comments unified: homgenize notation for transpose (**T) and conjugate transpose (**H)

This commit continues changes made in:
* f295357 2011-04-02
* d9d50d1 2011-04-02
* 16973f0 2011-04-08

Author: jip

TESTING/EIG/cbdt01.f

@@ -28,13 +28,13 @@
 *> \verbatim
 *>
 *> CBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are unitary
+*>    A = Q * B * P**H
+*> where Q (m by min(m,n)) and P**H (min(m,n) by n) are unitary
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm( A - Q * B * P**H ) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -49,7 +49,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**H.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -78,7 +78,7 @@
 *> \verbatim
 *>          Q is COMPLEX array, dimension (LDQ,N)
 *>          The m by min(m,n) unitary matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -103,8 +103,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is COMPLEX array, dimension (LDPT,N)
-*>          The min(m,n) by n unitary matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n unitary matrix P**H in the reduction
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -127,7 +127,7 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:  norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -187,7 +187,7 @@ SUBROUTINE CBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**H one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -265,7 +265,7 @@ SUBROUTINE CBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *
       ANORM = CLANGE( '1', M, N, A, LDA, RWORK )
       EPS = SLAMCH( 'Precision' )

TESTING/EIG/cbdt02.f

@@ -27,7 +27,8 @@
 *>
 *> \verbatim
 *>
-*> CBDT02 tests the change of basis C = U' * B by computing the residual
+*> CBDT02 tests the change of basis C = U**H * B by computing the
+*> residual
 *>
 *>    RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
 *>
@@ -66,7 +67,7 @@
 *> \param[in] C
 *> \verbatim
 *>          C is COMPLEX array, dimension (LDC,N)
-*>          The m by n matrix C, assumed to contain U' * B.
+*>          The m by n matrix C, assumed to contain U**H * B.
 *> \endverbatim
 *>
 *> \param[in] LDC

TESTING/EIG/dbdt01.f

@@ -27,13 +27,13 @@
 *> \verbatim
 *>
 *> DBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are orthogonal
+*>    A = Q * B * P**T
+*> where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm( A - Q * B * P**T ) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -48,7 +48,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**T.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -77,7 +77,7 @@
 *> \verbatim
 *>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
 *>          The m by min(m,n) orthogonal matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -102,8 +102,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is DOUBLE PRECISION array, dimension (LDPT,N)
-*>          The min(m,n) by n orthogonal matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n orthogonal matrix P**T in the reduction
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -121,7 +121,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:
+*>          norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -180,7 +181,7 @@ SUBROUTINE DBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**T one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -258,7 +259,7 @@ SUBROUTINE DBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *
       ANORM = DLANGE( '1', M, N, A, LDA, WORK )
       EPS = DLAMCH( 'Precision' )

TESTING/EIG/dbdt02.f

@@ -25,7 +25,8 @@
 *>
 *> \verbatim
 *>
-*> DBDT02 tests the change of basis C = U' * B by computing the residual
+*> DBDT02 tests the change of basis C = U**H * B by computing the
+*> residual
 *>
 *>    RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
 *>
@@ -64,7 +65,7 @@
 *> \param[in] C
 *> \verbatim
 *>          C is DOUBLE PRECISION array, dimension (LDC,N)
-*>          The m by n matrix C, assumed to contain U' * B.
+*>          The m by n matrix C, assumed to contain U**H * B.
 *> \endverbatim
 *>
 *> \param[in] LDC

TESTING/EIG/dlarhs.f

@@ -30,7 +30,7 @@
 *> DLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
 *>    op( A ) * X = B,
-*> where op( A ) may be A or A' (transpose of A).
+*> where op( A ) = A or A**T, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -81,8 +81,8 @@
 *>          TRANS is CHARACTER*1
 *>          Specifies the operation applied to the matrix A.
 *>          = 'N':  System is  A * x = b
-*>          = 'T':  System is  A'* x = b
-*>          = 'C':  System is  A'* x = b
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] M

TESTING/EIG/sbdt01.f

@@ -27,13 +27,13 @@
 *> \verbatim
 *>
 *> SBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are orthogonal
+*>    A = Q * B * P**T
+*> where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm( A - Q * B * P**T ) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -48,7 +48,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**T.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -77,7 +77,7 @@
 *> \verbatim
 *>          Q is REAL array, dimension (LDQ,N)
 *>          The m by min(m,n) orthogonal matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -102,8 +102,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is REAL array, dimension (LDPT,N)
-*>          The min(m,n) by n orthogonal matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n orthogonal matrix P**T in the reduction
+*>          A = Q * B * P**T.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -121,7 +121,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is REAL
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:
+*>          norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -180,7 +181,7 @@ SUBROUTINE SBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**T one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -258,7 +259,7 @@ SUBROUTINE SBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
 *
       ANORM = SLANGE( '1', M, N, A, LDA, WORK )
       EPS = SLAMCH( 'Precision' )

