Second and hopefully last pass to homgenize notation for transpose (**T) and conjugate transpose (**H)

Corresponds to bug0024

Please take a look and let me know if you find some old notation of transpose.
I am going to close bug0024.
Julie

Author: julielangou

SRC/cgebd2.f

@@ -17,7 +17,7 @@ SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
 *  =======
 *
 *  CGEBD2 reduces a complex general m by n matrix A to upper or lower
-*  real bidiagonal form B by a unitary transformation: Q' * A * P = B.
+*  real bidiagonal form B by a unitary transformation: Q**H * A * P = B.
 *
 *  If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
 *

SRC/cgels.f

@@ -299,9 +299,9 @@ SUBROUTINE CGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
 *
          ELSE
 *
-*           Overdetermined system of equations A' * X = B
+*           Overdetermined system of equations A**H * X = B
 *
-*           B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS)
+*           B(1:N,1:NRHS) := inv(R**H) * B(1:N,1:NRHS)
 *
             CALL CTRTRS( 'Upper', 'Conjugate transpose','Non-unit',
      $                   N, NRHS, A, LDA, B, LDB, INFO )
@@ -372,7 +372,7 @@ SUBROUTINE CGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
 *
          ELSE
 *
-*           overdetermined system min || A' * X - B ||
+*           overdetermined system min || A**H * X - B ||
 *
 *           B(1:N,1:NRHS) := Q * B(1:N,1:NRHS)
 *
@@ -382,7 +382,7 @@ SUBROUTINE CGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
 *
 *           workspace at least NRHS, optimally NRHS*NB
 *
-*           B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS)
+*           B(1:M,1:NRHS) := inv(L**H) * B(1:M,1:NRHS)
 *
             CALL CTRTRS( 'Lower', 'Conjugate transpose', 'Non-unit',
      $                   M, NRHS, A, LDA, B, LDB, INFO )

SRC/cgelsy.f

@@ -43,8 +43,8 @@ SUBROUTINE CGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK,
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**H [ inv(T11)*Q1**H*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  This routine is basically identical to the original xGELSX except

SRC/cggsvd.f

@@ -210,7 +210,7 @@ SUBROUTINE CGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
 *  TOLA    REAL
 *  TOLB    REAL
 *          TOLA and TOLB are the thresholds to determine the effective
-*          rank of (A',B')**H. Generally, they are set to
+*          rank of (A**H,B**H)**H. Generally, they are set to
 *                   TOLA = MAX(M,N)*norm(A)*MACHEPS,
 *                   TOLB = MAX(P,N)*norm(B)*MACHEPS.
 *          The size of TOLA and TOLB may affect the size of backward

SRC/cherfs.f

@@ -308,7 +308,7 @@ SUBROUTINE CHERFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(A').
+*              Multiply by diag(W)*inv(A**H).
 *
                CALL CHETRS( UPLO, N, 1, AF, LDAF, IPIV, WORK, N, INFO )
                DO 110 I = 1, N

SRC/chetd2.f

@@ -237,7 +237,7 @@ SUBROUTINE CHETD2( UPLO, N, A, LDA, D, E, TAU, INFO )
                CALL CAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v**H
+*                 A := A - v * w**H - w * v**H
 *
                CALL CHER2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,
      $                     A( I+1, I+1 ), LDA )

SRC/chetrd.f

@@ -237,7 +237,7 @@ SUBROUTINE CHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
      $                   LDWORK )
 *
 *           Update the unreduced submatrix A(1:i-1,1:i-1), using an
-*           update of the form:  A := A - V*W' - W*V**H
+*           update of the form:  A := A - V*W**H - W*V**H
 *
             CALL CHER2K( UPLO, 'No transpose', I-1, NB, -CONE,
      $                   A( 1, I ), LDA, WORK, LDWORK, ONE, A, LDA )
@@ -268,7 +268,7 @@ SUBROUTINE CHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
      $                   TAU( I ), WORK, LDWORK )
 *
 *           Update the unreduced submatrix A(i+nb:n,i+nb:n), using
-*           an update of the form:  A := A - V*W' - W*V**H
+*           an update of the form:  A := A - V*W**H - W*V**H
 *
             CALL CHER2K( UPLO, 'No transpose', N-I-NB+1, NB, -CONE,
      $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,

