Update LAPACK to 3.9.0

lapack-netlib/SRC/zcgesv.f

@@ -93,9 +93,9 @@
 *>          dimension (LDA,N)
 *>          On entry, the N-by-N coefficient matrix A.
 *>          On exit, if iterative refinement has been successfully used
-*>          (INFO.EQ.0 and ITER.GE.0, see description below), then A is
+*>          (INFO = 0 and ITER >= 0, see description below), then A is
 *>          unchanged, if double precision factorization has been used
-*>          (INFO.EQ.0 and ITER.LT.0, see description below), then the
+*>          (INFO = 0 and ITER < 0, see description below), then the
 *>          array A contains the factors L and U from the factorization
 *>          A = P*L*U; the unit diagonal elements of L are not stored.
 *> \endverbatim
@@ -112,8 +112,8 @@
 *>          The pivot indices that define the permutation matrix P;
 *>          row i of the matrix was interchanged with row IPIV(i).
 *>          Corresponds either to the single precision factorization
-*>          (if INFO.EQ.0 and ITER.GE.0) or the double precision
-*>          factorization (if INFO.EQ.0 and ITER.LT.0).
+*>          (if INFO = 0 and ITER >= 0) or the double precision
+*>          factorization (if INFO = 0 and ITER < 0).
 *> \endverbatim
 *>
 *> \param[in] B
@@ -421,7 +421,7 @@
    30 CONTINUE
 *
 *     If we are at this place of the code, this is because we have
-*     performed ITER=ITERMAX iterations and never satisified the stopping
+*     performed ITER=ITERMAX iterations and never satisfied the stopping
 *     criterion, set up the ITER flag accordingly and follow up on double
 *     precision routine.
 *

lapack-netlib/SRC/zcposv.f

@@ -111,9 +111,9 @@
 *>          elements need not be set and are assumed to be zero.
 *>
 *>          On exit, if iterative refinement has been successfully used
-*>          (INFO.EQ.0 and ITER.GE.0, see description below), then A is
+*>          (INFO = 0 and ITER >= 0, see description below), then A is
 *>          unchanged, if double precision factorization has been used
-*>          (INFO.EQ.0 and ITER.LT.0, see description below), then the
+*>          (INFO = 0 and ITER < 0, see description below), then the
 *>          array A contains the factor U or L from the Cholesky
 *>          factorization A = U**H*U or A = L*L**H.
 *> \endverbatim
@@ -431,7 +431,7 @@
    30 CONTINUE
 *
 *     If we are at this place of the code, this is because we have
-*     performed ITER=ITERMAX iterations and never satisified the
+*     performed ITER=ITERMAX iterations and never satisfied the
 *     stopping criterion, set up the ITER flag accordingly and follow
 *     up on double precision routine.
 *

lapack-netlib/SRC/zgbrfsx.f

@@ -75,7 +75,7 @@
 *>     Specifies the form of the system of equations:
 *>       = 'N':  A * X = B     (No transpose)
 *>       = 'T':  A**T * X = B  (Transpose)
-*>       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
+*>       = 'C':  A**H * X = B  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] EQUED
@@ -308,7 +308,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -344,14 +344,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -359,9 +359,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/zgbsvxx.f

@@ -431,7 +431,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -467,14 +467,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -482,9 +482,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the extra-precise refinement algorithm.
+*>            = 1.0:  Use the extra-precise refinement algorithm.
 *>              (other values are reserved for future use)
 *>
 *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

lapack-netlib/SRC/zgebak.f

@@ -48,10 +48,10 @@
 *> \verbatim
 *>          JOB is CHARACTER*1
 *>          Specifies the type of backward transformation required:
-*>          = 'N', do nothing, return immediately;
-*>          = 'P', do backward transformation for permutation only;
-*>          = 'S', do backward transformation for scaling only;
-*>          = 'B', do backward transformations for both permutation and
+*>          = 'N': do nothing, return immediately;
+*>          = 'P': do backward transformation for permutation only;
+*>          = 'S': do backward transformation for scaling only;
+*>          = 'B': do backward transformations for both permutation and
 *>                 scaling.
 *>          JOB must be the same as the argument JOB supplied to ZGEBAL.
 *> \endverbatim

