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Fix typos in comments (Reference-LAPACK PR 814)

This commit is contained in:
Martin Kroeker 2023-05-17 14:33:46 +02:00 committed by GitHub
parent 617e8bcfe7
commit a82c1443db
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GPG Key ID: 4AEE18F83AFDEB23
27 changed files with 59 additions and 61 deletions
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6
lapack-netlib/SRC/cgejsv.f
View File

@ -1819,7 +1819,7 @@
IF ( CONDR2 .GE. COND_OK ) THEN
* .. save the Householder vectors used for Q3
* (this overwrites the copy of R2, as it will not be
* needed in this branch, but it does not overwritte the
* needed in this branch, but it does not overwrite the
* Huseholder vectors of Q2.).
CALL CLACPY( 'U', NR, NR, V, LDV, CWORK(2*N+1), N )
* .. and the rest of the information on Q3 is in
@ -1842,7 +1842,7 @@
END IF
*
* Second preconditioning finished; continue with Jacobi SVD
* The input matrix is lower trinagular.
* The input matrix is lower triangular.
*
* Recover the right singular vectors as solution of a well
* conditioned triangular matrix equation.
@ -1886,7 +1886,7 @@
ELSE IF ( CONDR2 .LT. COND_OK ) THEN
*
* The matrix R2 is inverted. The solution of the matrix equation
* is Q3^* * V3 = the product of the Jacobi rotations (appplied to
* is Q3^* * V3 = the product of the Jacobi rotations (applied to
* the lower triangular L3 from the LQ factorization of
* R2=L3*Q3), pre-multiplied with the transposed Q3.
CALL CGESVJ( 'L', 'U', 'N', NR, NR, V, LDV, SVA, NR, U,

6
lapack-netlib/SRC/cgsvj0.f
View File

@ -117,7 +117,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -125,9 +125,9 @@
*> \param[in,out] V
*> \verbatim
*> V is COMPLEX array, dimension (LDV,N)
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

6
lapack-netlib/SRC/cgsvj1.f
View File

@ -147,7 +147,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -155,9 +155,9 @@
*> \param[in,out] V
*> \verbatim
*> V is COMPLEX array, dimension (LDV,N)
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

4
lapack-netlib/SRC/clalsa.f
View File

@ -42,9 +42,9 @@
*>
*> \verbatim
*>
*> CLALSA is an itermediate step in solving the least squares problem
*> CLALSA is an intermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> singular vectors are computed as products of simple orthorgonal
*> singular vectors are computed as products of simple orthogonal
*> matrices.).
*>
*> If ICOMPQ = 0, CLALSA applies the inverse of the left singular vector

2
lapack-netlib/SRC/cstegr.f
View File

@ -56,7 +56,7 @@
*>
*> Note : CSTEGR and CSTEMR work only on machines which follow
*> IEEE-754 floating-point standard in their handling of infinities and
*> NaNs. Normal execution may create these exceptiona values and hence
*> NaNs. Normal execution may create these exceptional values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
*> \endverbatim

2
lapack-netlib/SRC/ctgsen.f
View File

@ -339,7 +339,7 @@
*> [ kron(In2, B11) -kron(B22**H, In1) ].
*>
*> Here, Inx is the identity matrix of size nx and A22**H is the
*> conjuguate transpose of A22. kron(X, Y) is the Kronecker product between
*> conjugate transpose of A22. kron(X, Y) is the Kronecker product between
*> the matrices X and Y.
*>
*> When DIF(2) is small, small changes in (A, B) can cause large changes

