LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ stpt06()

 subroutine stpt06 ( real RCOND, real RCONDC, character UPLO, character DIAG, integer N, real, dimension( * ) AP, real, dimension( * ) WORK, real RAT )

STPT06

Purpose:
``` STPT06 computes a test ratio comparing RCOND (the reciprocal
condition number of a triangular matrix A) and RCONDC, the estimate
computed by STPCON.  Information about the triangular matrix A is
used if one estimate is zero and the other is non-zero to decide if
underflow in the estimate is justified.```
Parameters
 [in] RCOND ``` RCOND is REAL The estimate of the reciprocal condition number obtained by forming the explicit inverse of the matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ).``` [in] RCONDC ``` RCONDC is REAL The estimate of the reciprocal condition number computed by STPCON.``` [in] UPLO ``` UPLO is CHARACTER Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] DIAG ``` DIAG is CHARACTER Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] AP ``` AP is REAL array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.``` [out] WORK ` WORK is REAL array, dimension (N)` [out] RAT ``` RAT is REAL The test ratio. If both RCOND and RCONDC are nonzero, RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. If RAT = 0, the two estimates are exactly the same.```

Definition at line 110 of file stpt06.f.

111 *
112 * -- LAPACK test routine --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 *
116 * .. Scalar Arguments ..
117  CHARACTER DIAG, UPLO
118  INTEGER N
119  REAL RAT, RCOND, RCONDC
120 * ..
121 * .. Array Arguments ..
122  REAL AP( * ), WORK( * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  REAL ZERO, ONE
129  parameter( zero = 0.0e+0, one = 1.0e+0 )
130 * ..
131 * .. Local Scalars ..
132  REAL ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
133 * ..
134 * .. External Functions ..
135  REAL SLAMCH, SLANTP
136  EXTERNAL slamch, slantp
137 * ..
138 * .. Intrinsic Functions ..
139  INTRINSIC max, min
140 * ..
141 * .. External Subroutines ..
143 * ..
144 * .. Executable Statements ..
145 *
146  eps = slamch( 'Epsilon' )
147  rmax = max( rcond, rcondc )
148  rmin = min( rcond, rcondc )
149 *
150 * Do the easy cases first.
151 *
152  IF( rmin.LT.zero ) THEN
153 *
154 * Invalid value for RCOND or RCONDC, return 1/EPS.
155 *
156  rat = one / eps
157 *
158  ELSE IF( rmin.GT.zero ) THEN
159 *
160 * Both estimates are positive, return RMAX/RMIN - 1.
161 *
162  rat = rmax / rmin - one
163 *
164  ELSE IF( rmax.EQ.zero ) THEN
165 *
166 * Both estimates zero.
167 *
168  rat = zero
169 *
170  ELSE
171 *
172 * One estimate is zero, the other is non-zero. If the matrix is
173 * ill-conditioned, return the nonzero estimate multiplied by
174 * 1/EPS; if the matrix is badly scaled, return the nonzero
175 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
176 * element in absolute value in A.
177 *
178  smlnum = slamch( 'Safe minimum' )
179  bignum = one / smlnum
180  CALL slabad( smlnum, bignum )
181  anorm = slantp( 'M', uplo, diag, n, ap, work )
182 *
183  rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
184  END IF
185 *
186  RETURN
187 *
188 * End of STPT06
189 *
{"ft_lang_label":"__label__en","ft_lang_prob":0.72083074,"math_prob":0.9904996,"size":1723,"snap":"2021-43-2021-49","text_gpt3_token_len":524,"char_repetition_ratio":0.13612565,"word_repetition_ratio":0.033783782,"special_character_ratio":0.30354035,"punctuation_ratio":0.12820514,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99508184,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T22:58:39Z\",\"WARC-Record-ID\":\"<urn:uuid:8b23ec08-7a36-4f5f-b766-5766b52037b0>\",\"Content-Length\":\"23893\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e50d6189-ed0d-4325-95d2-bafb8c6fb9c0>\",\"WARC-Concurrent-To\":\"<urn:uuid:20f7b5b3-a33d-434d-a798-9068b3304a31>\",\"WARC-IP-Address\":\"160.36.131.221\",\"WARC-Target-URI\":\"https://www.netlib.org/lapack/explore-html/de/d6b/group__single__lin_gac0f3740d9d14489df17b2ad45a8470d1.html\",\"WARC-Payload-Digest\":\"sha1:5YFUCNH6H3VESOTMGKOC7UBVHWMG37VS\",\"WARC-Block-Digest\":\"sha1:3WTFVEBWBYPTUVQEHRFYP3CBYXJKYFSJ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363226.68_warc_CC-MAIN-20211205221915-20211206011915-00601.warc.gz\"}"}