style: Fix typo in docstrings

Issues were identified using the open-source tool codespell [1]
running the following command from the source directory:

[1] https://github.com/codespell-project/codespell#readme


$ codespell -q6 \
  --skip=".git,Doxyfile,Doxyfile_man,CMakeLists.txt,Makefile" \
  --regex="\w[a-z\-\_]+" \
  --ignore-words-list="fro,ith,nd,noe,numer" \
  --summary

[...]

-------8<-------
SUMMARY:
acoording     2
agressive     8
ajust        12
arithmetics   5
comleted      2
contraints    8
equaly        4
everytime     4
febuary       1
matix         8
otherwize     4
overwrittes   4
owerflow      8
parmeter      4
permutaions  32
specturm      8

SRC/VARIANTS/README

@@ -34,7 +34,7 @@ References:For a more detailed description please refer to
 =========
 
 These variants are compiled by default in the build process but they are not tested by default.
-The build process creates one new library per variants in the four arithmetics (single real/double real/single complex/double complex).
+The build process creates one new library per variants in the four arithmetic (single real/double real/single complex/double complex).
 The libraries are in the SRC/VARIANTS directory.
 
 Corresponding libraries created in SRC/VARIANTS:

SRC/cgejsv.f

@@ -1763,7 +1763,7 @@ SUBROUTINE CGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
             ELSE
 *
 *              .. ill-conditioned case: second QRF with pivoting
-*              Note that windowed pivoting would be equaly good
+*              Note that windowed pivoting would be equally good
 *              numerically, and more run-time efficient. So, in
 *              an optimal implementation, the next call to CGEQP3
 *              should be replaced with eg. CALL CGEQPX (ACM TOMS #782)
@@ -1821,7 +1821,7 @@ SUBROUTINE CGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
 *
                IF ( CONDR2 .GE. COND_OK ) THEN
 *                 .. save the Householder vectors used for Q3
-*                 (this overwrittes the copy of R2, as it will not be
+*                 (this overwrites the copy of R2, as it will not be
 *                 needed in this branch, but it does not overwritte the
 *                 Huseholder vectors of Q2.).
                   CALL CLACPY( 'U', NR, NR, V, LDV, CWORK(2*N+1), N )

SRC/cgesc2.f

@@ -91,7 +91,7 @@
 *> \verbatim
 *>          SCALE is REAL
 *>           On exit, SCALE contains the scale factor. SCALE is chosen
-*>           0 <= SCALE <= 1 to prevent owerflow in the solution.
+*>           0 <= SCALE <= 1 to prevent overflow in the solution.
 *> \endverbatim
 *
 *  Authors:

SRC/cgesvdq.f

@@ -717,7 +717,7 @@ SUBROUTINE CGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
 *
 *        Standard absolute error bound suffices. All sigma_i with
 *        sigma_i < N*EPS*||A||_F are flushed to zero. This is an
-*        agressive enforcement of lower numerical rank by introducing a
+*        aggressive enforcement of lower numerical rank by introducing a
 *        backward error of the order of N*EPS*||A||_F.
          NR = 1  
          RTMP = SQRT(REAL(N))*EPSLN
@@ -728,7 +728,7 @@ SUBROUTINE CGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
  3002    CONTINUE          
 *
       ELSEIF ( ACCLM ) THEN 
-*        .. similarly as above, only slightly more gentle (less agressive).
+*        .. similarly as above, only slightly more gentle (less aggressive).
 *        Sudden drop on the diagonal of R is used as the criterion for being
 *        close-to-rank-deficient. The threshold is set to EPSLN=SLAMCH('E').
 *        [[This can be made more flexible by replacing this hard-coded value
@@ -1039,7 +1039,7 @@ SUBROUTINE CGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
 *            vectors of R**H  
 *               [[The optimal ratio N/NR for using QRF instead of padding 
 *                 with zeros. Here hard coded to 2; it must be at least 
-*                 two due to work space contraints.]]
+*                 two due to work space constraints.]]
 *               OPTRATIO = ILAENV(6, 'CGESVD', 'S' // 'O', NR,N,0,0)
 *               OPTRATIO = MAX( OPTRATIO, 2 ) 
                 OPTRATIO = 2 
@@ -1156,7 +1156,7 @@ SUBROUTINE CGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
 *               is then N1 (N or M)
 *               [[The optimal ratio N/NR for using LQ instead of padding 
 *                 with zeros. Here hard coded to 2; it must be at least 
-*                 two due to work space contraints.]]
+*                 two due to work space constraints.]]
 *               OPTRATIO = ILAENV(6, 'CGESVD', 'S' // 'O', NR,N,0,0)
 *               OPTRATIO = MAX( OPTRATIO, 2 ) 
                OPTRATIO = 2 