lapack-netlib/SRC/zgeev.f

@@ -157,7 +157,7 @@
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
 *>          > 0:  if INFO = i, the QR algorithm failed to compute all the
 *>                eigenvalues, and no eigenvectors have been computed;
-*>                elements and i+1:N of W contain eigenvalues which have
+*>                elements i+1:N of W contain eigenvalues which have
 *>                converged.
 *> \endverbatim
 *

lapack-netlib/SRC/zgejsv.f

@@ -80,13 +80,13 @@
 *>              desirable, then this option is advisable. The input matrix A
 *>              is preprocessed with QR factorization with FULL (row and
 *>              column) pivoting.
-*>       = 'G'  Computation as with 'F' with an additional estimate of the
+*>       = 'G': Computation as with 'F' with an additional estimate of the
 *>              condition number of B, where A=B*D. If A has heavily weighted
 *>              rows, then using this condition number gives too pessimistic
 *>              error bound.
 *>       = 'A': Small singular values are not well determined by the data 
 *>              and are considered as noisy; the matrix is treated as
-*>              numerically rank defficient. The error in the computed
+*>              numerically rank deficient. The error in the computed
 *>              singular values is bounded by f(m,n)*epsilon*||A||.
 *>              The computed SVD A = U * S * V^* restores A up to
 *>              f(m,n)*epsilon*||A||.
@@ -117,7 +117,7 @@
 *>       = 'V': N columns of V are returned in the array V; Jacobi rotations
 *>              are not explicitly accumulated.
 *>       = 'J': N columns of V are returned in the array V, but they are
-*>              computed as the product of Jacobi rotations, if JOBT .EQ. 'N'.
+*>              computed as the product of Jacobi rotations, if JOBT = 'N'.
 *>       = 'W': V may be used as workspace of length N*N. See the description
 *>              of V.
 *>       = 'N': V is not computed.
@@ -131,7 +131,7 @@
 *>         specified range. If A .NE. 0 is scaled so that the largest singular
 *>         value of c*A is around SQRT(BIG), BIG=DLAMCH('O'), then JOBR issues
 *>         the licence to kill columns of A whose norm in c*A is less than
-*>         SQRT(SFMIN) (for JOBR.EQ.'R'), or less than SMALL=SFMIN/EPSLN,
+*>         SQRT(SFMIN) (for JOBR = 'R'), or less than SMALL=SFMIN/EPSLN,
 *>         where SFMIN=DLAMCH('S'), EPSLN=DLAMCH('E').
 *>       = 'N': Do not kill small columns of c*A. This option assumes that
 *>              BLAS and QR factorizations and triangular solvers are
@@ -229,7 +229,7 @@
 *>          If JOBU = 'F', then U contains on exit the M-by-M matrix of
 *>                         the left singular vectors, including an ONB
 *>                         of the orthogonal complement of the Range(A).
-*>          If JOBU = 'W'  .AND. (JOBV.EQ.'V' .AND. JOBT.EQ.'T' .AND. M.EQ.N),
+*>          If JOBU = 'W'  .AND. (JOBV = 'V' .AND. JOBT = 'T' .AND. M = N),
 *>                         then U is used as workspace if the procedure
 *>                         replaces A with A^*. In that case, [V] is computed
 *>                         in U as left singular vectors of A^* and then
@@ -251,7 +251,7 @@
 *>          V is COMPLEX*16 array, dimension ( LDV, N )
 *>          If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
 *>                         the right singular vectors;
-*>          If JOBV = 'W', AND (JOBU.EQ.'U' AND JOBT.EQ.'T' AND M.EQ.N),
+*>          If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
 *>                         then V is used as workspace if the pprocedure
 *>                         replaces A with A^*. In that case, [U] is computed
 *>                         in V as right singular vectors of A^* and then
@@ -282,7 +282,7 @@
 *>          Length of CWORK to confirm proper allocation of workspace.
 *>          LWORK depends on the job:
 *>
-*>          1. If only SIGMA is needed ( JOBU.EQ.'N', JOBV.EQ.'N' ) and
+*>          1. If only SIGMA is needed ( JOBU = 'N', JOBV = 'N' ) and
 *>            1.1 .. no scaled condition estimate required (JOBA.NE.'E'.AND.JOBA.NE.'G'):
 *>               LWORK >= 2*N+1. This is the minimal requirement.
 *>               ->> For optimal performance (blocked code) the optimal value
@@ -298,9 +298,9 @@
 *>               In general, the optimal length LWORK is computed as
 *>               LWORK >= max(N+LWORK(ZGEQP3),N+LWORK(ZGEQRF), LWORK(ZGESVJ),
 *>                            N*N+LWORK(ZPOCON)).
-*>          2. If SIGMA and the right singular vectors are needed (JOBV.EQ.'V'),
-*>             (JOBU.EQ.'N')
-*>            2.1   .. no scaled condition estimate requested (JOBE.EQ.'N'):    
+*>          2. If SIGMA and the right singular vectors are needed (JOBV = 'V'),
+*>             (JOBU = 'N')
+*>            2.1   .. no scaled condition estimate requested (JOBE = 'N'):    
 *>            -> the minimal requirement is LWORK >= 3*N.
 *>            -> For optimal performance, 
 *>               LWORK >= max(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
@@ -318,10 +318,10 @@
 *>               LWORK >= max(N+LWORK(ZGEQP3), LWORK(ZPOCON), N+LWORK(ZGESVJ),
 *>                       N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)).   
 *>          3. If SIGMA and the left singular vectors are needed
-*>            3.1  .. no scaled condition estimate requested (JOBE.EQ.'N'):
+*>            3.1  .. no scaled condition estimate requested (JOBE = 'N'):
 *>            -> the minimal requirement is LWORK >= 3*N.
 *>            -> For optimal performance:
-*>               if JOBU.EQ.'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
+*>               if JOBU = 'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
 *>               where NB is the optimal block size for ZGEQP3, ZGEQRF, ZUNMQR.
 *>               In general, the optimal length LWORK is computed as
 *>               LWORK >= max(N+LWORK(ZGEQP3), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMQR)). 
