1      SUBROUTINE STPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK,
2     $                   INFO )
3*
4*  -- LAPACK routine (version 3.0) --
5*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
6*     Courant Institute, Argonne National Lab, and Rice University
7*     March 31, 1993
8*
9*     .. Scalar Arguments ..
10      CHARACTER          DIAG, NORM, UPLO
11      INTEGER            INFO, N
12      REAL               RCOND
13*     ..
14*     .. Array Arguments ..
15      INTEGER            IWORK( * )
16      REAL               AP( * ), WORK( * )
17*     ..
18*
19*  Purpose
20*  =======
21*
22*  STPCON estimates the reciprocal of the condition number of a packed
23*  triangular matrix A, in either the 1-norm or the infinity-norm.
24*
25*  The norm of A is computed and an estimate is obtained for
26*  norm(inv(A)), then the reciprocal of the condition number is
27*  computed as
28*     RCOND = 1 / ( norm(A) * norm(inv(A)) ).
29*
30*  Arguments
31*  =========
32*
33*  NORM    (input) CHARACTER*1
34*          Specifies whether the 1-norm condition number or the
35*          infinity-norm condition number is required:
36*          = '1' or 'O':  1-norm;
37*          = 'I':         Infinity-norm.
38*
39*  UPLO    (input) CHARACTER*1
40*          = 'U':  A is upper triangular;
41*          = 'L':  A is lower triangular.
42*
43*  DIAG    (input) CHARACTER*1
44*          = 'N':  A is non-unit triangular;
45*          = 'U':  A is unit triangular.
46*
47*  N       (input) INTEGER
48*          The order of the matrix A.  N >= 0.
49*
50*  AP      (input) REAL array, dimension (N*(N+1)/2)
51*          The upper or lower triangular matrix A, packed columnwise in
52*          a linear array.  The j-th column of A is stored in the array
53*          AP as follows:
54*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
55*          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
56*          If DIAG = 'U', the diagonal elements of A are not referenced
57*          and are assumed to be 1.
58*
59*  RCOND   (output) REAL
60*          The reciprocal of the condition number of the matrix A,
61*          computed as RCOND = 1/(norm(A) * norm(inv(A))).
62*
63*  WORK    (workspace) REAL array, dimension (3*N)
64*
65*  IWORK   (workspace) INTEGER array, dimension (N)
66*
67*  INFO    (output) INTEGER
68*          = 0:  successful exit
69*          < 0:  if INFO = -i, the i-th argument had an illegal value
70*
71*  =====================================================================
72*
73*     .. Parameters ..
74      REAL               ONE, ZERO
75      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
76*     ..
77*     .. Local Scalars ..
78      LOGICAL            NOUNIT, ONENRM, UPPER
79      CHARACTER          NORMIN
80      INTEGER            IX, KASE, KASE1
81      REAL               AINVNM, ANORM, SCALE, SMLNUM, XNORM
82*     ..
83*     .. External Functions ..
84      LOGICAL            LSAME
85      INTEGER            ISAMAX
86      REAL               SLAMCH, SLANTP
87      EXTERNAL           LSAME, ISAMAX, SLAMCH, SLANTP
88*     ..
89*     .. External Subroutines ..
90      EXTERNAL           SLACON, SLATPS, SRSCL, XERBLA
91*     ..
92*     .. Intrinsic Functions ..
93      INTRINSIC          ABS, MAX, REAL
94*     ..
95*     .. Executable Statements ..
96*
97*     Test the input parameters.
98*
99      INFO = 0
100      UPPER = LSAME( UPLO, 'U' )
101      ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
102      NOUNIT = LSAME( DIAG, 'N' )
103*
104      IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
105         INFO = -1
106      ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
107         INFO = -2
108      ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
109         INFO = -3
110      ELSE IF( N.LT.0 ) THEN
111         INFO = -4
112      END IF
113      IF( INFO.NE.0 ) THEN
114         CALL XERBLA( 'STPCON', -INFO )
115         RETURN
116      END IF
117*
118*     Quick return if possible
119*
120      IF( N.EQ.0 ) THEN
121         RCOND = ONE
122         RETURN
123      END IF
124*
125      RCOND = ZERO
126      SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) )
127*
128*     Compute the norm of the triangular matrix A.
129*
130      ANORM = SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
131*
132*     Continue only if ANORM > 0.
133*
134      IF( ANORM.GT.ZERO ) THEN
135*
136*        Estimate the norm of the inverse of A.
137*
138         AINVNM = ZERO
139         NORMIN = 'N'
140         IF( ONENRM ) THEN
141            KASE1 = 1
142         ELSE
143            KASE1 = 2
144         END IF
145         KASE = 0
146   10    CONTINUE
147         CALL SLACON( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE )
148         IF( KASE.NE.0 ) THEN
149            IF( KASE.EQ.KASE1 ) THEN
150*
151*              Multiply by inv(A).
152*
153               CALL SLATPS( UPLO, 'No transpose', DIAG, NORMIN, N, AP,
154     $                      WORK, SCALE, WORK( 2*N+1 ), INFO )
155            ELSE
156*
157*              Multiply by inv(A').
158*
159               CALL SLATPS( UPLO, 'Transpose', DIAG, NORMIN, N, AP,
160     $                      WORK, SCALE, WORK( 2*N+1 ), INFO )
161            END IF
162            NORMIN = 'Y'
163*
164*           Multiply by 1/SCALE if doing so will not cause overflow.
165*
166            IF( SCALE.NE.ONE ) THEN
167               IX = ISAMAX( N, WORK, 1 )
168               XNORM = ABS( WORK( IX ) )
169               IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
170     $            GO TO 20
171               CALL SRSCL( N, SCALE, WORK, 1 )
172            END IF
173            GO TO 10
174         END IF
175*
176*        Compute the estimate of the reciprocal condition number.
177*
178         IF( AINVNM.NE.ZERO )
179     $      RCOND = ( ONE / ANORM ) / AINVNM
180      END IF
181*
182   20 CONTINUE
183      RETURN
184*
185*     End of STPCON
186*
187      END
188