 78: *
! 79: * .. Parameters ..
! 80: DOUBLE PRECISION ONE, ZERO
! 81: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 82: * ..
! 83: * .. Local Scalars ..
! 84: LOGICAL NOUNIT, ONENRM, UPPER
! 85: CHARACTER NORMIN
! 86: INTEGER IX, KASE, KASE1
! 87: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
! 88: COMPLEX*16 ZDUM
! 89: * ..
! 90: * .. Local Arrays ..
! 91: INTEGER ISAVE( 3 )
! 92: * ..
! 93: * .. External Functions ..
! 94: LOGICAL LSAME
! 95: INTEGER IZAMAX
! 96: DOUBLE PRECISION DLAMCH, ZLANTR
! 97: EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTR
! 98: * ..
! 99: * .. External Subroutines ..
! 100: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATRS
! 101: * ..
! 102: * .. Intrinsic Functions ..
! 103: INTRINSIC ABS, DBLE, DIMAG, MAX
! 104: * ..
! 105: * .. Statement Functions ..
! 106: DOUBLE PRECISION CABS1
! 107: * ..
! 108: * .. Statement Function definitions ..
! 109: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 110: * ..
! 111: * .. Executable Statements ..
! 112: *
! 113: * Test the input parameters.
! 114: *
! 115: INFO = 0
! 116: UPPER = LSAME( UPLO, 'U' )
! 117: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
! 118: NOUNIT = LSAME( DIAG, 'N' )
! 119: *
! 120: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
! 121: INFO = -1
! 122: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 123: INFO = -2
! 124: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
! 125: INFO = -3
! 126: ELSE IF( N.LT.0 ) THEN
! 127: INFO = -4
! 128: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 129: INFO = -6
! 130: END IF
! 131: IF( INFO.NE.0 ) THEN
! 132: CALL XERBLA( 'ZTRCON', -INFO )
! 133: RETURN
! 134: END IF
! 135: *
! 136: * Quick return if possible
! 137: *
! 138: IF( N.EQ.0 ) THEN
! 139: RCOND = ONE
! 140: RETURN
! 141: END IF
! 142: *
! 143: RCOND = ZERO
! 144: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
! 145: *
! 146: * Compute the norm of the triangular matrix A.
! 147: *
! 148: ANORM = ZLANTR( NORM, UPLO, DIAG, N, N, A, LDA, RWORK )
! 149: *
! 150: * Continue only if ANORM > 0.
! 151: *
! 152: IF( ANORM.GT.ZERO ) THEN
! 153: *
! 154: * Estimate the norm of the inverse of A.
! 155: *
! 156: AINVNM = ZERO
! 157: NORMIN = 'N'
! 158: IF( ONENRM ) THEN
! 159: KASE1 = 1
! 160: ELSE
! 161: KASE1 = 2
! 162: END IF
! 163: KASE = 0
! 164: 10 CONTINUE
! 165: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 166: IF( KASE.NE.0 ) THEN
! 167: IF( KASE.EQ.KASE1 ) THEN
! 168: *
! 169: * Multiply by inv(A).
! 170: *
! 171: CALL ZLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
! 172: $ LDA, WORK, SCALE, RWORK, INFO )
! 173: ELSE
! 174: *
! 175: * Multiply by inv(A').
! 176: *
! 177: CALL ZLATRS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
! 178: $ N, A, LDA, WORK, SCALE, RWORK, INFO )
! 179: END IF
! 180: NORMIN = 'Y'
! 181: *
! 182: * Multiply by 1/SCALE if doing so will not cause overflow.
! 183: *
! 184: IF( SCALE.NE.ONE ) THEN
! 185: IX = IZAMAX( N, WORK, 1 )
! 186: XNORM = CABS1( WORK( IX ) )
! 187: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
! 188: $ GO TO 20
! 189: CALL ZDRSCL( N, SCALE, WORK, 1 )
! 190: END IF
! 191: GO TO 10
! 192: END IF
! 193: *
! 194: * Compute the estimate of the reciprocal condition number.
! 195: *
! 196: IF( AINVNM.NE.ZERO )
! 197: $ RCOND = ( ONE / ANORM ) / AINVNM
! 198: END IF
! 199: *
! 200: 20 CONTINUE
! 201: RETURN
! 202: *
! 203: * End of ZTRCON
! 204: *
! 205: END
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