@@ -329,15 +329,15 @@
 *>               required (JOBA='E', or 'G').
 *>            -> the minimal requirement is LWORK >= 3*N.
 *>            -> For optimal performance:
-*>               if JOBU.EQ.'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
+*>               if JOBU = 'U' :: LWORK >= max(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB,
 *>               where NB is the optimal block size for ZGEQP3, ZGEQRF, ZUNMQR.
 *>               In general, the optimal length LWORK is computed as
 *>               LWORK >= max(N+LWORK(ZGEQP3),N+LWORK(ZPOCON),
 *>                        2*N+LWORK(ZGEQRF), N+LWORK(ZUNMQR)).
-*>          4. If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and 
-*>            4.1. if JOBV.EQ.'V'  
+*>          4. If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and 
+*>            4.1. if JOBV = 'V'  
 *>               the minimal requirement is LWORK >= 5*N+2*N*N. 
-*>            4.2. if JOBV.EQ.'J' the minimal requirement is 
+*>            4.2. if JOBV = 'J' the minimal requirement is 
 *>               LWORK >= 4*N+N*N.
 *>            In both cases, the allocated CWORK can accommodate blocked runs
 *>            of ZGEQP3, ZGEQRF, ZGELQF, SUNMQR, ZUNMLQ.
@@ -356,7 +356,7 @@
 *>                    of A. (See the description of SVA().)
 *>          RWORK(2) = See the description of RWORK(1).
 *>          RWORK(3) = SCONDA is an estimate for the condition number of
-*>                    column equilibrated A. (If JOBA .EQ. 'E' or 'G')
+*>                    column equilibrated A. (If JOBA = 'E' or 'G')
 *>                    SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1).
 *>                    It is computed using SPOCON. It holds
 *>                    N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA
@@ -375,7 +375,7 @@
 *>                    triangular factor in the first QR factorization.
 *>          RWORK(5) = an estimate of the scaled condition number of the
 *>                    triangular factor in the second QR factorization.
-*>          The following two parameters are computed if JOBT .EQ. 'T'.
+*>          The following two parameters are computed if JOBT = 'T'.
 *>          They are provided for a developer/implementer who is familiar
 *>          with the details of the method.
 *>          RWORK(6) = the entropy of A^* * A :: this is the Shannon entropy
@@ -456,23 +456,23 @@
 *>                     of JOBA and JOBR.
 *>          IWORK(2) = the number of the computed nonzero singular values
 *>          IWORK(3) = if nonzero, a warning message:
-*>                     If IWORK(3).EQ.1 then some of the column norms of A
+*>                     If IWORK(3) = 1 then some of the column norms of A
 *>                     were denormalized floats. The requested high accuracy
 *>                     is not warranted by the data.
-*>          IWORK(4) = 1 or -1. If IWORK(4) .EQ. 1, then the procedure used A^* to
+*>          IWORK(4) = 1 or -1. If IWORK(4) = 1, then the procedure used A^* to
 *>                     do the job as specified by the JOB parameters.
-*>          If the call to ZGEJSV is a workspace query (indicated by LWORK .EQ. -1 or
-*>          LRWORK .EQ. -1), then on exit IWORK(1) contains the required length of 
+*>          If the call to ZGEJSV is a workspace query (indicated by LWORK = -1 or
+*>          LRWORK = -1), then on exit IWORK(1) contains the required length of 
 *>          IWORK for the job parameters used in the call.
 *> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>           < 0  : if INFO = -i, then the i-th argument had an illegal value.
-*>           = 0 :  successful exit;
-*>           > 0 :  ZGEJSV  did not converge in the maximal allowed number
-*>                  of sweeps. The computed values may be inaccurate.
+*>           < 0:  if INFO = -i, then the i-th argument had an illegal value.
+*>           = 0:  successful exit;
+*>           > 0:  ZGEJSV  did not converge in the maximal allowed number
+*>                 of sweeps. The computed values may be inaccurate.
 *> \endverbatim
 *
 *  Authors:
@@ -1338,7 +1338,7 @@
       IF ( L2ABER ) THEN
 *        Standard absolute error bound suffices. All sigma_i with
 *        sigma_i < N*EPSLN*||A|| 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*EPSLN*||A||.
          TEMP1 = SQRT(DBLE(N))*EPSLN
          DO 3001 p = 2, N
@@ -1350,7 +1350,7 @@
  3001    CONTINUE
  3002    CONTINUE
       ELSE IF ( L2RANK ) 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 R1 is used as the criterion for
 *        close-to-rank-deficient.
          TEMP1 = SQRT(SFMIN)
@@ -1720,7 +1720,7 @@
             CALL ZPOCON('L',NR,CWORK(2*N+1),NR,ONE,TEMP1,
      $                   CWORK(2*N+NR*NR+1),RWORK,IERR)
             CONDR1 = ONE / SQRT(TEMP1)
-*           .. here need a second oppinion on the condition number
+*           .. here need a second opinion on the condition number
 *           .. then assume worst case scenario
 *           R1 is OK for inverse <=> CONDR1 .LT. DBLE(N)
 *           more conservative    <=> CONDR1 .LT. SQRT(DBLE(N))
@@ -1765,7 +1765,7 @@
             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 ZGEQP3
 *              should be replaced with eg. CALL ZGEQPX (ACM TOMS #782)
@@ -1823,7 +1823,7 @@
 *
                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 ZLACPY( 'U', NR, NR, V, LDV, CWORK(2*N+1), N )
@@ -2079,7 +2079,7 @@
 *
 *        This branch deploys a preconditioned Jacobi SVD with explicitly
 *        accumulated rotations. It is included as optional, mainly for
-*        experimental purposes. It does perfom well, and can also be used.
+*        experimental purposes. It does perform well, and can also be used.
 *        In this implementation, this branch will be automatically activated
 *        if the  condition number sigma_max(A) / sigma_min(A) is predicted
 *        to be greater than the overflow threshold. This is because the

