Merge pull request #176 from bnavigator/SLICOT-5.8

Update to SLICOT-Reference  v5.8

slycot/CMakeLists.txt

@@ -4,7 +4,7 @@
 # RvP, 180710
 
 # 
-set(SLICOT_FSOURCE 
+set(SLICOT_FSOURCE
 
 src/SLICOT-Reference/src/AB01MD.f
 src/SLICOT-Reference/src/AB01ND.f
@@ -106,6 +106,7 @@ src/SLICOT-Reference/src/MA01BD.f
 src/SLICOT-Reference/src/MA01BZ.f
 src/SLICOT-Reference/src/MA01CD.f
 src/SLICOT-Reference/src/MA02AD.f
+src/SLICOT-Reference/src/MA02AZ.f
 src/SLICOT-Reference/src/MA02BD.f
 src/SLICOT-Reference/src/MA02BZ.f
 src/SLICOT-Reference/src/MA02CD.f
@@ -157,6 +158,8 @@ src/SLICOT-Reference/src/MB01TD.f
 src/SLICOT-Reference/src/MB01UD.f
 src/SLICOT-Reference/src/MB01UW.f
 src/SLICOT-Reference/src/MB01UX.f
+src/SLICOT-Reference/src/MB01UY.f
+src/SLICOT-Reference/src/MB01UZ.f
 src/SLICOT-Reference/src/MB01VD.f
 src/SLICOT-Reference/src/MB01WD.f
 src/SLICOT-Reference/src/MB01XD.f
@@ -253,13 +256,16 @@ src/SLICOT-Reference/src/MB03QW.f
 src/SLICOT-Reference/src/MB03QX.f
 src/SLICOT-Reference/src/MB03QY.f
 src/SLICOT-Reference/src/MB03RD.f
+src/SLICOT-Reference/src/MB03RW.f
 src/SLICOT-Reference/src/MB03RX.f
 src/SLICOT-Reference/src/MB03RY.f
+src/SLICOT-Reference/src/MB03RZ.f
 src/SLICOT-Reference/src/MB03SD.f
 src/SLICOT-Reference/src/MB03TD.f
 src/SLICOT-Reference/src/MB03TS.f
 src/SLICOT-Reference/src/MB03UD.f
 src/SLICOT-Reference/src/MB03VD.f
+src/SLICOT-Reference/src/MB03VW.f
 src/SLICOT-Reference/src/MB03VY.f
 src/SLICOT-Reference/src/MB03WA.f
 src/SLICOT-Reference/src/MB03WD.f
@@ -427,10 +433,12 @@ src/SLICOT-Reference/src/SB03MX.f
 src/SLICOT-Reference/src/SB03MY.f
 src/SLICOT-Reference/src/SB03OD.f
 src/SLICOT-Reference/src/SB03OR.f
+src/SLICOT-Reference/src/SB03OS.f
 src/SLICOT-Reference/src/SB03OT.f
 src/SLICOT-Reference/src/SB03OU.f
 src/SLICOT-Reference/src/SB03OV.f
 src/SLICOT-Reference/src/SB03OY.f
+src/SLICOT-Reference/src/SB03OZ.f
 src/SLICOT-Reference/src/SB03PD.f
 src/SLICOT-Reference/src/SB03QD.f
 src/SLICOT-Reference/src/SB03QX.f
@@ -512,11 +520,15 @@ src/SLICOT-Reference/src/SG03AD.f
 src/SLICOT-Reference/src/SG03AX.f
 src/SLICOT-Reference/src/SG03AY.f
 src/SLICOT-Reference/src/SG03BD.f
+src/SLICOT-Reference/src/SG03BR.f
+src/SLICOT-Reference/src/SG03BS.f
+src/SLICOT-Reference/src/SG03BT.f
 src/SLICOT-Reference/src/SG03BU.f
 src/SLICOT-Reference/src/SG03BV.f
 src/SLICOT-Reference/src/SG03BW.f
 src/SLICOT-Reference/src/SG03BX.f
 src/SLICOT-Reference/src/SG03BY.f
+src/SLICOT-Reference/src/SG03BZ.f
 src/SLICOT-Reference/src/TB01ID.f
 src/SLICOT-Reference/src/TB01IZ.f
 src/SLICOT-Reference/src/TB01KD.f
@@ -580,11 +592,17 @@ src/SLICOT-Reference/src/TG01HY.f
 src/SLICOT-Reference/src/TG01ID.f
 src/SLICOT-Reference/src/TG01JD.f
 src/SLICOT-Reference/src/TG01JY.f
+src/SLICOT-Reference/src/TG01KD.f
+src/SLICOT-Reference/src/TG01KZ.f
 src/SLICOT-Reference/src/TG01LD.f
 src/SLICOT-Reference/src/TG01LY.f
 src/SLICOT-Reference/src/TG01MD.f
 src/SLICOT-Reference/src/TG01ND.f
 src/SLICOT-Reference/src/TG01NX.f
+src/SLICOT-Reference/src/TG01OA.f
+src/SLICOT-Reference/src/TG01OB.f
+src/SLICOT-Reference/src/TG01OD.f
+src/SLICOT-Reference/src/TG01OZ.f
 src/SLICOT-Reference/src/TG01PD.f
 src/SLICOT-Reference/src/TG01QD.f
 src/SLICOT-Reference/src/TG01WD.f

