Annotation of rpl/lapack/lapack/dspcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
! 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 DLACN2 in place of DLACON, 5 Feb 03, SJH.
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER UPLO
! 13: INTEGER INFO, N
! 14: DOUBLE PRECISION ANORM, RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: INTEGER IPIV( * ), IWORK( * )
! 18: DOUBLE PRECISION AP( * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * DSPCON estimates the reciprocal of the condition number (in the
! 25: * 1-norm) of a real symmetric packed matrix A using the factorization
! 26: * A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
! 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: * Specifies whether the details of the factorization are stored
! 36: * as an upper or lower triangular matrix.
! 37: * = 'U': Upper triangular, form is A = U*D*U**T;
! 38: * = 'L': Lower triangular, form is A = L*D*L**T.
! 39: *
! 40: * N (input) INTEGER
! 41: * The order of the matrix A. N >= 0.
! 42: *
! 43: * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 44: * The block diagonal matrix D and the multipliers used to
! 45: * obtain the factor U or L as computed by DSPTRF, stored as a
! 46: * packed triangular matrix.
! 47: *
! 48: * IPIV (input) INTEGER array, dimension (N)
! 49: * Details of the interchanges and the block structure of D
! 50: * as determined by DSPTRF.
! 51: *
! 52: * ANORM (input) DOUBLE PRECISION
! 53: * The 1-norm of the original matrix A.
! 54: *
! 55: * RCOND (output) DOUBLE PRECISION
! 56: * The reciprocal of the condition number of the matrix A,
! 57: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 58: * estimate of the 1-norm of inv(A) computed in this routine.
! 59: *
! 60: * WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
! 61: *
! 62: * IWORK (workspace) INTEGER array, dimension (N)
! 63: *
! 64: * INFO (output) INTEGER
! 65: * = 0: successful exit
! 66: * < 0: if INFO = -i, the i-th argument had an illegal value
! 67: *
! 68: * =====================================================================
! 69: *
! 70: * .. Parameters ..
! 71: DOUBLE PRECISION ONE, ZERO
! 72: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 73: * ..
! 74: * .. Local Scalars ..
! 75: LOGICAL UPPER
! 76: INTEGER I, IP, KASE
! 77: DOUBLE PRECISION AINVNM
! 78: * ..
! 79: * .. Local Arrays ..
! 80: INTEGER ISAVE( 3 )
! 81: * ..
! 82: * .. External Functions ..
! 83: LOGICAL LSAME
! 84: EXTERNAL LSAME
! 85: * ..
! 86: * .. External Subroutines ..
! 87: EXTERNAL DLACN2, DSPTRS, XERBLA
! 88: * ..
! 89: * .. Executable Statements ..
! 90: *
! 91: * Test the input parameters.
! 92: *
! 93: INFO = 0
! 94: UPPER = LSAME( UPLO, 'U' )
! 95: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 96: INFO = -1
! 97: ELSE IF( N.LT.0 ) THEN
! 98: INFO = -2
! 99: ELSE IF( ANORM.LT.ZERO ) THEN
! 100: INFO = -5
! 101: END IF
! 102: IF( INFO.NE.0 ) THEN
! 103: CALL XERBLA( 'DSPCON', -INFO )
! 104: RETURN
! 105: END IF
! 106: *
! 107: * Quick return if possible
! 108: *
! 109: RCOND = ZERO
! 110: IF( N.EQ.0 ) THEN
! 111: RCOND = ONE
! 112: RETURN
! 113: ELSE IF( ANORM.LE.ZERO ) THEN
! 114: RETURN
! 115: END IF
! 116: *
! 117: * Check that the diagonal matrix D is nonsingular.
! 118: *
! 119: IF( UPPER ) THEN
! 120: *
! 121: * Upper triangular storage: examine D from bottom to top
! 122: *
! 123: IP = N*( N+1 ) / 2
! 124: DO 10 I = N, 1, -1
! 125: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
! 126: $ RETURN
! 127: IP = IP - I
! 128: 10 CONTINUE
! 129: ELSE
! 130: *
! 131: * Lower triangular storage: examine D from top to bottom.
! 132: *
! 133: IP = 1
! 134: DO 20 I = 1, N
! 135: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
! 136: $ RETURN
! 137: IP = IP + N - I + 1
! 138: 20 CONTINUE
! 139: END IF
! 140: *
! 141: * Estimate the 1-norm of the inverse.
! 142: *
! 143: KASE = 0
! 144: 30 CONTINUE
! 145: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 146: IF( KASE.NE.0 ) THEN
! 147: *
! 148: * Multiply by inv(L*D*L') or inv(U*D*U').
! 149: *
! 150: CALL DSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
! 151: GO TO 30
! 152: END IF
! 153: *
! 154: * Compute the estimate of the reciprocal condition number.
! 155: *
! 156: IF( AINVNM.NE.ZERO )
! 157: $ RCOND = ( ONE / AINVNM ) / ANORM
! 158: *
! 159: RETURN
! 160: *
! 161: * End of DSPCON
! 162: *
! 163: END
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