SRC: report all-zero Y in GEDMD scaling as diagnostic

Treat the all-zero Y case in the JOBS='Y' scaling path as a degenerate input diagnostic instead of an illegal argument.

Previously this path returned INFO = -10 and called XERBLA, which made the condition look like an invalid tenth argument. However, an all-zero Y matrix is not an illegal argument by itself; it is a degenerate data case detected under the JOBS='Y' scaling semantics.

Introduce INFO = 5 for this early-return condition and document it as a positive diagnostic code. The GEDMDQ wrappers now propagate INFO = 5 as a terminal diagnostic from the underlying GEDMD call.

Author: nakatamaho

SRC/cgedmd.f90

@@ -118,7 +118,7 @@
 !>           by a diagonal matrix D so that Y*D has unit
 !>           nonzero columns (in the Euclidean 2-norm)
 !>           If all columns of Y are zero, the procedure returns
-!>           with INFO = -10.
+!>           with INFO = 5.
 !>    'N' :: No data scaling.
 !>    \endverbatim
 !.....
@@ -469,8 +469,7 @@
 !>    \verbatim
 !>    INFO (output) INTEGER
 !>    -i < 0 :: On entry, the i-th argument had an
-!>              illegal value. If JOBS == 'Y' and all columns
-!>              of Y are zero, INFO = -10.
+!>              illegal value.
 !>       = 0 :: Successful return.
 !>       = 1 :: Void input. Quick exit (M=0 or N=0).
 !>       = 2 :: The SVD computation of X did not converge.
@@ -485,6 +484,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -876,11 +879,9 @@ SUBROUTINE CGEDMD( JOBS, JOBZ, JOBR, JOBF,  WHTSVD,   &
             END IF
          END DO
          IF ( K == N ) THEN
-         ! All columns of Y are zero. Return error code -10.
-         ! (the 10th input variable had an illegal value)
+         ! All columns of Y are zero. Return diagnostic code 5.
          K = 0
-         INFO = -10
-         CALL XERBLA('CGEDMD',-INFO)
+         INFO = 5
          RETURN
          END IF
          DO i = 1, N

SRC/cgedmdq.f90

@@ -538,6 +538,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -795,8 +799,8 @@ SUBROUTINE CGEDMDQ( JOBS,  JOBZ, JOBR, JOBQ, JOBT, JOBF,   &
                   EIGS, Z, LDZ, RES, B,  LDB,   V, LDV,    &
                   S, LDS, ZWORK(MINMN+1), LZWORK-MINMN,    &
                   WORK,   LWORK, IWORK, LIWORK, INFO1 )
-      IF ( INFO1 == 2 .OR. INFO1 == 3 ) THEN
-          ! Return with error code. See CGEDMD for details.
+      IF ( INFO1 == 2 .OR. INFO1 == 3 .OR. INFO1 == 5 ) THEN
+          ! Return with terminal diagnostic or error code.
           INFO = INFO1
           RETURN
       ELSE

SRC/dgedmd.f90

@@ -116,7 +116,7 @@
 !>           by a diagonal matrix D so that Y*D has unit
 !>           nonzero columns (in the Euclidean 2-norm)
 !>           If all columns of Y are zero, the procedure returns
-!>           with INFO = -10.
+!>           with INFO = 5.
 !>    'N' :: No data scaling.
 !>    \endverbatim
 !.....
@@ -503,8 +503,7 @@
 !>    \verbatim
 !>    INFO (output) INTEGER
 !>    -i < 0 :: On entry, the i-th argument had an
-!>              illegal value. If JOBS == 'Y' and all columns
-!>              of Y are zero, INFO = -10.
+!>              illegal value.
 !>       = 0 :: Successful return.
 !>       = 1 :: Void input. Quick exit (M=0 or N=0).
 !>       = 2 :: The SVD computation of X did not converge.
@@ -519,6 +518,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -897,11 +900,9 @@ SUBROUTINE DGEDMD( JOBS, JOBZ, JOBR, JOBF,  WHTSVD,  &
             END IF
          END DO
          IF ( K == N ) THEN
-         ! All columns of Y are zero. Return error code -10.
-         ! (the 10th input variable had an illegal value)
+         ! All columns of Y are zero. Return diagnostic code 5.
          K = 0
-         INFO = -10
-         CALL XERBLA('DGEDMD',-INFO)
+         INFO = 5
          RETURN
          END IF
          DO i = 1, N

SRC/dgedmdq.f90

@@ -557,6 +557,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -807,8 +811,8 @@ SUBROUTINE DGEDMDQ( JOBS,  JOBZ, JOBR, JOBQ, JOBT, JOBF,   &
                    REIG, IMEIG, Z, LDZ, RES, B, LDB, V,     &
                    LDV, S, LDS, WORK(MINMN+1), LWORK-MINMN, &
                    IWORK, LIWORK, INFO1 )
-      IF ( INFO1 == 2 .OR. INFO1 == 3 ) THEN
-          ! Return with error code. See DGEDMD for details.
+      IF ( INFO1 == 2 .OR. INFO1 == 3 .OR. INFO1 == 5 ) THEN
+          ! Return with terminal diagnostic or error code.
           INFO = INFO1
           RETURN
       ELSE