8
lapack-netlib/SRC/dgejsv.f
View File

@ -362,7 +362,7 @@
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (M+3*N).
*> IWORK is INTEGER array, dimension (MAX(3,M+3*N)).
*> On exit,
*> IWORK(1) = the numerical rank determined after the initial
*> QR factorization with pivoting. See the descriptions
@ -1386,7 +1386,7 @@
IF ( CONDR2 .GE. COND_OK ) THEN
* .. save the Householder vectors used for Q3
* (this overwrites the copy of R2, as it will not be
* needed in this branch, but it does not overwritte the
* needed in this branch, but it does not overwrite the
* Huseholder vectors of Q2.).
CALL DLACPY( 'U', NR, NR, V, LDV, WORK(2*N+1), N )
* .. and the rest of the information on Q3 is in
@ -1409,7 +1409,7 @@
END IF
*
* Second preconditioning finished; continue with Jacobi SVD
* The input matrix is lower trinagular.
* The input matrix is lower triangular.
*
* Recover the right singular vectors as solution of a well
* conditioned triangular matrix equation.
@ -1454,7 +1454,7 @@
* :) .. the input matrix A is very likely a relative of
* the Kahan matrix :)
* The matrix R2 is inverted. The solution of the matrix equation
* is Q3^T*V3 = the product of the Jacobi rotations (appplied to
* is Q3^T*V3 = the product of the Jacobi rotations (applied to
* the lower triangular L3 from the LQ factorization of
* R2=L3*Q3), pre-multiplied with the transposed Q3.
CALL DGESVJ( 'L', 'U', 'N', NR, NR, V, LDV, SVA, NR, U,

6
lapack-netlib/SRC/dgsvj0.f
View File

@ -117,7 +117,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -125,9 +125,9 @@
*> \param[in,out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,N)
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

6
lapack-netlib/SRC/dgsvj1.f
View File

@ -147,7 +147,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -155,9 +155,9 @@
*> \param[in,out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,N)
*> If JOBV = 'V', then N rows of V are post-multipled by a
*> If JOBV = 'V', then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

4
lapack-netlib/SRC/dlalsa.f
View File

@ -43,9 +43,9 @@
*>
*> \verbatim
*>
*> DLALSA is an itermediate step in solving the least squares problem
*> DLALSA is an intermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> singular vectors are computed as products of simple orthorgonal
*> singular vectors are computed as products of simple orthogonal
*> matrices.).
*>
*> If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector

2
lapack-netlib/SRC/dlarre.f
View File

@ -51,7 +51,7 @@
*> DSTEMR to compute the eigenvectors of T.
*> The accuracy varies depending on whether bisection is used to
*> find a few eigenvalues or the dqds algorithm (subroutine DLASQ2) to
*> conpute all and then discard any unwanted one.
*> compute all and then discard any unwanted one.
*> As an added benefit, DLARRE also outputs the n
*> Gerschgorin intervals for the matrices L_i D_i L_i^T.
*> \endverbatim

2
lapack-netlib/SRC/dstegr.f
View File

@ -56,7 +56,7 @@
*>
*> Note : DSTEGR and DSTEMR work only on machines which follow
*> IEEE-754 floating-point standard in their handling of infinities and
*> NaNs. Normal execution may create these exceptiona values and hence
*> NaNs. Normal execution may create these exceptional values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
*> \endverbatim

5
lapack-netlib/SRC/dtgevc.f
View File

@ -52,7 +52,7 @@
*>
*> S*x = w*P*x, (y**H)*S = w*(y**H)*P,
*>
*> where y**H denotes the conjugate tranpose of y.
*> where y**H denotes the conjugate transpose of y.
*> The eigenvalues are not input to this routine, but are computed
*> directly from the diagonal blocks of S and P.
*>
@ -337,7 +337,7 @@
EXTERNAL LSAME, DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DGEMV, DLABAD, DLACPY, DLAG2, DLALN2, XERBLA
EXTERNAL DGEMV, DLACPY, DLAG2, DLALN2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
@ -463,7 +463,6 @@
*
SAFMIN = DLAMCH( 'Safe minimum' )
BIG = ONE / SAFMIN
CALL DLABAD( SAFMIN, BIG )
ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
SMALL = SAFMIN*N / ULP
BIG = ONE / SMALL

4
lapack-netlib/SRC/iparam2stage.F
View File

@ -89,14 +89,14 @@
*>
*> \param[in] NBI
*> \verbatim
*> NBI is INTEGER which is the used in the reduciton,
*> NBI is INTEGER which is the used in the reduction,
*> (e.g., the size of the band), needed to compute workspace
*> and LHOUS2.
*> \endverbatim
*>
*> \param[in] IBI
*> \verbatim
*> IBI is INTEGER which represent the IB of the reduciton,
*> IBI is INTEGER which represent the IB of the reduction,
*> needed to compute workspace and LHOUS2.
*> \endverbatim
*>

