test routines for new QRT subroutines:

xQRT04 tests xGEQRT and xGEMQRT
xQRT05 tests xTPQRT and xTPMQRT

8 files changed, 1737 insertions, 0 deletions

diff --git a/TESTING/LIN/cqrt04.f b/TESTING/LIN/cqrt04.f
new file mode 100644
index 00000000..eb9b3686
--- /dev/null
+++ b/TESTING/LIN/cqrt04.f
@@ -0,0 +1,214 @@
+      SUBROUTINE CQRT04(M,N,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, NB, LDT
+*     .. Return values ..
+      REAL RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  CQRT04 tests CGEQRT and CGEMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= Min(M,N).
+*
+*  RESULT  (output) REAL array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*
+*     ..
+*     .. Local allocatable arrays 
+      COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      REAL ZERO
+      COMPLEX ONE, CZERO
+      PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, L
+      REAL   ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      REAL SLAMCH 
+      REAL CLANGE, CLANSY
+      LOGICAL  LSAME
+      EXTERNAL SLAMCH, CLANGE, CLANSY, LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC  MAX, MIN      
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /      
+*      
+      EPS = SLAMCH( 'Epsilon' )
+      K = MIN(M,N)
+      L = MAX(M,N)
+      LWORK = MAX(2,L)*MAX(2,L)*NB
+*
+*     Dynamically allocate local arrays
+*
+      ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 
+     $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 
+     $           D(N,M), DF(N,M) )
+*
+*     Put random numbers into A and copy to AF
+*
+      LDT=NB
+      DO J=1,N
+         CALL CLARNV( 2, ISEED, M, A( 1, J ) )
+      END DO
+      CALL CLACPY( 'Full', M, N, A, M, AF, M )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL CGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
+*
+*     Generate the m-by-m matrix Q
+*
+      CALL CLASET( 'Full', M, M, CZERO, ONE, Q, M )
+      CALL CGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL CLASET( 'Full', M, N, CZERO, CZERO, R, M )
+      CALL CLACPY( 'Upper', M, N, AF, M, R, M )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
+      ANORM = CLANGE( '1', M, N, A, M, RWORK )
+      RESID = CLANGE( '1', M, N, R, M, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL CLASET( 'Full', M, M, CZERO, ONE, R, M )
+      CALL CHERK( 'U', 'C', M, M, REAL(-ONE), Q, M, REAL(ONE), R, M )
+      RESID = CLANSY( '1', 'Upper', M, R, M, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL CLARNV( 2, ISEED, M, C( 1, J ) )
+      END DO
+      CNORM = CLANGE( '1', M, N, C, M, RWORK)
+      CALL CLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as Q*C
+*
+      CALL CGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL CGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = CLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL CLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as QT*C
+*
+      CALL CGEMQRT( 'L', 'C', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = CLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M
+         CALL CLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = CLANGE( '1', N, M, D, N, RWORK)
+      CALL CLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL CGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL CGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = CLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL CLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL CGEMQRT( 'R', 'C', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL CGEMM( 'N', 'C', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = CLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+*
+      RETURN
+      END
+
diff --git a/TESTING/LIN/cqrt05.f b/TESTING/LIN/cqrt05.f
new file mode 100644
index 00000000..5a2f39fa
--- /dev/null
+++ b/TESTING/LIN/cqrt05.f
@@ -0,0 +1,222 @@
+      SUBROUTINE CQRT05(M,N,L,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, L, NB, LDT
+*     .. Return values ..
+      REAL RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  CQRT05 tests CTPQRT and CTPMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in lower part of the test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  L       (input) INTEGER
+*          The number of rows of the upper trapezoidal part the
+*          lower test matrix.  0 <= L <= M.
+*          
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= N.
+*
+*  RESULT  (output) REAL array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*      
+*     ..
+*     .. Local allocatable arrays 
+      COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      REAL ZERO
+      COMPLEX ONE, CZERO
+      PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, M2
+      REAL   ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      REAL SLAMCH 
+      REAL CLANGE, CLANSY
+      LOGICAL  LSAME