lapack-netlib/SRC/zgelq.f

@@ -1,3 +1,4 @@
+*> \brief \b ZGELQ
 *
 *  Definition:
 *  ===========
@@ -17,7 +18,17 @@
 *  =============
 *>
 *> \verbatim
-*> ZGELQ computes a LQ factorization of an M-by-N matrix A.
+*>
+*> ZGELQ computes an LQ factorization of a complex M-by-N matrix A:
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a N-by-N orthogonal matrix;
+*>    L is an lower-triangular M-by-M matrix;
+*>    0 is a M-by-(N-M) zero matrix, if M < N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -138,7 +149,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>
@@ -159,10 +170,10 @@
       SUBROUTINE ZGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N, TSIZE, LWORK

lapack-netlib/SRC/zgelq2.f

@@ -33,8 +33,16 @@
 *>
 *> \verbatim
 *>
-*> ZGELQ2 computes an LQ factorization of a complex m by n matrix A:
-*> A = L * Q.
+*> ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A:
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a n-by-n orthogonal matrix;
+*>    L is an lower-triangular m-by-m matrix;
+*>    0 is a m-by-(n-m) zero matrix, if m < n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -96,7 +104,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complex16GEcomputational
 *
@@ -121,10 +129,10 @@
 *  =====================================================================
       SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/zgelqf.f