SRC/cgsvj1.f

@@ -61,7 +61,7 @@
 *> In terms of the columns of A, the first N1 columns are rotated 'against'
 *> the remaining N-N1 columns, trying to increase the angle between the
 *> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
-*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
+*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parameter.
 *> The number of sweeps is given in NSWEEP and the orthogonality threshold
 *> is given in TOL.
 *> \endverbatim

SRC/chetrd_he2hb.f

@@ -363,7 +363,7 @@ SUBROUTINE CHETRD_HE2HB( UPLO, N, KD, A, LDA, AB, LDAB, TAU,
 *
 *
 *     Set the workspace of the triangular matrix T to zero once such a
-*     way everytime T is generated the upper/lower portion will be always zero  
+*     way every time T is generated the upper/lower portion will be always zero
 *   
       CALL CLASET( "A", LDT, KD, ZERO, ZERO, WORK( TPOS ), LDT )
 *

SRC/chetrf_aa.f

@@ -256,7 +256,7 @@ SUBROUTINE CHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
      $                      A( MAX(1, J), J+1 ), LDA,
      $                      IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
 *
-*        Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*        Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
 *
          DO J2 = J+2, MIN(N, J+JB+1)
             IPIV( J2 ) = IPIV( J2 ) + J
@@ -376,7 +376,7 @@ SUBROUTINE CHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
      $                      A( J+1, MAX(1, J) ), LDA,
      $                      IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
 *
-*        Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*        Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
 *
          DO J2 = J+2, MIN(N, J+JB+1)
             IPIV( J2 ) = IPIV( J2 ) + J

SRC/chseqr.f

@@ -139,7 +139,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>           The leading dimension of the array Z.  if COMPZ = 'I' or
-*>           COMPZ = 'V', then LDZ >= MAX(1,N).  Otherwize, LDZ >= 1.
+*>           COMPZ = 'V', then LDZ >= MAX(1,N).  Otherwise, LDZ >= 1.
 *> \endverbatim
 *>
 *> \param[out] WORK

SRC/cla_wwaddw.f

@@ -36,7 +36,7 @@
 *>    CLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
 *>
 *>    This works for all extant IBM's hex and binary floating point
-*>    arithmetics, but not for decimal.
+*>    arithmetic, but not for decimal.
 *> \endverbatim
 *
 *  Arguments:

SRC/clahqr.f

@@ -148,7 +148,7 @@
 *>                  If INFO > 0 and WANTT is .FALSE., then on exit,
 *>                  the remaining unconverged eigenvalues are the
 *>                  eigenvalues of the upper Hessenberg matrix
-*>                  rows and columns ILO thorugh INFO of the final,
+*>                  rows and columns ILO through INFO of the final,
 *>                  output value of H.
 *>
 *>                  If INFO > 0 and WANTT is .TRUE., then on exit

SRC/csyconvf.f

@@ -294,7 +294,7 @@ SUBROUTINE CSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Convert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in factorization order where i decreases from N to 1
 *
             I = N
@@ -347,7 +347,7 @@ SUBROUTINE CSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Revert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in reverse factorization order where i increases from 1 to N
 *
             I = 1
@@ -438,7 +438,7 @@ SUBROUTINE CSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Convert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in factorization order where k increases from 1 to N
 *
             I = 1
@@ -491,7 +491,7 @@ SUBROUTINE CSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Revert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in reverse factorization order where i decreases from N to 1
 *
             I = N

SRC/csyconvf_rook.f

@@ -285,7 +285,7 @@ SUBROUTINE CSYCONVF_ROOK( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Convert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in factorization order where i decreases from N to 1
 *
             I = N
@@ -336,7 +336,7 @@ SUBROUTINE CSYCONVF_ROOK( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Revert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in reverse factorization order where i increases from 1 to N
 *
             I = 1
@@ -426,7 +426,7 @@ SUBROUTINE CSYCONVF_ROOK( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Convert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in factorization order where i increases from 1 to N
 *
             I = 1
@@ -477,7 +477,7 @@ SUBROUTINE CSYCONVF_ROOK( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Revert PERMUTATIONS
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in reverse factorization order where i decreases from N to 1
 *
             I = N

