--- 
:name: ctrsna
:md5sum: e91cc890d0ea7dbba10a9adc422212aa
:category: :subroutine
:arguments: 
- job: 
    :type: char
    :intent: input
- howmny: 
    :type: char
    :intent: input
- select: 
    :type: logical
    :intent: input
    :dims: 
    - n
- n: 
    :type: integer
    :intent: input
- t: 
    :type: complex
    :intent: input
    :dims: 
    - ldt
    - n
- ldt: 
    :type: integer
    :intent: input
- vl: 
    :type: complex
    :intent: input
    :dims: 
    - ldvl
    - m
- ldvl: 
    :type: integer
    :intent: input
- vr: 
    :type: complex
    :intent: input
    :dims: 
    - ldvr
    - m
- ldvr: 
    :type: integer
    :intent: input
- s: 
    :type: real
    :intent: output
    :dims: 
    - mm
- sep: 
    :type: real
    :intent: output
    :dims: 
    - mm
- mm: 
    :type: integer
    :intent: input
- m: 
    :type: integer
    :intent: output
- work: 
    :type: complex
    :intent: workspace
    :dims: 
    - "lsame_(&job,\"E\") ? 0 : ldwork"
    - "lsame_(&job,\"E\") ? 0 : n+6"
- ldwork: 
    :type: integer
    :intent: input
- rwork: 
    :type: real
    :intent: workspace
    :dims: 
    - "lsame_(&job,\"E\") ? 0 : n"
- info: 
    :type: integer
    :intent: output
:substitutions: 
  ldwork: "((lsame_(&job,\"V\")) || (lsame_(&job,\"B\"))) ? n : 1"
  mm: m
:fortran_help: "      SUBROUTINE CTRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, S, SEP, MM, M, WORK, LDWORK, RWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  CTRSNA estimates reciprocal condition numbers for specified\n\
  *  eigenvalues and/or right eigenvectors of a complex upper triangular\n\
  *  matrix T (or of any matrix Q*T*Q**H with Q unitary).\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  JOB     (input) CHARACTER*1\n\
  *          Specifies whether condition numbers are required for\n\
  *          eigenvalues (S) or eigenvectors (SEP):\n\
  *          = 'E': for eigenvalues only (S);\n\
  *          = 'V': for eigenvectors only (SEP);\n\
  *          = 'B': for both eigenvalues and eigenvectors (S and SEP).\n\
  *\n\
  *  HOWMNY  (input) CHARACTER*1\n\
  *          = 'A': compute condition numbers for all eigenpairs;\n\
  *          = 'S': compute condition numbers for selected eigenpairs\n\
  *                 specified by the array SELECT.\n\
  *\n\
  *  SELECT  (input) LOGICAL array, dimension (N)\n\
  *          If HOWMNY = 'S', SELECT specifies the eigenpairs for which\n\
  *          condition numbers are required. To select condition numbers\n\
  *          for the j-th eigenpair, SELECT(j) must be set to .TRUE..\n\
  *          If HOWMNY = 'A', SELECT is not referenced.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix T. N >= 0.\n\
  *\n\
  *  T       (input) COMPLEX array, dimension (LDT,N)\n\
  *          The upper triangular matrix T.\n\
  *\n\
  *  LDT     (input) INTEGER\n\
  *          The leading dimension of the array T. LDT >= max(1,N).\n\
  *\n\
  *  VL      (input) COMPLEX array, dimension (LDVL,M)\n\
  *          If JOB = 'E' or 'B', VL must contain left eigenvectors of T\n\
  *          (or of any Q*T*Q**H with Q unitary), corresponding to the\n\
  *          eigenpairs specified by HOWMNY and SELECT. The eigenvectors\n\
  *          must be stored in consecutive columns of VL, as returned by\n\
  *          CHSEIN or CTREVC.\n\
  *          If JOB = 'V', VL is not referenced.\n\
  *\n\
  *  LDVL    (input) INTEGER\n\
  *          The leading dimension of the array VL.\n\
  *          LDVL >= 1; and if JOB = 'E' or 'B', LDVL >= N.\n\
  *\n\
  *  VR      (input) COMPLEX array, dimension (LDVR,M)\n\
  *          If JOB = 'E' or 'B', VR must contain right eigenvectors of T\n\
  *          (or of any Q*T*Q**H with Q unitary), corresponding to the\n\
