LAPACK 3.3.1
Linear Algebra PACKage

stpcon.f

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00001       SUBROUTINE STPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK,
00002      $                   INFO )
00003 *
00004 *  -- LAPACK routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH.
00010 *
00011 *     .. Scalar Arguments ..
00012       CHARACTER          DIAG, NORM, UPLO
00013       INTEGER            INFO, N
00014       REAL               RCOND
00015 *     ..
00016 *     .. Array Arguments ..
00017       INTEGER            IWORK( * )
00018       REAL               AP( * ), WORK( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *  STPCON estimates the reciprocal of the condition number of a packed
00025 *  triangular matrix A, in either the 1-norm or the infinity-norm.
00026 *
00027 *  The norm of A is computed and an estimate is obtained for
00028 *  norm(inv(A)), then the reciprocal of the condition number is
00029 *  computed as
00030 *     RCOND = 1 / ( norm(A) * norm(inv(A)) ).
00031 *
00032 *  Arguments
00033 *  =========
00034 *
00035 *  NORM    (input) CHARACTER*1
00036 *          Specifies whether the 1-norm condition number or the
00037 *          infinity-norm condition number is required:
00038 *          = '1' or 'O':  1-norm;
00039 *          = 'I':         Infinity-norm.
00040 *
00041 *  UPLO    (input) CHARACTER*1
00042 *          = 'U':  A is upper triangular;
00043 *          = 'L':  A is lower triangular.
00044 *
00045 *  DIAG    (input) CHARACTER*1
00046 *          = 'N':  A is non-unit triangular;
00047 *          = 'U':  A is unit triangular.
00048 *
00049 *  N       (input) INTEGER
00050 *          The order of the matrix A.  N >= 0.
00051 *
00052 *  AP      (input) REAL array, dimension (N*(N+1)/2)
00053 *          The upper or lower triangular matrix A, packed columnwise in
00054 *          a linear array.  The j-th column of A is stored in the array
00055 *          AP as follows:
00056 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00057 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00058 *          If DIAG = 'U', the diagonal elements of A are not referenced
00059 *          and are assumed to be 1.
00060 *
00061 *  RCOND   (output) REAL
00062 *          The reciprocal of the condition number of the matrix A,
00063 *          computed as RCOND = 1/(norm(A) * norm(inv(A))).
00064 *
00065 *  WORK    (workspace) REAL array, dimension (3*N)
00066 *
00067 *  IWORK   (workspace) INTEGER array, dimension (N)
00068 *
00069 *  INFO    (output) INTEGER
00070 *          = 0:  successful exit
00071 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00072 *
00073 *  =====================================================================
00074 *
00075 *     .. Parameters ..
00076       REAL               ONE, ZERO
00077       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00078 *     ..
00079 *     .. Local Scalars ..
00080       LOGICAL            NOUNIT, ONENRM, UPPER
00081       CHARACTER          NORMIN
00082       INTEGER            IX, KASE, KASE1
00083       REAL               AINVNM, ANORM, SCALE, SMLNUM, XNORM
00084 *     ..
00085 *     .. Local Arrays ..
00086       INTEGER            ISAVE( 3 )
00087 *     ..
00088 *     .. External Functions ..
00089       LOGICAL            LSAME
00090       INTEGER            ISAMAX
00091       REAL               SLAMCH, SLANTP
00092       EXTERNAL           LSAME, ISAMAX, SLAMCH, SLANTP
00093 *     ..
00094 *     .. External Subroutines ..
00095       EXTERNAL           SLACN2, SLATPS, SRSCL, XERBLA
00096 *     ..
00097 *     .. Intrinsic Functions ..
00098       INTRINSIC          ABS, MAX, REAL
00099 *     ..
00100 *     .. Executable Statements ..
00101 *
00102 *     Test the input parameters.
00103 *
00104       INFO = 0
00105       UPPER = LSAME( UPLO, 'U' )
00106       ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
00107       NOUNIT = LSAME( DIAG, 'N' )
00108 *
00109       IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
00110          INFO = -1
00111       ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00112          INFO = -2
00113       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00114          INFO = -3
00115       ELSE IF( N.LT.0 ) THEN
00116          INFO = -4
00117       END IF
00118       IF( INFO.NE.0 ) THEN
00119          CALL XERBLA( 'STPCON', -INFO )
00120          RETURN
00121       END IF
00122 *
00123 *     Quick return if possible
00124 *
00125       IF( N.EQ.0 ) THEN
00126          RCOND = ONE
00127          RETURN
00128       END IF
00129 *
00130       RCOND = ZERO
00131       SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) )
00132 *
00133 *     Compute the norm of the triangular matrix A.
00134 *
00135       ANORM = SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
00136 *
00137 *     Continue only if ANORM > 0.
00138 *
00139       IF( ANORM.GT.ZERO ) THEN
00140 *
00141 *        Estimate the norm of the inverse of A.
00142 *
00143          AINVNM = ZERO
00144          NORMIN = 'N'
00145          IF( ONENRM ) THEN
00146             KASE1 = 1
00147          ELSE
00148             KASE1 = 2
00149          END IF
00150          KASE = 0
00151    10    CONTINUE
00152          CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
00153          IF( KASE.NE.0 ) THEN
00154             IF( KASE.EQ.KASE1 ) THEN
00155 *
00156 *              Multiply by inv(A).
00157 *
00158                CALL SLATPS( UPLO, 'No transpose', DIAG, NORMIN, N, AP,
00159      $                      WORK, SCALE, WORK( 2*N+1 ), INFO )
00160             ELSE
00161 *
00162 *              Multiply by inv(A**T).
00163 *
00164                CALL SLATPS( UPLO, 'Transpose', DIAG, NORMIN, N, AP,
00165      $                      WORK, SCALE, WORK( 2*N+1 ), INFO )
00166             END IF
00167             NORMIN = 'Y'
00168 *
00169 *           Multiply by 1/SCALE if doing so will not cause overflow.
00170 *
00171             IF( SCALE.NE.ONE ) THEN
00172                IX = ISAMAX( N, WORK, 1 )
00173                XNORM = ABS( WORK( IX ) )
00174                IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
00175      $            GO TO 20
00176                CALL SRSCL( N, SCALE, WORK, 1 )
00177             END IF
00178             GO TO 10
00179          END IF
00180 *
00181 *        Compute the estimate of the reciprocal condition number.
00182 *
00183          IF( AINVNM.NE.ZERO )
00184      $      RCOND = ( ONE / ANORM ) / AINVNM
00185       END IF
00186 *
00187    20 CONTINUE
00188       RETURN
00189 *
00190 *     End of STPCON
00191 *
00192       END
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