slycot/math.py

@@ -29,7 +29,7 @@ def mb03rd(n, A, X=None, jobx='U', sort='N', pmax=1.0, tol=0.0):
     To reduce a matrix `A` in real Schur form to a block-diagonal form
     using well-conditioned non-orthogonal similarity transformations.
     The condition numbers of the transformations used for reduction
-    are roughly bounded by `pmax`*`pmax`, where `pmax` is a given value.
+    are roughly bounded by `pmax`, where `pmax` is a given value.
     The transformations are optionally postmultiplied in a given
     matrix `X`. The real Schur form is optionally ordered, so that
     clustered eigenvalues are grouped in the same block.

slycot/src/synthesis.pyf

@@ -365,7 +365,7 @@ subroutine sb03od(dico,fact,trans,n,m,a,lda,q,ldq,b,ldb,scale,wr,wi,dwork,ldwork
     double precision intent(out),dimension(n),depend(n) :: wr
     double precision intent(out),dimension(n),depend(n) :: wi
     double precision intent(hide,cache),dimension(ldwork) :: dwork
-    integer optional,check(ldwork>=max(1,4*n + min(m,n))),depend(n,m) :: ldwork=max(1,4*n + min(m,n))
+    integer optional,check(ldwork>=max(1,4*n)),depend(n,m) :: ldwork=max(1,4*n)
     integer intent(out) :: info    
 end subroutine sb03od
 subroutine sb04md(n,m,a,lda,b,ldb,c,ldc,z,ldz,iwork,dwork,ldwork,info) ! in SB04MD.f

slycot/synthesis.py

@@ -839,7 +839,7 @@ def sb03od(n,m,A,Q,B,dico,fact='N',trans='N',ldwork=None):
     set less than or equal to 1 to avoid overflow in X. If matrix B
     has full rank then the solution matrix X will be positive-definite
     and hence the Cholesky factor U will be nonsingular, but if B is
-    rank deficient then X may be only positive semi-definite and U
+    rank deficient, then X may be only positive semi-definite and U
     will be singular.
 
     In the case of equation (1) the matrix A must be stable (that
@@ -850,28 +850,28 @@ def sb03od(n,m,A,Q,B,dico,fact='N',trans='N',ldwork=None):
     Parameters
     ----------
     n : int
-        The order of the matrix A and the number of columns in
-        matrix op(B).  n >= 0.
+        The order of the matrix A and the number of columns of
+        the matrix op(B).  n >= 0.
     m : int
         The number of rows in matrix op(B).  m >= 0.
     A : (n, n) array_like
         On entry, the leading n-by-n part of this array must
         contain the matrix A. If fact = 'F', then A contains
         an upper quasi-triangular matrix S in Schur canonical
         form; the elements below the upper Hessenberg part of the
-        array A are not referenced.
+        array A are then not referenced.
         On exit, the leading n-by-n upper Hessenberg part of this
         array contains the upper quasi-triangular matrix S in
         Schur canonical form from the Shur factorization of A.
-        The contents of array A is not modified if fact = 'F'.
+        The contents of the array A is not modified if fact = 'F'.
     Q : (n, n) array_like
         On entry, if fact = 'F', then the leading n-by-n part of
         this array must contain the orthogonal matrix Q of the
         Schur factorization of A.
         Otherwise, Q need not be set on entry.
         On exit, the leading n-by-n part of this array contains
         the orthogonal matrix Q of the Schur factorization of A.
-        The contents of array Q is not modified if fact = 'F'.
+        The contents of the array Q is not modified if fact = 'F'.
     B : (m, n) array_like
         On entry, if trans = 'N', the leading m-by-n part of this
         array must contain the coefficient matrix B of the
@@ -901,7 +901,7 @@ def sb03od(n,m,A,Q,B,dico,fact='N',trans='N',ldwork=None):
             := 'T':  op(K) = K**T (Transpose).
     ldwork : int, optional
         The length of the array DWORK.
-        If m > 0, ldwork >= max(1, 4*n + min(m, n));
+        If m > 0, ldwork >= max(1, 4*n);
         If m = 0, ldwork >= 1.
         For optimum performance ldwork should sometimes be larger.
 
@@ -915,24 +915,15 @@ def sb03od(n,m,A,Q,B,dico,fact='N',trans='N',ldwork=None):
         The scale factor, scale, set less than or equal to 1 to
         prevent the solution overflowing.
     w : (n, ) complex ndarray
-        If fact = 'N', this array contains the eigenvalues of A.
+        The eigenvalues of A.
 