@@ -34,7 +34,15 @@
 *> \verbatim
 *>
 *> ZGELQF computes an LQ factorization of a complex M-by-N matrix A:
-*> A = L * Q.
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a N-by-N orthogonal matrix;
+*>    L is an lower-triangular M-by-M matrix;
+*>    0 is a M-by-(N-M) zero matrix, if M < N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -110,7 +118,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complex16GEcomputational
 *
@@ -135,10 +143,10 @@
 *  =====================================================================
       SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/zgemlq.f

@@ -1,3 +1,4 @@
+*> \brief \b ZGEMLQ
 *
 *  Definition:
 *  ===========
@@ -142,7 +143,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>

lapack-netlib/SRC/zgemqr.f

@@ -1,3 +1,4 @@
+*> \brief \b ZGEMQR
 *
 *  Definition:
 *  ===========
@@ -144,7 +145,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>

lapack-netlib/SRC/zgeqr.f

@@ -1,3 +1,4 @@
+*> \brief \b ZGEQR
 *
 *  Definition:
 *  ===========
@@ -17,7 +18,18 @@
 *  =============
 *>
 *> \verbatim
-*> ZGEQR computes a QR factorization of an M-by-N matrix A.
+*>
+*> ZGEQR computes a QR factorization of a complex M-by-N matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -138,7 +150,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>
@@ -160,10 +172,10 @@
       SUBROUTINE ZGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N, TSIZE, LWORK

lapack-netlib/SRC/zgeqr2.f

@@ -33,8 +33,17 @@
 *>
 *> \verbatim
 *>
-*> ZGEQR2 computes a QR factorization of a complex m by n matrix A:
-*> A = Q * R.
+*> ZGEQR2 computes a QR factorization of a complex m-by-n matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a m-by-m orthogonal matrix;
+*>    R is an upper-triangular n-by-n matrix;
+*>    0 is a (m-n)-by-n zero matrix, if m > n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -96,7 +105,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complex16GEcomputational
 *
@@ -121,10 +130,10 @@
 *  =====================================================================
       SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/zgeqr2p.f

@@ -33,8 +33,18 @@
 *>
 *> \verbatim
 *>
-*> ZGEQR2P computes a QR factorization of a complex m by n matrix A:
-*> A = Q * R. The diagonal entries of R are real and nonnegative.
+*> ZGEQR2P computes a QR factorization of a complex m-by-n matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a m-by-m orthogonal matrix;
+*>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
+*>    entries;
+*>    0 is a (m-n)-by-n zero matrix, if m > n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -97,7 +107,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complex16GEcomputational
 *
@@ -124,10 +134,10 @@
 *  =====================================================================
       SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/zgeqrf.f

@@ -34,7 +34,16 @@
 *> \verbatim
 *>
 *> ZGEQRF computes a QR factorization of a complex M-by-N matrix A:
-*> A = Q * R.
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -111,7 +120,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complex16GEcomputational
 *
@@ -136,10 +145,10 @@
 *  =====================================================================
       SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/zgeqrfp.f

@@ -33,8 +33,18 @@
 *>
 *> \verbatim
 *>
-*> ZGEQRFP computes a QR factorization of a complex M-by-N matrix A:
-*> A = Q * R. The diagonal entries of R are real and nonnegative.
+*> ZGEQR2P computes a QR factorization of a complex M-by-N matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix with nonnegative diagonal
+*>    entries;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -112,7 +122,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup complex16GEcomputational
 *
@@ -139,10 +149,10 @@
 *  =====================================================================
       SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/zgerfsx.f