6
lapack-netlib/SRC/sgejsv.f
View File

@ -1386,7 +1386,7 @@
IF ( CONDR2 .GE. COND_OK ) THEN
* .. save the Householder vectors used for Q3
* (this overwrites the copy of R2, as it will not be
* needed in this branch, but it does not overwritte the
* needed in this branch, but it does not overwrite the
* Huseholder vectors of Q2.).
CALL SLACPY( 'U', NR, NR, V, LDV, WORK(2*N+1), N )
* .. and the rest of the information on Q3 is in
@ -1409,7 +1409,7 @@
END IF
*
* Second preconditioning finished; continue with Jacobi SVD
* The input matrix is lower trinagular.
* The input matrix is lower triangular.
*
* Recover the right singular vectors as solution of a well
* conditioned triangular matrix equation.
@ -1454,7 +1454,7 @@
* :) .. the input matrix A is very likely a relative of
* the Kahan matrix :)
* The matrix R2 is inverted. The solution of the matrix equation
* is Q3^T*V3 = the product of the Jacobi rotations (appplied to
* is Q3^T*V3 = the product of the Jacobi rotations (applied to
* the lower triangular L3 from the LQ factorization of
* R2=L3*Q3), pre-multiplied with the transposed Q3.
CALL SGESVJ( 'L', 'U', 'N', NR, NR, V, LDV, SVA, NR, U,

6
lapack-netlib/SRC/sgsvj0.f
View File

@ -117,7 +117,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -125,9 +125,9 @@
*> \param[in,out] V
*> \verbatim
*> V is REAL array, dimension (LDV,N)
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

6
lapack-netlib/SRC/sgsvj1.f
View File

@ -147,7 +147,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -155,9 +155,9 @@
*> \param[in,out] V
*> \verbatim
*> V is REAL array, dimension (LDV,N)
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

4
lapack-netlib/SRC/slalsa.f
View File

@ -43,9 +43,9 @@
*>
*> \verbatim
*>
*> SLALSA is an itermediate step in solving the least squares problem
*> SLALSA is an intermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> singular vectors are computed as products of simple orthorgonal
*> singular vectors are computed as products of simple orthogonal
*> matrices.).
*>
*> If ICOMPQ = 0, SLALSA applies the inverse of the left singular vector

2
lapack-netlib/SRC/slarre.f
View File

@ -51,7 +51,7 @@
*> SSTEMR to compute the eigenvectors of T.
*> The accuracy varies depending on whether bisection is used to
*> find a few eigenvalues or the dqds algorithm (subroutine SLASQ2) to
*> conpute all and then discard any unwanted one.
*> compute all and then discard any unwanted one.
*> As an added benefit, SLARRE also outputs the n
*> Gerschgorin intervals for the matrices L_i D_i L_i^T.
*> \endverbatim

2
lapack-netlib/SRC/sstegr.f
View File

@ -56,7 +56,7 @@
*>
*> Note : SSTEGR and SSTEMR work only on machines which follow
*> IEEE-754 floating-point standard in their handling of infinities and
*> NaNs. Normal execution may create these exceptiona values and hence
*> NaNs. Normal execution may create these exceptional values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
*> \endverbatim

5
lapack-netlib/SRC/stgevc.f
View File

@ -52,7 +52,7 @@
*>
*> S*x = w*P*x, (y**H)*S = w*(y**H)*P,
*>
*> where y**H denotes the conjugate tranpose of y.
*> where y**H denotes the conjugate transpose of y.
*> The eigenvalues are not input to this routine, but are computed
*> directly from the diagonal blocks of S and P.
*>
@ -337,7 +337,7 @@
EXTERNAL LSAME, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SGEMV, SLABAD, SLACPY, SLAG2, SLALN2, XERBLA
EXTERNAL SGEMV, SLACPY, SLAG2, SLALN2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
@ -463,7 +463,6 @@
*
SAFMIN = SLAMCH( 'Safe minimum' )
BIG = ONE / SAFMIN
CALL SLABAD( SAFMIN, BIG )
ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
SMALL = SAFMIN*N / ULP
BIG = ONE / SMALL