SRC/csytrf_aa.f

@@ -256,7 +256,7 @@ SUBROUTINE CSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
      $                   A( MAX(1, J), J+1 ), LDA,
      $                   IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
 *
-*        Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*        Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
 *
          DO J2 = J+2, MIN(N, J+JB+1)
             IPIV( J2 ) = IPIV( J2 ) + J
@@ -375,7 +375,7 @@ SUBROUTINE CSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
      $                   A( J+1, MAX(1, J) ), LDA,
      $                   IPIV( J+1 ), WORK, N, WORK( N*NB+1 ) )
 *
-*        Ajust IPIV and apply it back (J-th step picks (J+1)-th pivot)
+*        Adjust IPIV and apply it back (J-th step picks (J+1)-th pivot)
 *
          DO J2 = J+2, MIN(N, J+JB+1)
             IPIV( J2 ) = IPIV( J2 ) + J

SRC/dgejsv.f

@@ -1335,7 +1335,7 @@ SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
             ELSE
 *
 *              .. ill-conditioned case: second QRF with pivoting
-*              Note that windowed pivoting would be equaly good
+*              Note that windowed pivoting would be equally good
 *              numerically, and more run-time efficient. So, in
 *              an optimal implementation, the next call to DGEQP3
 *              should be replaced with eg. CALL SGEQPX (ACM TOMS #782)
@@ -1388,7 +1388,7 @@ SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
 *
                IF ( CONDR2 .GE. COND_OK ) THEN
 *                 .. save the Householder vectors used for Q3
-*                 (this overwrittes the copy of R2, as it will not be
+*                 (this overwrites the copy of R2, as it will not be
 *                 needed in this branch, but it does not overwritte the
 *                 Huseholder vectors of Q2.).
                   CALL DLACPY( 'U', NR, NR, V, LDV, WORK(2*N+1), N )

SRC/dgesc2.f

@@ -90,7 +90,7 @@
 *> \verbatim
 *>          SCALE is DOUBLE PRECISION
 *>          On exit, SCALE contains the scale factor. SCALE is chosen
-*>          0 <= SCALE <= 1 to prevent owerflow in the solution.
+*>          0 <= SCALE <= 1 to prevent overflow in the solution.
 *> \endverbatim
 *
 *  Authors:
@@ -151,7 +151,7 @@ SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )
 *     ..
 *     .. Executable Statements ..
 *
-*      Set constant to control owerflow
+*      Set constant to control overflow
 *
       EPS = DLAMCH( 'P' )
       SMLNUM = DLAMCH( 'S' ) / EPS

SRC/dgesvdq.f

@@ -717,7 +717,7 @@ SUBROUTINE DGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
 *
 *        Standard absolute error bound suffices. All sigma_i with
 *        sigma_i < N*EPS*||A||_F are flushed to zero. This is an
-*        agressive enforcement of lower numerical rank by introducing a
+*        aggressive enforcement of lower numerical rank by introducing a
 *        backward error of the order of N*EPS*||A||_F.
          NR = 1  
          RTMP = SQRT(DBLE(N))*EPSLN
@@ -728,7 +728,7 @@ SUBROUTINE DGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
  3002    CONTINUE          
 *
       ELSEIF ( ACCLM ) THEN 
-*        .. similarly as above, only slightly more gentle (less agressive).
+*        .. similarly as above, only slightly more gentle (less aggressive).
 *        Sudden drop on the diagonal of R is used as the criterion for being
 *        close-to-rank-deficient. The threshold is set to EPSLN=DLAMCH('E').
 *        [[This can be made more flexible by replacing this hard-coded value
@@ -1032,7 +1032,7 @@ SUBROUTINE DGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
 *            vectors of R**T 
 *               [[The optimal ratio N/NR for using QRF instead of padding 
 *                 with zeros. Here hard coded to 2; it must be at least 
-*                 two due to work space contraints.]]
+*                 two due to work space constraints.]]
 *               OPTRATIO = ILAENV(6, 'DGESVD', 'S' // 'O', NR,N,0,0)
 *               OPTRATIO = MAX( OPTRATIO, 2 ) 
                 OPTRATIO = 2 
@@ -1147,7 +1147,7 @@ SUBROUTINE DGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA,
 *               is then N1 (N or M)
 *               [[The optimal ratio N/NR for using LQ instead of padding 
 *                 with zeros. Here hard coded to 2; it must be at least 
-*                 two due to work space contraints.]]
+*                 two due to work space constraints.]]
 *               OPTRATIO = ILAENV(6, 'DGESVD', 'S' // 'O', NR,N,0,0)
 *               OPTRATIO = MAX( OPTRATIO, 2 ) 
                OPTRATIO = 2 