     Raises
     ------
     SlycotArithmeticError
-        :info = 3 and fact == 'F' and dico == 'C':
-            The Schur factor S supplied in the array A is not
-            stable (that is, one or more of the eigenvalues of
-            S has a non-negative real part)
-        :info = 3 and dico == 'D':
-            The Schur factor S
-            supplied in the array A is not convergent (that is,
-            one or more of the eigenvalues of S lies outside the
-            unit circle)
         :info = 4:
             FACT = 'F' and the Schur factor S supplied in
             the array A has two or more consecutive non-zero
-            elements on the first sub-diagonal, so that there is
+            elements on the first subdiagonal, so that there is
             a block larger than 2-by-2 on the diagonal
         :info = 5:
             FACT = 'F' and the Schur factor S supplied in
@@ -977,14 +968,24 @@ def sb03od(n,m,A,Q,B,dico,fact='N',trans='N',ldwork=None):
             more of the eigenvalues of A lies outside the unit
             circle); however, A still has been factored
             and the eigenvalues of A are returned in WR and WI.
+        :info = 3 and fact == 'F' and dico == 'C':
+            The Schur factor S supplied in the array A is not
+            stable (that is, one or more of the eigenvalues of
+            S has a non-negative real part);
+            the eigenvalues of A are still returned in w.
+        :info = 3 and dico == 'D':
+            The Schur factor S supplied in the array A is not
+            convergent (that is, one or more of the eigenvalues
+            of S lies outside the unit circle);
+            the eigenvalues of A are still returned in w.
     """
     hidden = ' (hidden by the wrapper)'
     arg_list = ['dico','fact', 'trans', 'n', 'm', 'a', 'lda'+hidden, 'q',
         'ldq'+hidden, 'b', 'ldb'+hidden, 'scale', 'wr'+hidden,
         'wi'+hidden, 'dwork'+hidden, 'ldwork', 'info'+hidden]
     if ldwork is None:
         if m > 0:
-            ldwork = max(1,4*n + min(m,n))
+            ldwork = max(1,4*n)
         elif m == 0:
             ldwork = 1
     if dico != 'C' and dico != 'D':
@@ -2333,9 +2334,6 @@ def sg03bd(n,m,A,E,Q,Z,B,dico,fact='N',trans='N',ldwork=None):
         Hessenberg part of the array A are not referenced.
         If fact = 'N', then the leading n-by-n part of this
         array must contain the matrix A.
-        On exit, the leading n-by-n part of this array contains
-        the generalized Schur factor A_s of the matrix A. (A_s is
-        an upper quasitriangular matrix.)
     E : (n, n) array_like
         On entry, if fact = 'F', then the leading n-by-n upper
         triangular part of this array must contain the
@@ -2407,9 +2405,9 @@ def sg03bd(n,m,A,E,Q,Z,B,dico,fact='N',trans='N',ldwork=None):
     scale : float
         The scale factor set to avoid overflow in U.
         0 < scale <= 1.
-    alpha : (n, ) complex ndarray
+    lambda : (n, ) complex ndarray
         If INFO = 0, 3, 5, 6, or 7, then
-        (alpha(j), j=1,...,n, are the
+        ((j), j=1,...,n, are the
         eigenvalues of the matrix pencil A - lambda * E.
 
     Raises
@@ -2463,7 +2461,7 @@ def sg03bd(n,m,A,E,Q,Z,B,dico,fact='N',trans='N',ldwork=None):
     alpha = _np.zeros(n,'complex64')
     alpha.real = alphar[0:n]
     alpha.imag = alphai[0:n]
-    return U,scale,alpha/beta
+    return U, scale, alpha/beta
 
 
 def sb10fd(n,m,np,ncon,nmeas,gamma,A,B,C,D,tol=0.0,ldwork=None):

slycot/tests/test_sb.py

@@ -192,9 +192,9 @@ def test_sb10fd_2():
                                                                 'dico': 'C'}),
      (synthesis.sb03od, SlycotResultWarning,   [1, 2],         {'dico': 'C',
                                                                 'fact': 'N'}),
-     (synthesis.sb03od, SlycotResultWarning,   [1, 2],         {'dico': 'D',
+     (synthesis.sb03od, SlycotResultWarning,   [1, 2, 3],      {'dico': 'D',
                                                                 'fact': 'N'}),
-     (synthesis.sb03od, SlycotArithmeticError, [3, 4, 5, 6],   {'dico': 'D',
+     (synthesis.sb03od, SlycotArithmeticError, [4, 5, 6],      {'dico': 'D',
                                                                 'fact': 'F'}),
      (synthesis.sb04md, SlycotArithmeticError, 2,              {'m': 1}),
      (synthesis.sb04qd, SlycotArithmeticError, 3,              {'m': 2}),