First pass to homgenize notation for transpose (**T) and conjugate transpose (**H)

Corresponds to bug0024

Author: julielangou

SRC/cgbbrd.f

@@ -20,20 +20,20 @@ SUBROUTINE CGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
 *  =======
 *
 *  CGBBRD reduces a complex general m-by-n band matrix A to real upper
-*  bidiagonal form B by a unitary transformation: Q' * A * P = B.
+*  bidiagonal form B by a unitary transformation: Q**H * A * P = B.
 *
-*  The routine computes B, and optionally forms Q or P', or computes
-*  Q'*C for a given matrix C.
+*  The routine computes B, and optionally forms Q or P**H, or computes
+*  Q**H*C for a given matrix C.
 *
 *  Arguments
 *  =========
 *
 *  VECT    (input) CHARACTER*1
-*          Specifies whether or not the matrices Q and P' are to be
+*          Specifies whether or not the matrices Q and P**H are to be
 *          formed.
-*          = 'N': do not form Q or P';
+*          = 'N': do not form Q or P**H;
 *          = 'Q': form Q only;
-*          = 'P': form P' only;
+*          = 'P': form P**H only;
 *          = 'B': form both.
 *
 *  M       (input) INTEGER
@@ -86,7 +86,7 @@ SUBROUTINE CGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,NCC)
 *          On entry, an m-by-ncc matrix C.
-*          On exit, C is overwritten by Q'*C.
+*          On exit, C is overwritten by Q**H*C.
 *          C is not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
@@ -165,7 +165,7 @@ SUBROUTINE CGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
          RETURN
       END IF
 *
-*     Initialize Q and P' to the unit matrix, if needed
+*     Initialize Q and P**H to the unit matrix, if needed
 *
       IF( WANTQ )
      $   CALL CLASET( 'Full', M, M, CZERO, CONE, Q, LDQ )
@@ -338,7 +338,7 @@ SUBROUTINE CGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
 *
                IF( WANTPT ) THEN
 *
-*                 accumulate product of plane rotations in P'
+*                 accumulate product of plane rotations in P**H
 *
                   DO 60 J = J1, J2, KB1
                      CALL CROT( N, PT( J+KUN-1, 1 ), LDPT,

SRC/cgbcon.f

@@ -187,13 +187,13 @@ SUBROUTINE CGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
      $                   KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL CLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             IF( LNOTI ) THEN
                DO 30 J = N - 1, 1, -1

SRC/cgebd2.f

@@ -87,7 +87,7 @@ SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
@@ -100,7 +100,7 @@ SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, v and u are complex vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
@@ -170,7 +170,7 @@ SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
             D( I ) = ALPHA
             A( I, I ) = ONE
 *
-*           Apply H(i)' to A(i:m,i+1:n) from the left
+*           Apply H(i)**H to A(i:m,i+1:n) from the left
 *
             IF( I.LT.N )
      $         CALL CLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
@@ -233,7 +233,7 @@ SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
                E( I ) = ALPHA
                A( I+1, I ) = ONE
 *
-*              Apply H(i)' to A(i+1:m,i+1:n) from the left
+*              Apply H(i)**H to A(i+1:m,i+1:n) from the left
 *
                CALL CLARF( 'Left', M-I, N-I, A( I+1, I ), 1,
      $                     CONJG( TAUQ( I ) ), A( I+1, I+1 ), LDA,

SRC/cgebrd.f

@@ -100,7 +100,7 @@ SUBROUTINE CGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
@@ -113,7 +113,7 @@ SUBROUTINE CGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
@@ -233,7 +233,7 @@ SUBROUTINE CGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
      $                WORK( LDWRKX*NB+1 ), LDWRKY )
 *
 *        Update the trailing submatrix A(i+ib:m,i+ib:n), using
-*        an update of the form  A := A - V*Y' - X*U'
+*        an update of the form  A := A - V*Y**H - X*U**H
 *
          CALL CGEMM( 'No transpose', 'Conjugate transpose', M-I-NB+1,
      $               N-I-NB+1, NB, -ONE, A( I+NB, I ), LDA,

SRC/cgecon.f

@@ -156,13 +156,13 @@ SUBROUTINE CGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
      $                   A, LDA, WORK, SU, RWORK( N+1 ), INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL CLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, A, LDA, WORK, SU, RWORK( N+1 ),
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL CLATRS( 'Lower', 'Conjugate transpose', 'Unit', NORMIN,
      $                   N, A, LDA, WORK, SL, RWORK, INFO )

SRC/cgehd2.f

@@ -16,7 +16,7 @@ SUBROUTINE CGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
 *  =======
 *
 *  CGEHD2 reduces a complex general matrix A to upper Hessenberg form H
-*  by a unitary similarity transformation:  Q' * A * Q = H .
+*  by a unitary similarity transformation:  Q**H * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -63,7 +63,7 @@ SUBROUTINE CGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -134,7 +134,7 @@ SUBROUTINE CGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
          CALL CLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ),
      $               A( 1, I+1 ), LDA, WORK )
 *
-*        Apply H(i)' to A(i+1:ihi,i+1:n) from the left
+*        Apply H(i)**H to A(i+1:ihi,i+1:n) from the left
 *
          CALL CLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1,
      $               CONJG( TAU( I ) ), A( I+1, I+1 ), LDA, WORK )

SRC/cgehrd.f

@@ -16,7 +16,7 @@ SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *  =======
 *
 *  CGEHRD reduces a complex general matrix A to upper Hessenberg form H by
-*  an unitary similarity transformation:  Q' * A * Q = H .
+*  an unitary similarity transformation:  Q**H * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -75,7 +75,7 @@ SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -223,14 +223,14 @@ SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
             IB = MIN( NB, IHI-I )
 *
 *           Reduce columns i:i+ib-1 to Hessenberg form, returning the
-*           matrices V and T of the block reflector H = I - V*T*V'
+*           matrices V and T of the block reflector H = I - V*T*V**H
 *           which performs the reduction, and also the matrix Y = A*V*T
 *
             CALL CLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
      $                   WORK, LDWORK )
 *
 *           Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
-*           right, computing  A := A - Y * V'. V(i+ib,ib-1) must be set
+*           right, computing  A := A - Y * V**H. V(i+ib,ib-1) must be set
 *           to 1
 *
             EI = A( I+IB, I+IB-1 )

SRC/cgelq2.f

@@ -53,11 +53,11 @@ SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO )
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
+*     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in

SRC/cgelqf.f

@@ -64,11 +64,11 @@ SUBROUTINE CGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
+*     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in

SRC/cgels.f

@@ -278,7 +278,7 @@ SUBROUTINE CGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
 *
 *           Least-Squares Problem min || A * X - B ||
 *
-*           B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*           B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS)
 *
             CALL CUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A,
      $                   LDA, WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
@@ -360,7 +360,7 @@ SUBROUTINE CGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
    30          CONTINUE
    40       CONTINUE
 *
-*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS)
+*           B(1:N,1:NRHS) := Q(1:N,:)**H * B(1:M,1:NRHS)
 *
             CALL CUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A,
      $                   LDA, WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,