Annotation of rpl/lapack/lapack/zhpcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
! 9: *
! 10: * .. Scalar Arguments ..
! 11: CHARACTER UPLO
! 12: INTEGER INFO, N
! 13: DOUBLE PRECISION ANORM, RCOND
! 14: * ..
! 15: * .. Array Arguments ..
! 16: INTEGER IPIV( * )
! 17: COMPLEX*16 AP( * ), WORK( * )
! 18: * ..
! 19: *
! 20: * Purpose
! 21: * =======
! 22: *
! 23: * ZHPCON estimates the reciprocal of the condition number of a complex
! 24: * Hermitian packed matrix A using the factorization A = U*D*U**H or
! 25: * A = L*D*L**H computed by ZHPTRF.
! 26: *
! 27: * An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 28: * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
! 29: *
! 30: * Arguments
! 31: * =========
! 32: *
! 33: * UPLO (input) CHARACTER*1
! 34: * Specifies whether the details of the factorization are stored
! 35: * as an upper or lower triangular matrix.
! 36: * = 'U': Upper triangular, form is A = U*D*U**H;
! 37: * = 'L': Lower triangular, form is A = L*D*L**H.
! 38: *
! 39: * N (input) INTEGER
! 40: * The order of the matrix A. N >= 0.
! 41: *
! 42: * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
! 43: * The block diagonal matrix D and the multipliers used to
! 44: * obtain the factor U or L as computed by ZHPTRF, stored as a
! 45: * packed triangular matrix.
! 46: *
! 47: * IPIV (input) INTEGER array, dimension (N)
! 48: * Details of the interchanges and the block structure of D
! 49: * as determined by ZHPTRF.
! 50: *
! 51: * ANORM (input) DOUBLE PRECISION
! 52: * The 1-norm of the original matrix A.
! 53: *
! 54: * RCOND (output) DOUBLE PRECISION
! 55: * The reciprocal of the condition number of the matrix A,
! 56: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 57: * estimate of the 1-norm of inv(A) computed in this routine.
! 58: *
! 59: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 60: *
! 61: * INFO (output) INTEGER
! 62: * = 0: successful exit
! 63: * < 0: if INFO = -i, the i-th argument had an illegal value
! 64: *
! 65: * =====================================================================
! 66: *
! 67: * .. Parameters ..
! 68: DOUBLE PRECISION ONE, ZERO
! 69: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 70: * ..
! 71: * .. Local Scalars ..
! 72: LOGICAL UPPER
! 73: INTEGER I, IP, KASE
! 74: DOUBLE PRECISION AINVNM
! 75: * ..
! 76: * .. Local Arrays ..
! 77: INTEGER ISAVE( 3 )
! 78: * ..
! 79: * .. External Functions ..
! 80: LOGICAL LSAME
! 81: EXTERNAL LSAME
! 82: * ..
! 83: * .. External Subroutines ..
! 84: EXTERNAL XERBLA, ZHPTRS, ZLACN2
! 85: * ..
! 86: * .. Executable Statements ..
! 87: *
! 88: * Test the input parameters.
! 89: *
! 90: INFO = 0
! 91: UPPER = LSAME( UPLO, 'U' )
! 92: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 93: INFO = -1
! 94: ELSE IF( N.LT.0 ) THEN
! 95: INFO = -2
! 96: ELSE IF( ANORM.LT.ZERO ) THEN
! 97: INFO = -5
! 98: END IF
! 99: IF( INFO.NE.0 ) THEN
! 100: CALL XERBLA( 'ZHPCON', -INFO )
! 101: RETURN
! 102: END IF
! 103: *
! 104: * Quick return if possible
! 105: *
! 106: RCOND = ZERO
! 107: IF( N.EQ.0 ) THEN
! 108: RCOND = ONE
! 109: RETURN
! 110: ELSE IF( ANORM.LE.ZERO ) THEN
! 111: RETURN
! 112: END IF
! 113: *
! 114: * Check that the diagonal matrix D is nonsingular.
! 115: *
! 116: IF( UPPER ) THEN
! 117: *
! 118: * Upper triangular storage: examine D from bottom to top
! 119: *
! 120: IP = N*( N+1 ) / 2
! 121: DO 10 I = N, 1, -1
! 122: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
! 123: $ RETURN
! 124: IP = IP - I
! 125: 10 CONTINUE
! 126: ELSE
! 127: *
! 128: * Lower triangular storage: examine D from top to bottom.
! 129: *
! 130: IP = 1
! 131: DO 20 I = 1, N
! 132: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
! 133: $ RETURN
! 134: IP = IP + N - I + 1
! 135: 20 CONTINUE
! 136: END IF
! 137: *
! 138: * Estimate the 1-norm of the inverse.
! 139: *
! 140: KASE = 0
! 141: 30 CONTINUE
! 142: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
! 143: IF( KASE.NE.0 ) THEN
! 144: *
! 145: * Multiply by inv(L*D*L') or inv(U*D*U').
! 146: *
! 147: CALL ZHPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
! 148: GO TO 30
! 149: END IF
! 150: *
! 151: * Compute the estimate of the reciprocal condition number.
! 152: *
! 153: IF( AINVNM.NE.ZERO )
! 154: $ RCOND = ( ONE / AINVNM ) / ANORM
! 155: *
! 156: RETURN
! 157: *
! 158: * End of ZHPCON
! 159: *
! 160: END
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