@@ -74,7 +74,7 @@
 *>     Specifies the form of the system of equations:
 *>       = 'N':  A * X = B     (No transpose)
 *>       = 'T':  A**T * X = B  (Transpose)
-*>       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
+*>       = 'C':  A**H * X = B  (Conjugate transpose)
 *> \endverbatim
 *>
 *> \param[in] EQUED
@@ -283,7 +283,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -319,14 +319,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -334,9 +334,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/zgesc2.f

@@ -91,7 +91,7 @@
 *> \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:

lapack-netlib/SRC/zgesvdx.f

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*     SUBROUTINE CGESVDX( JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU,
+*     SUBROUTINE ZGESVDX( JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU,
 *    $                    IL, IU, NS, S, U, LDU, VT, LDVT, WORK,
 *    $                    LWORK, RWORK, IWORK, INFO )
 *

lapack-netlib/SRC/zgesvj.f

@@ -89,12 +89,12 @@
 *>          Specifies whether to compute the right singular vectors, that
 *>          is, the matrix V:
 *>          = 'V' or 'J': the matrix V is computed and returned in the array V
-*>          = 'A' : the Jacobi rotations are applied to the MV-by-N
+*>          = 'A':  the Jacobi rotations are applied to the MV-by-N
 *>                  array V. In other words, the right singular vector
 *>                  matrix V is not computed explicitly; instead it is
 *>                  applied to an MV-by-N matrix initially stored in the
 *>                  first MV rows of V.
-*>          = 'N' : the matrix V is not computed and the array V is not
+*>          = 'N':  the matrix V is not computed and the array V is not
 *>                  referenced
 *> \endverbatim
 *>
@@ -116,8 +116,8 @@
 *>          A is COMPLEX*16 array, dimension (LDA,N)
 *>          On entry, the M-by-N matrix A.
 *>          On exit,
-*>          If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C':
-*>                 If INFO .EQ. 0 :
+*>          If JOBU = 'U' .OR. JOBU = 'C':
+*>                 If INFO = 0 :
 *>                 RANKA orthonormal columns of U are returned in the
 *>                 leading RANKA columns of the array A. Here RANKA <= N
 *>                 is the number of computed singular values of A that are
@@ -127,9 +127,9 @@
 *>                 in the array RWORK as RANKA=NINT(RWORK(2)). Also see the
 *>                 descriptions of SVA and RWORK. The computed columns of U
 *>                 are mutually numerically orthogonal up to approximately
-*>                 TOL=SQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'),
+*>                 TOL=SQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU = 'C'),
 *>                 see the description of JOBU.
-*>                 If INFO .GT. 0,
+*>                 If INFO > 0,
 *>                 the procedure ZGESVJ did not converge in the given number
 *>                 of iterations (sweeps). In that case, the computed
 *>                 columns of U may not be orthogonal up to TOL. The output
@@ -137,8 +137,8 @@
 *>                 values in SVA(1:N)) and V is still a decomposition of the
 *>                 input matrix A in the sense that the residual
 *>                 || A - SCALE * U * SIGMA * V^* ||_2 / ||A||_2 is small.
-*>          If JOBU .EQ. 'N':
-*>                 If INFO .EQ. 0 :
+*>          If JOBU = 'N':
+*>                 If INFO = 0 :
 *>                 Note that the left singular vectors are 'for free' in the
 *>                 one-sided Jacobi SVD algorithm. However, if only the
 *>                 singular values are needed, the level of numerical
@@ -147,7 +147,7 @@
 *>                 numerically orthogonal up to approximately M*EPS. Thus,
 *>                 on exit, A contains the columns of U scaled with the
 *>                 corresponding singular values.
-*>                 If INFO .GT. 0 :
+*>                 If INFO > 0:
 *>                 the procedure ZGESVJ did not converge in the given number
 *>                 of iterations (sweeps).
 *> \endverbatim
@@ -162,9 +162,9 @@
 *> \verbatim
 *>          SVA is DOUBLE PRECISION array, dimension (N)
 *>          On exit,
-*>          If INFO .EQ. 0 :
+*>          If INFO = 0 :