TESTING/EIG/sbdt02.f

@@ -25,7 +25,8 @@
 *>
 *> \verbatim
 *>
-*> SBDT02 tests the change of basis C = U' * B by computing the residual
+*> SBDT02 tests the change of basis C = U**H * B by computing the
+*> residual
 *>
 *>    RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ),
 *>
@@ -64,7 +65,7 @@
 *> \param[in] C
 *> \verbatim
 *>          C is REAL array, dimension (LDC,N)
-*>          The m by n matrix C, assumed to contain U' * B.
+*>          The m by n matrix C, assumed to contain U**H * B.
 *> \endverbatim
 *>
 *> \param[in] LDC

TESTING/EIG/slarhs.f

@@ -30,7 +30,7 @@
 *> SLARHS chooses a set of NRHS random solution vectors and sets
 *> up the right hand sides for the linear system
 *>    op( A ) * X = B,
-*> where op( A ) may be A or A' (transpose of A).
+*> where op( A ) = A or A**T, depending on TRANS.
 *> \endverbatim
 *
 *  Arguments:
@@ -81,8 +81,8 @@
 *>          TRANS is CHARACTER*1
 *>          Specifies the operation applied to the matrix A.
 *>          = 'N':  System is  A * x = b
-*>          = 'T':  System is  A'* x = b
-*>          = 'C':  System is  A'* x = b
+*>          = 'T':  B := A**T * X  (Transpose)
+*>          = 'C':  B := A**H * X  (Conjugate transpose = Transpose)
 *> \endverbatim
 *>
 *> \param[in] M

TESTING/EIG/zbdt01.f

@@ -28,13 +28,13 @@
 *> \verbatim
 *>
 *> ZBDT01 reconstructs a general matrix A from its bidiagonal form
-*>    A = Q * B * P'
-*> where Q (m by min(m,n)) and P' (min(m,n) by n) are unitary
+*>    A = Q * B * P**H
+*> where Q (m by min(m,n)) and P**H (min(m,n) by n) are unitary
 *> matrices and B is bidiagonal.
 *>
 *> The test ratio to test the reduction is
-*>    RESID = norm( A - Q * B * PT ) / ( n * norm(A) * EPS )
-*> where PT = P' and EPS is the machine precision.
+*>    RESID = norm( A - Q * B * P**H ) / ( n * norm(A) * EPS )
+*> where EPS is the machine precision.
 *> \endverbatim
 *
 *  Arguments:
@@ -49,7 +49,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>          The number of columns of the matrices A and P'.
+*>          The number of columns of the matrices A and P**H.
 *> \endverbatim
 *>
 *> \param[in] KD
@@ -78,7 +78,7 @@
 *> \verbatim
 *>          Q is COMPLEX*16 array, dimension (LDQ,N)
 *>          The m by min(m,n) unitary matrix Q in the reduction
-*>          A = Q * B * P'.
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDQ
@@ -103,8 +103,8 @@
 *> \param[in] PT
 *> \verbatim
 *>          PT is COMPLEX*16 array, dimension (LDPT,N)
-*>          The min(m,n) by n unitary matrix P' in the reduction
-*>          A = Q * B * P'.
+*>          The min(m,n) by n unitary matrix P**H in the reduction
+*>          A = Q * B * P**H.
 *> \endverbatim
 *>
 *> \param[in] LDPT
@@ -127,7 +127,8 @@
 *> \param[out] RESID
 *> \verbatim
 *>          RESID is DOUBLE PRECISION
-*>          The test ratio:  norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*>          The test ratio:
+*>          norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *> \endverbatim
 *
 *  Authors:
@@ -187,7 +188,7 @@ SUBROUTINE ZBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          RETURN
       END IF
 *
-*     Compute A - Q * B * P' one column at a time.
+*     Compute A - Q * B * P**H one column at a time.
 *
       RESID = ZERO
       IF( KD.NE.0 ) THEN
@@ -265,7 +266,7 @@ SUBROUTINE ZBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
          END IF
       END IF
 *
-*     Compute norm(A - Q * B * P') / ( n * norm(A) * EPS )
+*     Compute norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
 *
       ANORM = ZLANGE( '1', M, N, A, LDA, RWORK )
       EPS = DLAMCH( 'Precision' )