6
lapack-netlib/SRC/zgejsv.f
View File

@ -1821,7 +1821,7 @@
IF ( CONDR2 .GE. COND_OK ) THEN
* .. save the Householder vectors used for Q3
* (this overwrites the copy of R2, as it will not be
* needed in this branch, but it does not overwritte the
* needed in this branch, but it does not overwrite the
* Huseholder vectors of Q2.).
CALL ZLACPY( 'U', NR, NR, V, LDV, CWORK(2*N+1), N )
* .. and the rest of the information on Q3 is in
@ -1844,7 +1844,7 @@
END IF
*
* Second preconditioning finished; continue with Jacobi SVD
* The input matrix is lower trinagular.
* The input matrix is lower triangular.
*
* Recover the right singular vectors as solution of a well
* conditioned triangular matrix equation.
@ -1888,7 +1888,7 @@
ELSE IF ( CONDR2 .LT. COND_OK ) THEN
*
* The matrix R2 is inverted. The solution of the matrix equation
* is Q3^* * V3 = the product of the Jacobi rotations (appplied to
* is Q3^* * V3 = the product of the Jacobi rotations (applied to
* the lower triangular L3 from the LQ factorization of
* R2=L3*Q3), pre-multiplied with the transposed Q3.
CALL ZGESVJ( 'L', 'U', 'N', NR, NR, V, LDV, SVA, NR, U,

6
lapack-netlib/SRC/zgsvj0.f
View File

@ -117,7 +117,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -125,9 +125,9 @@
*> \param[in,out] V
*> \verbatim
*> V is COMPLEX*16 array, dimension (LDV,N)
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

6
lapack-netlib/SRC/zgsvj1.f
View File

@ -147,7 +147,7 @@
*> \param[in] MV
*> \verbatim
*> MV is INTEGER
*> If JOBV = 'A', then MV rows of V are post-multipled by a
*> If JOBV = 'A', then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then MV is not referenced.
*> \endverbatim
@ -155,9 +155,9 @@
*> \param[in,out] V
*> \verbatim
*> V is COMPLEX*16 array, dimension (LDV,N)
*> If JOBV = 'V' then N rows of V are post-multipled by a
*> If JOBV = 'V' then N rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'A' then MV rows of V are post-multipled by a
*> If JOBV = 'A' then MV rows of V are post-multiplied by a
*> sequence of Jacobi rotations.
*> If JOBV = 'N', then V is not referenced.
*> \endverbatim

4
lapack-netlib/SRC/zlalsa.f
View File

@ -42,9 +42,9 @@
*>
*> \verbatim
*>
*> ZLALSA is an itermediate step in solving the least squares problem
*> ZLALSA is an intermediate step in solving the least squares problem
*> by computing the SVD of the coefficient matrix in compact form (The
*> singular vectors are computed as products of simple orthorgonal
*> singular vectors are computed as products of simple orthogonal
*> matrices.).
*>
*> If ICOMPQ = 0, ZLALSA applies the inverse of the left singular vector

2
lapack-netlib/SRC/zstegr.f
View File

@ -56,7 +56,7 @@
*>
*> Note : ZSTEGR and ZSTEMR work only on machines which follow
*> IEEE-754 floating-point standard in their handling of infinities and
*> NaNs. Normal execution may create these exceptiona values and hence
*> NaNs. Normal execution may create these exceptional values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
*> \endverbatim

2
lapack-netlib/SRC/ztgsy2.f
View File

@ -57,7 +57,7 @@
*> Z = [ kron(In, A) -kron(B**H, Im) ] (2)
*> [ kron(In, D) -kron(E**H, Im) ],
*>
*> Ik is the identity matrix of size k and X**H is the conjuguate transpose of X.
*> Ik is the identity matrix of size k and X**H is the conjugate transpose of X.
*> kron(X, Y) is the Kronecker product between the matrices X and Y.
*>
*> If TRANS = 'C', y in the conjugate transposed system Z**H*y = scale*b