 *>          depending on the value SCALE = RWORK(1), we have:
-*>                 If SCALE .EQ. ONE:
+*>                 If SCALE = ONE:
 *>                 SVA(1:N) contains the computed singular values of A.
 *>                 During the computation SVA contains the Euclidean column
 *>                 norms of the iterated matrices in the array A.
@@ -173,7 +173,7 @@
 *>                 factored representation is due to the fact that some of the
 *>                 singular values of A might underflow or overflow.
 *>
-*>          If INFO .GT. 0 :
+*>          If INFO > 0:
 *>          the procedure ZGESVJ did not converge in the given number of
 *>          iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.
 *> \endverbatim
@@ -181,7 +181,7 @@
 *> \param[in] MV
 *> \verbatim
 *>          MV is INTEGER
-*>          If JOBV .EQ. 'A', then the product of Jacobi rotations in ZGESVJ
+*>          If JOBV = 'A', then the product of Jacobi rotations in ZGESVJ
 *>          is applied to the first MV rows of V. See the description of JOBV.
 *> \endverbatim
 *>
@@ -199,16 +199,16 @@
 *> \param[in] LDV
 *> \verbatim
 *>          LDV is INTEGER
-*>          The leading dimension of the array V, LDV .GE. 1.
-*>          If JOBV .EQ. 'V', then LDV .GE. max(1,N).
-*>          If JOBV .EQ. 'A', then LDV .GE. max(1,MV) .
+*>          The leading dimension of the array V, LDV >= 1.
+*>          If JOBV = 'V', then LDV >= max(1,N).
+*>          If JOBV = 'A', then LDV >= max(1,MV) .
 *> \endverbatim
 *>
 *> \param[in,out] CWORK
 *> \verbatim
 *>          CWORK is COMPLEX*16 array, dimension (max(1,LWORK))
 *>          Used as workspace.
-*>          If on entry LWORK .EQ. -1, then a workspace query is assumed and
+*>          If on entry LWORK = -1, then a workspace query is assumed and
 *>          no computation is done; CWORK(1) is set to the minial (and optimal)
 *>          length of CWORK.
 *> \endverbatim
@@ -223,7 +223,7 @@
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension (max(6,LRWORK))
 *>          On entry,
-*>          If JOBU .EQ. 'C' :
+*>          If JOBU = 'C' :
 *>          RWORK(1) = CTOL, where CTOL defines the threshold for convergence.
 *>                    The process stops if all columns of A are mutually
 *>                    orthogonal up to CTOL*EPS, EPS=DLAMCH('E').
@@ -243,11 +243,11 @@
 *>          RWORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.
 *>                    This is useful information in cases when ZGESVJ did
 *>                    not converge, as it can be used to estimate whether
-*>                    the output is stil useful and for post festum analysis.
+*>                    the output is still useful and for post festum analysis.
 *>          RWORK(6) = the largest absolute value over all sines of the
 *>                    Jacobi rotation angles in the last sweep. It can be
 *>                    useful for a post festum analysis.
-*>         If on entry LRWORK .EQ. -1, then a workspace query is assumed and
+*>         If on entry LRWORK = -1, then a workspace query is assumed and
 *>         no computation is done; RWORK(1) is set to the minial (and optimal)
 *>         length of RWORK.
 *> \endverbatim
@@ -261,9 +261,9 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          = 0 : successful exit.
-*>          < 0 : if INFO = -i, then the i-th argument had an illegal value
-*>          > 0 : ZGESVJ did not converge in the maximal allowed number
+*>          = 0:  successful exit.
+*>          < 0:  if INFO = -i, then the i-th argument had an illegal value
+*>          > 0:  ZGESVJ did not converge in the maximal allowed number
 *>                (NSWEEP=30) of sweeps. The output may still be useful.
 *>                See the description of RWORK.
 *> \endverbatim

lapack-netlib/SRC/zgesvxx.f

@@ -411,7 +411,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -447,14 +447,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension NPARAMS
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -462,9 +462,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the extra-precise refinement algorithm.
+*>            = 1.0:  Use the extra-precise refinement algorithm.
 *>              (other values are reserved for future use)
 *>
 *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