SRC/chetri2x.f

@@ -156,7 +156,7 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
 
       IF( UPPER ) THEN
 *
-*        invA = P * inv(U**H)*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**H)*inv(D)*inv(U)*P**H.
 *
         CALL CTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -269,7 +269,7 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
              END IF
            END DO
 *    
-*       U11T*invD1*U11->U11
+*       U11**H*invD1*U11->U11
 *
         CALL CTRMM('L','U','C','U',NNB, NNB,
      $             CONE,A(CUT+1,CUT+1),LDA,WORK(U11+1,1),N+NB+1)
@@ -280,20 +280,20 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
             END DO
          END DO
 *
-*          U01'invD*U01->A(CUT+I,CUT+J)
+*          U01**H*invD*U01->A(CUT+I,CUT+J)
 *
          CALL CGEMM('C','N',NNB,NNB,CUT,CONE,A(1,CUT+1),LDA,
      $              WORK,N+NB+1, ZERO, WORK(U11+1,1), N+NB+1)
 *
-*        U11 =  U11T*invD1*U11 + U01'invD*U01
+*        U11 =  U11**H*invD1*U11 + U01**H*invD*U01
 *
          DO I=1,NNB
             DO J=I,NNB
               A(CUT+I,CUT+J)=A(CUT+I,CUT+J)+WORK(U11+I,J)
             END DO
          END DO
 *
-*        U01 =  U00T*invD0*U01
+*        U01 =  U00**H*invD0*U01
 *
          CALL CTRMM('L',UPLO,'C','U',CUT, NNB,
      $             CONE,A,LDA,WORK,N+NB+1)
@@ -311,7 +311,7 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
 *
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U**H)*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P**H: P * inv(U**H)*inv(D)*inv(U) *P**H
 *  
             I=1
             DO WHILE ( I .LE. N )
@@ -333,7 +333,7 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
 *
 *        LOWER...
 *
-*        invA = P * inv(U**H)*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**H)*inv(D)*inv(U)*P**H.
 *
          CALL CTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -440,7 +440,7 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
              END IF
            END DO
 *    
-*       L11T*invD1*L11->L11
+*       L11**H*invD1*L11->L11
 *
         CALL CTRMM('L',UPLO,'C','U',NNB, NNB,
      $             CONE,A(CUT+1,CUT+1),LDA,WORK(U11+1,1),N+NB+1)
@@ -453,21 +453,21 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
 *
         IF ( (CUT+NNB) .LT. N ) THEN
 *
-*          L21T*invD2*L21->A(CUT+I,CUT+J)
+*          L21**H*invD2*L21->A(CUT+I,CUT+J)
 *
          CALL CGEMM('C','N',NNB,NNB,N-NNB-CUT,CONE,A(CUT+NNB+1,CUT+1)
      $             ,LDA,WORK,N+NB+1, ZERO, WORK(U11+1,1), N+NB+1)
 
 *
-*        L11 =  L11T*invD1*L11 + U01'invD*U01
+*        L11 =  L11**H*invD1*L11 + U01**H*invD*U01
 *
          DO I=1,NNB
             DO J=1,I
               A(CUT+I,CUT+J)=A(CUT+I,CUT+J)+WORK(U11+I,J)
             END DO
          END DO
 *
-*        L01 =  L22T*invD2*L21
+*        L01 =  L22**H*invD2*L21
 *
          CALL CTRMM('L',UPLO,'C','U', N-NNB-CUT, NNB,
      $             CONE,A(CUT+NNB+1,CUT+NNB+1),LDA,WORK,N+NB+1)
@@ -480,7 +480,7 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
          END DO
        ELSE
 *
-*        L11 =  L11T*invD1*L11
+*        L11 =  L11**H*invD1*L11
 *
          DO I=1,NNB
             DO J=1,I
@@ -494,7 +494,7 @@ SUBROUTINE CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
            CUT=CUT+NNB
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U**H)*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P**H: P * inv(U**H)*inv(D)*inv(U) *P**H
 * 
             I=N
             DO WHILE ( I .GE. 1 )

SRC/chfrk.f

@@ -26,11 +26,11 @@ SUBROUTINE CHFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
 *
 *  CHFRK performs one of the Hermitian rank--k operations
 *
-*     C := alpha*A*conjg( A' ) + beta*C,
+*     C := alpha*A*A**H + beta*C,
 *
 *  or
 *
-*     C := alpha*conjg( A' )*A + beta*C,
+*     C := alpha*A**H*A + beta*C,
 *
 *  where alpha and beta are real scalars, C is an n--by--n Hermitian
 *  matrix and A is an n--by--k matrix in the first case and a k--by--n
@@ -60,9 +60,9 @@ SUBROUTINE CHFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
 *           On entry,  TRANS  specifies the operation to be performed as
 *           follows:
 *
-*              TRANS = 'N' or 'n'   C := alpha*A*conjg( A' ) + beta*C.
+*              TRANS = 'N' or 'n'   C := alpha*A*A**H + beta*C.
 *
-*              TRANS = 'C' or 'c'   C := alpha*conjg( A' )*A + beta*C.
+*              TRANS = 'C' or 'c'   C := alpha*A**H*A + beta*C.
 *
 *           Unchanged on exit.
 *

SRC/chprfs.f

@@ -306,7 +306,7 @@ SUBROUTINE CHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(A').
+*              Multiply by diag(W)*inv(A**H).
 *
                CALL CHPTRS( UPLO, N, 1, AFP, IPIV, WORK, N, INFO )
                DO 110 I = 1, N