Fix typos in comments (Reference-LAPACK PR 814)

lapack-netlib/SRC/cgejsv.f

@@ -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,

lapack-netlib/SRC/cgsvj0.f

@@ -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

lapack-netlib/SRC/cgsvj1.f

@@ -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

lapack-netlib/SRC/clalsa.f

@@ -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

lapack-netlib/SRC/cstegr.f

@@ -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

lapack-netlib/SRC/ctgsen.f

@@ -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

lapack-netlib/SRC/dgejsv.f

@@ -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,

lapack-netlib/SRC/dgsvj0.f

@@ -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

lapack-netlib/SRC/dgsvj1.f

@@ -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

lapack-netlib/SRC/dlalsa.f

@@ -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

lapack-netlib/SRC/dlarre.f

@@ -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

lapack-netlib/SRC/dstegr.f

@@ -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

lapack-netlib/SRC/dtgevc.f

@@ -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

lapack-netlib/SRC/iparam2stage.F

@@ -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
 *>

lapack-netlib/SRC/sgejsv.f

@@ -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,

lapack-netlib/SRC/sgsvj0.f

@@ -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

lapack-netlib/SRC/sgsvj1.f

@@ -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

lapack-netlib/SRC/slalsa.f

@@ -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

lapack-netlib/SRC/slarre.f

@@ -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

lapack-netlib/SRC/sstegr.f

@@ -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

lapack-netlib/SRC/stgevc.f

@@ -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

lapack-netlib/SRC/zgejsv.f

@@ -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,

lapack-netlib/SRC/zgsvj0.f

@@ -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

lapack-netlib/SRC/zgsvj1.f

@@ -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

lapack-netlib/SRC/zlalsa.f

@@ -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

lapack-netlib/SRC/zstegr.f

@@ -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

lapack-netlib/SRC/ztgsy2.f

@@ -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