  *          eigenpairs specified by HOWMNY and SELECT. The eigenvectors\n\
  *          must be stored in consecutive columns of VR, as returned by\n\
  *          CHSEIN or CTREVC.\n\
  *          If JOB = 'V', VR is not referenced.\n\
  *\n\
  *  LDVR    (input) INTEGER\n\
  *          The leading dimension of the array VR.\n\
  *          LDVR >= 1; and if JOB = 'E' or 'B', LDVR >= N.\n\
  *\n\
  *  S       (output) REAL array, dimension (MM)\n\
  *          If JOB = 'E' or 'B', the reciprocal condition numbers of the\n\
  *          selected eigenvalues, stored in consecutive elements of the\n\
  *          array. Thus S(j), SEP(j), and the j-th columns of VL and VR\n\
  *          all correspond to the same eigenpair (but not in general the\n\
  *          j-th eigenpair, unless all eigenpairs are selected).\n\
  *          If JOB = 'V', S is not referenced.\n\
  *\n\
  *  SEP     (output) REAL array, dimension (MM)\n\
  *          If JOB = 'V' or 'B', the estimated reciprocal condition\n\
  *          numbers of the selected eigenvectors, stored in consecutive\n\
  *          elements of the array.\n\
  *          If JOB = 'E', SEP is not referenced.\n\
  *\n\
  *  MM      (input) INTEGER\n\
  *          The number of elements in the arrays S (if JOB = 'E' or 'B')\n\
  *           and/or SEP (if JOB = 'V' or 'B'). MM >= M.\n\
  *\n\
  *  M       (output) INTEGER\n\
  *          The number of elements of the arrays S and/or SEP actually\n\
  *          used to store the estimated condition numbers.\n\
  *          If HOWMNY = 'A', M is set to N.\n\
  *\n\
  *  WORK    (workspace) COMPLEX array, dimension (LDWORK,N+6)\n\
  *          If JOB = 'E', WORK is not referenced.\n\
  *\n\
  *  LDWORK  (input) INTEGER\n\
  *          The leading dimension of the array WORK.\n\
  *          LDWORK >= 1; and if JOB = 'V' or 'B', LDWORK >= N.\n\
  *\n\
  *  RWORK   (workspace) REAL array, dimension (N)\n\
  *          If JOB = 'E', RWORK is not referenced.\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0: successful exit\n\
  *          < 0: if INFO = -i, the i-th argument had an illegal value\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  The reciprocal of the condition number of an eigenvalue lambda is\n\
  *  defined as\n\
  *\n\
  *          S(lambda) = |v'*u| / (norm(u)*norm(v))\n\
  *\n\
  *  where u and v are the right and left eigenvectors of T corresponding\n\
  *  to lambda; v' denotes the conjugate transpose of v, and norm(u)\n\
  *  denotes the Euclidean norm. These reciprocal condition numbers always\n\
  *  lie between zero (very badly conditioned) and one (very well\n\
  *  conditioned). If n = 1, S(lambda) is defined to be 1.\n\
  *\n\
  *  An approximate error bound for a computed eigenvalue W(i) is given by\n\
  *\n\
  *                      EPS * norm(T) / S(i)\n\
  *\n\
  *  where EPS is the machine precision.\n\
  *\n\
  *  The reciprocal of the condition number of the right eigenvector u\n\
  *  corresponding to lambda is defined as follows. Suppose\n\
  *\n\
  *              T = ( lambda  c  )\n\
  *                  (   0    T22 )\n\
  *\n\
  *  Then the reciprocal condition number is\n\
  *\n\
  *          SEP( lambda, T22 ) = sigma-min( T22 - lambda*I )\n\
  *\n\
  *  where sigma-min denotes the smallest singular value. We approximate\n\
  *  the smallest singular value by the reciprocal of an estimate of the\n\
  *  one-norm of the inverse of T22 - lambda*I. If n = 1, SEP(1) is\n\
  *  defined to be abs(T(1,1)).\n\
  *\n\
  *  An approximate error bound for a computed right eigenvector VR(i)\n\
  *  is given by\n\
  *\n\
  *                      EPS * norm(T) / SEP(i)\n\
  *\n\
  *  =====================================================================\n\
  *\n"
