Annotation of rpl/lapack/lapack/zpocon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK,
! 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 ZLACN2 in place of ZLACON, 10 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: DOUBLE PRECISION RWORK( * )
! 18: COMPLEX*16 A( LDA, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * ZPOCON estimates the reciprocal of the condition number (in the
! 25: * 1-norm) of a complex Hermitian positive definite matrix using the
! 26: * Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
! 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) COMPLEX*16 array, dimension (LDA,N)
! 42: * The triangular factor U or L from the Cholesky factorization
! 43: * A = U**H*U or A = L*L**H, as computed by ZPOTRF.
! 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 Hermitian 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) COMPLEX*16 array, dimension (2*N)
! 57: *
! 58: * RWORK (workspace) DOUBLE PRECISION 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: COMPLEX*16 ZDUM
! 76: * ..
! 77: * .. Local Arrays ..
! 78: INTEGER ISAVE( 3 )
! 79: * ..
! 80: * .. External Functions ..
! 81: LOGICAL LSAME
! 82: INTEGER IZAMAX
! 83: DOUBLE PRECISION DLAMCH
! 84: EXTERNAL LSAME, IZAMAX, DLAMCH
! 85: * ..
! 86: * .. External Subroutines ..
! 87: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATRS
! 88: * ..
! 89: * .. Intrinsic Functions ..
! 90: INTRINSIC ABS, DBLE, DIMAG, MAX
! 91: * ..
! 92: * .. Statement Functions ..
! 93: DOUBLE PRECISION CABS1
! 94: * ..
! 95: * .. Statement Function definitions ..
! 96: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 97: * ..
! 98: * .. Executable Statements ..
! 99: *
! 100: * Test the input parameters.
! 101: *
! 102: INFO = 0
! 103: UPPER = LSAME( UPLO, 'U' )
! 104: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 105: INFO = -1
! 106: ELSE IF( N.LT.0 ) THEN
! 107: INFO = -2
! 108: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 109: INFO = -4
! 110: ELSE IF( ANORM.LT.ZERO ) THEN
! 111: INFO = -5
! 112: END IF
! 113: IF( INFO.NE.0 ) THEN
! 114: CALL XERBLA( 'ZPOCON', -INFO )
! 115: RETURN
! 116: END IF
! 117: *
! 118: * Quick return if possible
! 119: *
! 120: RCOND = ZERO
! 121: IF( N.EQ.0 ) THEN
! 122: RCOND = ONE
! 123: RETURN
! 124: ELSE IF( ANORM.EQ.ZERO ) THEN
! 125: RETURN
! 126: END IF
! 127: *
! 128: SMLNUM = DLAMCH( 'Safe minimum' )
! 129: *
! 130: * Estimate the 1-norm of inv(A).
! 131: *
! 132: KASE = 0
! 133: NORMIN = 'N'
! 134: 10 CONTINUE
! 135: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 136: IF( KASE.NE.0 ) THEN
! 137: IF( UPPER ) THEN
! 138: *
! 139: * Multiply by inv(U').
! 140: *
! 141: CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
! 142: $ NORMIN, N, A, LDA, WORK, SCALEL, RWORK, INFO )
! 143: NORMIN = 'Y'
! 144: *
! 145: * Multiply by inv(U).
! 146: *
! 147: CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
! 148: $ A, LDA, WORK, SCALEU, RWORK, INFO )
! 149: ELSE
! 150: *
! 151: * Multiply by inv(L).
! 152: *
! 153: CALL ZLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
! 154: $ A, LDA, WORK, SCALEL, RWORK, INFO )
! 155: NORMIN = 'Y'
! 156: *
! 157: * Multiply by inv(L').
! 158: *
! 159: CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Non-unit',
! 160: $ NORMIN, N, A, LDA, WORK, SCALEU, RWORK, INFO )
! 161: END IF
! 162: *
! 163: * Multiply by 1/SCALE if doing so will not cause overflow.
! 164: *
! 165: SCALE = SCALEL*SCALEU
! 166: IF( SCALE.NE.ONE ) THEN
! 167: IX = IZAMAX( N, WORK, 1 )
! 168: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
! 169: $ GO TO 20
! 170: CALL ZDRSCL( N, SCALE, WORK, 1 )
! 171: END IF
! 172: GO TO 10
! 173: END IF
! 174: *
! 175: * Compute the estimate of the reciprocal condition number.
! 176: *
! 177: IF( AINVNM.NE.ZERO )
! 178: $ RCOND = ( ONE / AINVNM ) / ANORM
! 179: *
! 180: 20 CONTINUE
! 181: RETURN
! 182: *
! 183: * End of ZPOCON
! 184: *
! 185: END
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