SRC/dgetc2.f

@@ -85,7 +85,7 @@
 *> \verbatim
 *>          INFO is INTEGER
 *>           = 0: successful exit
-*>           > 0: if INFO = k, U(k, k) is likely to produce owerflow if
+*>           > 0: if INFO = k, U(k, k) is likely to produce overflow if
 *>                we try to solve for x in Ax = b. So U is perturbed to
 *>                avoid the overflow.
 *> \endverbatim

SRC/dgsvj0.f

@@ -1045,7 +1045,7 @@ SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
 
  1993 CONTINUE
 *     end i=1:NSWEEP loop
-* #:) Reaching this point means that the procedure has comleted the given
+* #:) Reaching this point means that the procedure has completed the given
 *     number of iterations.
       INFO = NSWEEP - 1
       GO TO 1995

SRC/dgsvj1.f

@@ -61,7 +61,7 @@
 *> In terms of the columns of A, the first N1 columns are rotated 'against'
 *> the remaining N-N1 columns, trying to increase the angle between the
 *> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
-*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
+*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parameter.
 *> The number of sweeps is given in NSWEEP and the orthogonality threshold
 *> is given in TOL.
 *> \endverbatim

SRC/dhseqr.f

@@ -156,7 +156,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>           The leading dimension of the array Z.  if COMPZ = 'I' or
-*>           COMPZ = 'V', then LDZ >= MAX(1,N).  Otherwize, LDZ >= 1.
+*>           COMPZ = 'V', then LDZ >= MAX(1,N).  Otherwise, LDZ >= 1.
 *> \endverbatim
 *>
 *> \param[out] WORK

SRC/dla_wwaddw.f

@@ -36,7 +36,7 @@
 *>    DLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
 *>
 *>    This works for all extant IBM's hex and binary floating point
-*>    arithmetics, but not for decimal.
+*>    arithmetic, but not for decimal.
 *> \endverbatim
 *
 *  Arguments:

SRC/dlahqr.f

@@ -160,7 +160,7 @@
 *>                  If INFO > 0 and WANTT is .FALSE., then on exit,
 *>                  the remaining unconverged eigenvalues are the
 *>                  eigenvalues of the upper Hessenberg matrix rows
-*>                  and columns ILO thorugh INFO of the final, output
+*>                  and columns ILO through INFO of the final, output
 *>                  value of H.
 *>
 *>                  If INFO > 0 and WANTT is .TRUE., then on exit

SRC/dlatdf.f

@@ -85,7 +85,7 @@
 *>          RHS is DOUBLE PRECISION array, dimension (N)
 *>          On entry, RHS contains contributions from other subsystems.
 *>          On exit, RHS contains the solution of the subsystem with
-*>          entries acoording to the value of IJOB (see above).
+*>          entries according to the value of IJOB (see above).
 *> \endverbatim
 *>
 *> \param[in,out] RDSUM

SRC/dsyconvf.f

@@ -291,7 +291,7 @@ SUBROUTINE DSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Convert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in factorization order where i decreases from N to 1
 *
             I = N
@@ -344,7 +344,7 @@ SUBROUTINE DSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Revert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of upper part of A
+*           Apply permutations to submatrices of upper part of A
 *           in reverse factorization order where i increases from 1 to N
 *
             I = 1
@@ -435,7 +435,7 @@ SUBROUTINE DSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Convert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in factorization order where k increases from 1 to N
 *
             I = 1
@@ -488,7 +488,7 @@ SUBROUTINE DSYCONVF( UPLO, WAY, N, A, LDA, E, IPIV, INFO )
 *
 *           Revert PERMUTATIONS and IPIV
 *
-*           Apply permutaions to submatrices of lower part of A
+*           Apply permutations to submatrices of lower part of A
 *           in reverse factorization order where i decreases from N to 1
 *
             I = N