SRC/sgedmd.f90

@@ -117,7 +117,7 @@
 !>           by a diagonal matrix D so that Y*D has unit
 !>           nonzero columns (in the Euclidean 2-norm)
 !>           If all columns of Y are zero, the procedure returns
-!>           with INFO = -10.
+!>           with INFO = 5.
 !>    'N' :: No data scaling.
 !>    \endverbatim
 !.....
@@ -503,8 +503,7 @@
 !>    \verbatim
 !>    INFO (output) INTEGER
 !>    -i < 0 :: On entry, the i-th argument had an
-!>              illegal value. If JOBS == 'Y' and all columns
-!>              of Y are zero, INFO = -10.
+!>              illegal value.
 !>       = 0 :: Successful return.
 !>       = 1 :: Void input. Quick exit (M=0 or N=0).
 !>       = 2 :: The SVD computation of X did not converge.
@@ -519,6 +518,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -897,11 +900,9 @@ SUBROUTINE SGEDMD( JOBS, JOBZ, JOBR, JOBF,  WHTSVD,  &
             END IF
          END DO
          IF ( K == N ) THEN
-         ! All columns of Y are zero. Return error code -10.
-         ! (the 10th input variable had an illegal value)
+         ! All columns of Y are zero. Return diagnostic code 5.
          K = 0
-         INFO = -10
-         CALL XERBLA('SGEDMD',-INFO)
+         INFO = 5
          RETURN
          END IF
          DO i = 1, N

SRC/sgedmdq.f90

@@ -557,6 +557,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -806,8 +810,8 @@ SUBROUTINE SGEDMDQ( JOBS,  JOBZ, JOBR, JOBQ, JOBT, JOBF,   &
                    REIG, IMEIG, Z, LDZ, RES, B, LDB, V,     &
                    LDV, S, LDS, WORK(MINMN+1), LWORK-MINMN, IWORK,  &
                    LIWORK, INFO1 )
-      IF ( INFO1 == 2 .OR. INFO1 == 3 ) THEN
-          ! Return with error code.
+      IF ( INFO1 == 2 .OR. INFO1 == 3 .OR. INFO1 == 5 ) THEN
+          ! Return with terminal diagnostic or error code.
           INFO = INFO1
           RETURN
       ELSE

SRC/zgedmd.f90

@@ -118,7 +118,7 @@
 !>           by a diagonal matrix D so that Y*D has unit
 !>           nonzero columns (in the Euclidean 2-norm)
 !>           If all columns of Y are zero, the procedure returns
-!>           with INFO = -10.
+!>           with INFO = 5.
 !>    'N' :: No data scaling.
 !>    \endverbatim
 !.....
@@ -469,8 +469,7 @@
 !>    \verbatim
 !>    INFO (output) INTEGER
 !>    -i < 0 :: On entry, the i-th argument had an
-!>              illegal value. If JOBS == 'Y' and all columns
-!>              of Y are zero, INFO = -10.
+!>              illegal value.
 !>       = 0 :: Successful return.
 !>       = 1 :: Void input. Quick exit (M=0 or N=0).
 !>       = 2 :: The SVD computation of X did not converge.
@@ -485,6 +484,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -876,11 +879,9 @@ SUBROUTINE ZGEDMD( JOBS, JOBZ, JOBR, JOBF,  WHTSVD,   &
             END IF
          END DO
          IF ( K == N ) THEN
-         ! All columns of Y are zero. Return error code -10.
-         ! (the 10th input variable had an illegal value)
+         ! All columns of Y are zero. Return diagnostic code 5.
          K = 0
-         INFO = -10
-         CALL XERBLA('ZGEDMD',-INFO)
+         INFO = 5
          RETURN
          END IF
          DO i = 1, N

SRC/zgedmdq.f90

@@ -537,6 +537,10 @@
 !>              to zero if JOBS=='C'. The computation proceeds
 !>              with original or modified data and warning
 !>              flag is set with INFO=4.
+!>       = 5 :: If JOBS == 'Y' and all columns of Y are zero,
+!>              the procedure returns early with K = 0. This is
+!>              reported as a degenerate input diagnostic, not
+!>              as an illegal argument.
 !>    \endverbatim
 !
 !  Authors:
@@ -796,8 +800,8 @@ SUBROUTINE ZGEDMDQ( JOBS,  JOBZ, JOBR, JOBQ, JOBT, JOBF,   &
                   EIGS, Z, LDZ, RES, B,  LDB,   V, LDV,    &
                   S, LDS, ZWORK(MINMN+1), LZWORK-MINMN, &
                   WORK,   LWORK, IWORK, LIWORK, INFO1 )
-      IF ( INFO1 == 2 .OR. INFO1 == 3 ) THEN
-          ! Return with error code. See ZGEDMD for details.
+      IF ( INFO1 == 2 .OR. INFO1 == 3 .OR. INFO1 == 5 ) THEN
+          ! Return with terminal diagnostic or error code.
           INFO = INFO1
           RETURN
       ELSE