lapack-netlib/SRC/zgetsls.f

@@ -1,3 +1,5 @@
+*> \brief \b ZGETSLS
+*
 *  Definition:
 *  ===========
 *

lapack-netlib/SRC/zggesx.f

@@ -120,10 +120,10 @@
 *> \verbatim
 *>          SENSE is CHARACTER*1
 *>          Determines which reciprocal condition numbers are computed.
-*>          = 'N' : None are computed;
-*>          = 'E' : Computed for average of selected eigenvalues only;
-*>          = 'V' : Computed for selected deflating subspaces only;
-*>          = 'B' : Computed for both.
+*>          = 'N': None are computed;
+*>          = 'E': Computed for average of selected eigenvalues only;
+*>          = 'V': Computed for selected deflating subspaces only;
+*>          = 'B': Computed for both.
 *>          If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
 *> \endverbatim
 *>

lapack-netlib/SRC/zgsvj0.f

@@ -117,7 +117,7 @@
 *> \param[in] MV
 *> \verbatim
 *>          MV is INTEGER
-*>          If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
+*>          If JOBV = 'A', then MV rows of V are post-multipled 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 .EQ. 'V' then N rows of V are post-multipled by a
+*>          If JOBV = 'V' then N rows of V are post-multipled by a
 *>                           sequence of Jacobi rotations.
-*>          If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
+*>          If JOBV = 'A' then MV rows of V are post-multipled by a
 *>                           sequence of Jacobi rotations.
 *>          If JOBV = 'N',   then V is not referenced.
 *> \endverbatim
@@ -136,8 +136,8 @@
 *> \verbatim
 *>          LDV is INTEGER
 *>          The leading dimension of the array V,  LDV >= 1.
-*>          If JOBV = 'V', LDV .GE. N.
-*>          If JOBV = 'A', LDV .GE. MV.
+*>          If JOBV = 'V', LDV >= N.
+*>          If JOBV = 'A', LDV >= MV.
 *> \endverbatim
 *>
 *> \param[in] EPS
@@ -157,7 +157,7 @@
 *>          TOL is DOUBLE PRECISION
 *>          TOL is the threshold for Jacobi rotations. For a pair
 *>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
-*>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
+*>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
 *> \endverbatim
 *>
 *> \param[in] NSWEEP
@@ -175,14 +175,14 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          LWORK is the dimension of WORK. LWORK .GE. M.
+*>          LWORK is the dimension of WORK. LWORK >= M.
 *> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          = 0 : successful exit.
-*>          < 0 : if INFO = -i, then the i-th argument had an illegal value
+*>          = 0:  successful exit.
+*>          < 0:  if INFO = -i, then the i-th argument had an illegal value
 *> \endverbatim
 *
 *  Authors:

lapack-netlib/SRC/zgsvj1.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
@@ -147,7 +147,7 @@
 *> \param[in] MV
 *> \verbatim
 *>          MV is INTEGER
-*>          If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
+*>          If JOBV = 'A', then MV rows of V are post-multipled 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 .EQ. 'V' then N rows of V are post-multipled by a
+*>          If JOBV = 'V' then N rows of V are post-multipled by a
 *>                           sequence of Jacobi rotations.
-*>          If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
+*>          If JOBV = 'A' then MV rows of V are post-multipled by a
 *>                           sequence of Jacobi rotations.
 *>          If JOBV = 'N',   then V is not referenced.
 *> \endverbatim
@@ -166,8 +166,8 @@
 *> \verbatim
 *>          LDV is INTEGER
 *>          The leading dimension of the array V,  LDV >= 1.
-*>          If JOBV = 'V', LDV .GE. N.
-*>          If JOBV = 'A', LDV .GE. MV.
+*>          If JOBV = 'V', LDV >= N.
+*>          If JOBV = 'A', LDV >= MV.
 *> \endverbatim
 *>
 *> \param[in] EPS
@@ -187,7 +187,7 @@
 *>          TOL is DOUBLE PRECISION
 *>          TOL is the threshold for Jacobi rotations. For a pair
 *>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
-*>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
+*>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
 *> \endverbatim
 *>
 *> \param[in] NSWEEP
@@ -205,14 +205,14 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          LWORK is the dimension of WORK. LWORK .GE. M.
+*>          LWORK is the dimension of WORK. LWORK >= M.
 *> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          = 0 : successful exit.
-*>          < 0 : if INFO = -i, then the i-th argument had an illegal value
+*>          = 0:  successful exit.
+*>          < 0:  if INFO = -i, then the i-th argument had an illegal value
 *> \endverbatim
 *
 *  Authors: