--- 
:name: ctgsyl
:md5sum: 353e93545b3d9d5928409ecbfb8864c2
:category: :subroutine
:arguments: 
- trans: 
    :type: char
    :intent: input
- ijob: 
    :type: integer
    :intent: input
- m: 
    :type: integer
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: complex
    :intent: input
    :dims: 
    - lda
    - m
- lda: 
    :type: integer
    :intent: input
- b: 
    :type: complex
    :intent: input
    :dims: 
    - ldb
    - n
- ldb: 
    :type: integer
    :intent: input
- c: 
    :type: complex
    :intent: input/output
    :dims: 
    - ldc
    - n
- ldc: 
    :type: integer
    :intent: input
- d: 
    :type: complex
    :intent: input
    :dims: 
    - ldd
    - m
- ldd: 
    :type: integer
    :intent: input
- e: 
    :type: complex
    :intent: input
    :dims: 
    - lde
    - n
- lde: 
    :type: integer
    :intent: input
- f: 
    :type: complex
    :intent: input/output
    :dims: 
    - ldf
    - n
- ldf: 
    :type: integer
    :intent: input
- scale: 
    :type: real
    :intent: output
- dif: 
    :type: real
    :intent: output
- work: 
    :type: complex
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
    :option: true
    :default: "((ijob==1||ijob==2)&&lsame_(&trans,\"N\")) ? 2*m*n : 1"
- iwork: 
    :type: integer
    :intent: workspace
    :dims: 
    - m+n+2
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE CTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, IWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  CTGSYL solves the generalized Sylvester equation:\n\
  *\n\
  *              A * R - L * B = scale * C            (1)\n\
  *              D * R - L * E = scale * F\n\
  *\n\
  *  where R and L are unknown m-by-n matrices, (A, D), (B, E) and\n\
  *  (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,\n\
  *  respectively, with complex entries. A, B, D and E are upper\n\
  *  triangular (i.e., (A,D) and (B,E) in generalized Schur form).\n\
  *\n\
  *  The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1\n\
  *  is an output scaling factor chosen to avoid overflow.\n\
  *\n\
  *  In matrix notation (1) is equivalent to solve Zx = scale*b, where Z\n\
  *  is defined as\n\
  *\n\
  *         Z = [ kron(In, A)  -kron(B', Im) ]        (2)\n\
  *             [ kron(In, D)  -kron(E', Im) ],\n\
  *\n\
  *  Here Ix is the identity matrix of size x and X' is the conjugate\n\
  *  transpose of X. Kron(X, Y) is the Kronecker product between the\n\
  *  matrices X and Y.\n\
  *\n\
  *  If TRANS = 'C', y in the conjugate transposed system Z'*y = scale*b\n\
  *  is solved for, which is equivalent to solve for R and L in\n\
  *\n\
  *              A' * R + D' * L = scale * C           (3)\n\
  *              R * B' + L * E' = scale * -F\n\
  *\n\
  *  This case (TRANS = 'C') is used to compute an one-norm-based estimate\n\
  *  of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)\n\
  *  and (B,E), using CLACON.\n\
  *\n\
  *  If IJOB >= 1, CTGSYL computes a Frobenius norm-based estimate of\n\
  *  Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the\n\
  *  reciprocal of the smallest singular value of Z.\n\
  *\n\
  *  This is a level-3 BLAS algorithm.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  TRANS   (input) CHARACTER*1\n\
  *          = 'N': solve the generalized sylvester equation (1).\n\
  *          = 'C': solve the \"conjugate transposed\" system (3).\n\
  *\n\
  *  IJOB    (input) INTEGER\n\
  *          Specifies what kind of functionality to be performed.\n\
  *          =0: solve (1) only.\n\
  *          =1: The functionality of 0 and 3.\n\
  *          =2: The functionality of 0 and 4.\n\
  *          =3: Only an estimate of Dif[(A,D), (B,E)] is computed.\n\
  *              (look ahead strategy is used).\n\
  *          =4: Only an estimate of Dif[(A,D), (B,E)] is computed.\n\
  *              (CGECON on sub-systems is used).\n\
  *          Not referenced if TRANS = 'C'.\n\
  *\n\
  *  M       (input) INTEGER\n\
  *          The order of the matrices A and D, and the row dimension of\n\
  *          the matrices C, F, R and L.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrices B and E, and the column dimension\n\
  *          of the matrices C, F, R and L.\n\
  *\n\
  *  A       (input) COMPLEX array, dimension (LDA, M)\n\
  *          The upper triangular matrix A.\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of the array A. LDA >= max(1, M).\n\
  *\n\
  *  B       (input) COMPLEX array, dimension (LDB, N)\n\
  *          The upper triangular matrix B.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *          The leading dimension of the array B. LDB >= max(1, N).\n\
  *\n\
  *  C       (input/output) COMPLEX array, dimension (LDC, N)\n\
  *          On entry, C contains the right-hand-side of the first matrix\n\
  *          equation in (1) or (3).\n\
  *          On exit, if IJOB = 0, 1 or 2, C has been overwritten by\n\
  *          the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,\n\
  *          the solution achieved during the computation of the\n\
  *          Dif-estimate.\n\
  *\n\
  *  LDC     (input) INTEGER\n\
  *          The leading dimension of the array C. LDC >= max(1, M).\n\
  *\n\
  *  D       (input) COMPLEX array, dimension (LDD, M)\n\
  *          The upper triangular matrix D.\n\
  *\n\
  *  LDD     (input) INTEGER\n\
  *          The leading dimension of the array D. LDD >= max(1, M).\n\
  *\n\
  *  E       (input) COMPLEX array, dimension (LDE, N)\n\
  *          The upper triangular matrix E.\n\
  *\n\
  *  LDE     (input) INTEGER\n\
  *          The leading dimension of the array E. LDE >= max(1, N).\n\
  *\n\
  *  F       (input/output) COMPLEX array, dimension (LDF, N)\n\
  *          On entry, F contains the right-hand-side of the second matrix\n\
  *          equation in (1) or (3).\n\
  *          On exit, if IJOB = 0, 1 or 2, F has been overwritten by\n\
  *          the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,\n\
  *          the solution achieved during the computation of the\n\
  *          Dif-estimate.\n\
  *\n\
  *  LDF     (input) INTEGER\n\
  *          The leading dimension of the array F. LDF >= max(1, M).\n\
  *\n\
  *  DIF     (output) REAL\n\
  *          On exit DIF is the reciprocal of a lower bound of the\n\
  *          reciprocal of the Dif-function, i.e. DIF is an upper bound of\n\
  *          Dif[(A,D), (B,E)] = sigma-min(Z), where Z as in (2).\n\
  *          IF IJOB = 0 or TRANS = 'C', DIF is not referenced.\n\
  *\n\
  *  SCALE   (output) REAL\n\
  *          On exit SCALE is the scaling factor in (1) or (3).\n\
  *          If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,\n\
  *          to a slightly perturbed system but the input matrices A, B,\n\
  *          D and E have not been changed. If SCALE = 0, R and L will\n\
  *          hold the solutions to the homogenious system with C = F = 0.\n\
  *\n\
  *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))\n\
  *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The dimension of the array WORK. LWORK > = 1.\n\
  *          If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal size of the WORK array, returns\n\
  *          this value as the first entry of the WORK array, and no error\n\
  *          message related to LWORK is issued by XERBLA.\n\
  *\n\
  *  IWORK   (workspace) INTEGER array, dimension (M+N+2)\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *            =0: successful exit\n\
  *            <0: If INFO = -i, the i-th argument had an illegal value.\n\
  *            >0: (A, D) and (B, E) have common or very close\n\
  *                eigenvalues.\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  Based on contributions by\n\
  *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,\n\
  *     Umea University, S-901 87 Umea, Sweden.\n\
  *\n\
  *  [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software\n\
  *      for Solving the Generalized Sylvester Equation and Estimating the\n\
  *      Separation between Regular Matrix Pairs, Report UMINF - 93.23,\n\
  *      Department of Computing Science, Umea University, S-901 87 Umea,\n\
  *      Sweden, December 1993, Revised April 1994, Also as LAPACK Working\n\
  *      Note 75.  To appear in ACM Trans. on Math. Software, Vol 22,\n\
  *      No 1, 1996.\n\
  *\n\
  *  [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester\n\
  *      Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.\n\
  *      Appl., 15(4):1045-1060, 1994.\n\
  *\n\
  *  [3] B. Kagstrom and L. Westin, Generalized Schur Methods with\n\
  *      Condition Estimators for Solving the Generalized Sylvester\n\
  *      Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,\n\
  *      July 1989, pp 745-751.\n\
  *\n\
  *  =====================================================================\n\
  *  Replaced various illegal calls to CCOPY by calls to CLASET.\n\
  *  Sven Hammarling, 1/5/02.\n\
  *\n"