Annotation of rpl/lapack/lapack/zpbcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, 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 UPLO
! 13: INTEGER INFO, KD, LDAB, N
! 14: DOUBLE PRECISION ANORM, RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: DOUBLE PRECISION RWORK( * )
! 18: COMPLEX*16 AB( LDAB, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * ZPBCON estimates the reciprocal of the condition number (in the
! 25: * 1-norm) of a complex Hermitian positive definite band matrix using
! 26: * the Cholesky factorization A = U**H*U or A = L*L**H computed by
! 27: * ZPBTRF.
! 28: *
! 29: * An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 30: * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * UPLO (input) CHARACTER*1
! 36: * = 'U': Upper triangular factor stored in AB;
! 37: * = 'L': Lower triangular factor stored in AB.
! 38: *
! 39: * N (input) INTEGER
! 40: * The order of the matrix A. N >= 0.
! 41: *
! 42: * KD (input) INTEGER
! 43: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 44: * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
! 45: *
! 46: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
! 47: * The triangular factor U or L from the Cholesky factorization
! 48: * A = U**H*U or A = L*L**H of the band matrix A, stored in the
! 49: * first KD+1 rows of the array. The j-th column of U or L is
! 50: * stored in the j-th column of the array AB as follows:
! 51: * if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
! 52: * if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
! 53: *
! 54: * LDAB (input) INTEGER
! 55: * The leading dimension of the array AB. LDAB >= KD+1.
! 56: *
! 57: * ANORM (input) DOUBLE PRECISION
! 58: * The 1-norm (or infinity-norm) of the Hermitian band matrix A.
! 59: *
! 60: * RCOND (output) DOUBLE PRECISION
! 61: * The reciprocal of the condition number of the matrix A,
! 62: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 63: * estimate of the 1-norm of inv(A) computed in this routine.
! 64: *
! 65: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 66: *
! 67: * RWORK (workspace) DOUBLE PRECISION 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 UPPER
! 81: CHARACTER NORMIN
! 82: INTEGER IX, KASE
! 83: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
! 84: COMPLEX*16 ZDUM
! 85: * ..
! 86: * .. Local Arrays ..
! 87: INTEGER ISAVE( 3 )
! 88: * ..
! 89: * .. External Functions ..
! 90: LOGICAL LSAME
! 91: INTEGER IZAMAX
! 92: DOUBLE PRECISION DLAMCH
! 93: EXTERNAL LSAME, IZAMAX, DLAMCH
! 94: * ..
! 95: * .. External Subroutines ..
! 96: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS
! 97: * ..
! 98: * .. Intrinsic Functions ..
! 99: INTRINSIC ABS, DBLE, DIMAG
! 100: * ..
! 101: * .. Statement Functions ..
! 102: DOUBLE PRECISION CABS1
! 103: * ..
! 104: * .. Statement Function definitions ..
! 105: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 106: * ..
! 107: * .. Executable Statements ..
! 108: *
! 109: * Test the input parameters.
! 110: *
! 111: INFO = 0
! 112: UPPER = LSAME( UPLO, 'U' )
! 113: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 114: INFO = -1
! 115: ELSE IF( N.LT.0 ) THEN
! 116: INFO = -2
! 117: ELSE IF( KD.LT.0 ) THEN
! 118: INFO = -3
! 119: ELSE IF( LDAB.LT.KD+1 ) THEN
! 120: INFO = -5
! 121: ELSE IF( ANORM.LT.ZERO ) THEN
! 122: INFO = -6
! 123: END IF
! 124: IF( INFO.NE.0 ) THEN
! 125: CALL XERBLA( 'ZPBCON', -INFO )
! 126: RETURN
! 127: END IF
! 128: *
! 129: * Quick return if possible
! 130: *
! 131: RCOND = ZERO
! 132: IF( N.EQ.0 ) THEN
! 133: RCOND = ONE
! 134: RETURN
! 135: ELSE IF( ANORM.EQ.ZERO ) THEN
! 136: RETURN
! 137: END IF
! 138: *
! 139: SMLNUM = DLAMCH( 'Safe minimum' )
! 140: *
! 141: * Estimate the 1-norm of the inverse.
! 142: *
! 143: KASE = 0
! 144: NORMIN = 'N'
! 145: 10 CONTINUE
! 146: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 147: IF( KASE.NE.0 ) THEN
! 148: IF( UPPER ) THEN
! 149: *
! 150: * Multiply by inv(U').
! 151: *
! 152: CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
! 153: $ NORMIN, N, KD, AB, LDAB, WORK, SCALEL, RWORK,
! 154: $ INFO )
! 155: NORMIN = 'Y'
! 156: *
! 157: * Multiply by inv(U).
! 158: *
! 159: CALL ZLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
! 160: $ KD, AB, LDAB, WORK, SCALEU, RWORK, INFO )
! 161: ELSE
! 162: *
! 163: * Multiply by inv(L).
! 164: *
! 165: CALL ZLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
! 166: $ KD, AB, LDAB, WORK, SCALEL, RWORK, INFO )
! 167: NORMIN = 'Y'
! 168: *
! 169: * Multiply by inv(L').
! 170: *
! 171: CALL ZLATBS( 'Lower', 'Conjugate transpose', 'Non-unit',
! 172: $ NORMIN, N, KD, AB, LDAB, WORK, SCALEU, RWORK,
! 173: $ INFO )
! 174: END IF
! 175: *
! 176: * Multiply by 1/SCALE if doing so will not cause overflow.
! 177: *
! 178: SCALE = SCALEL*SCALEU
! 179: IF( SCALE.NE.ONE ) THEN
! 180: IX = IZAMAX( N, WORK, 1 )
! 181: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
! 182: $ GO TO 20
! 183: CALL ZDRSCL( N, SCALE, WORK, 1 )
! 184: END IF
! 185: GO TO 10
! 186: END IF
! 187: *
! 188: * Compute the estimate of the reciprocal condition number.
! 189: *
! 190: IF( AINVNM.NE.ZERO )
! 191: $ RCOND = ( ONE / AINVNM ) / ANORM
! 192: *
! 193: 20 CONTINUE
! 194: *
! 195: RETURN
! 196: *
! 197: * End of ZPBCON
! 198: *
! 199: END
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