+      EXTERNAL SLAMCH, CLANGE, CLANSY, LSAME
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /
+*      
+      EPS = SLAMCH( 'Epsilon' )
+      K = N
+      M2 = M+N
+      LWORK = M2*M2*NB
+*
+*     Dynamically allocate all arrays
+*
+      ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
+     $           WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 
+     $           D(N,M2),DF(N,M2) )
+*
+*     Put random stuff into A
+*
+      LDT=NB
+      CALL CLASET( 'Full', M2, N, CZERO, CZERO, A, M2 )
+      DO J=1,N
+         CALL CLARNV( 2, ISEED, J, A( 1, J ) )
+         CALL CLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) )
+         CALL CLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) )
+      END DO
+*
+*     Copy the matrix A to the array AF.
+*
+      CALL CLACPY( 'Full', M2, N, A, M2, AF, M2 )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL CTPQRT( M,N,L,NB,AF,M2,AF(N+1,1),M2,T,LDT,WORK,INFO)
+*
+*     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
+*
+      CALL CLASET( 'Full', M2, M2, CZERO, ONE, Q, M2 )
+      CALL CGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL CLASET( 'Full', M2, N, CZERO, CZERO, R, M2 )
+      CALL CLACPY( 'Upper', M2, N, AF, M2, R, M2 )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL CGEMM( 'C', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
+      ANORM = CLANGE( '1', M2, N, A, M2, RWORK )
+      RESID = CLANGE( '1', M2, N, R, M2, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL CLASET( 'Full', M2, M2, CZERO, ONE, R, M2 )
+      CALL CHERK( 'U', 'C', M2, M2, REAL(-ONE), Q, M2, REAL(ONE), 
+     $            R, M2 )
+      RESID = CLANSY( '1', 'Upper', M2, R, M2, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL CLARNV( 2, ISEED, M2, C( 1, J ) )
+      END DO
+      CNORM = CLANGE( '1', M2, N, C, M2, RWORK)
+      CALL CLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as Q*C
+*
+      CALL CTPMQRT( 'L','N', M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $               CF(N+1,1),M2,WORK,INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL CGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 )
+      RESID = CLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL CLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as QT*C
+*
+      CALL CTPMQRT( 'L','C',M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $              CF(N+1,1),M2,WORK,INFO) 
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL CGEMM('C','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
+      RESID = CLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M2
+         CALL CLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = CLANGE( '1', N, M2, D, N, RWORK)
+      CALL CLACPY( 'Full', N, M2, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL CTPMQRT('R','N',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL CGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
+      RESID = CLANGE('1',N, M2,DF,N,RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL CLACPY('Full',N,M2,D,N,DF,N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL CTPMQRT('R','C',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)     
+       
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL CGEMM( 'N', 'C', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
+      RESID = CLANGE( '1', N, M2, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+      RETURN
+      END
+
diff --git a/TESTING/LIN/dqrt04.f b/TESTING/LIN/dqrt04.f
new file mode 100644
index 00000000..18ecc005
--- /dev/null
+++ b/TESTING/LIN/dqrt04.f
@@ -0,0 +1,212 @@
+      SUBROUTINE DQRT04(M,N,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, NB, LDT
+*     .. Return values ..
+      DOUBLE PRECISION RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  DQRT04 tests DGEQRT and DGEMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= Min(M,N).
+*
+*  RESULT  (output) DOUBLE PRECISION array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*
+*     ..
+*     .. Local allocatable arrays 
+      DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      DOUBLE PRECISION ONE, ZERO
+      PARAMETER( ZERO = 0.0, ONE = 1.0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, L
+      DOUBLE PRECISION   ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
+      LOGICAL  LSAME
+      EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC  MAX, MIN      
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /      
+*      
+      EPS = DLAMCH( 'Epsilon' )
+      K = MIN(M,N)
+      L = MAX(M,N)
+      LWORK = MAX(2,L)*MAX(2,L)*NB
+*
+*     Dynamically allocate local arrays
+*
+      ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 
+     $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 
+     $           D(N,M), DF(N,M) )
+*
+*     Put random numbers into A and copy to AF
+*
+      LDT=NB
+      DO J=1,N
+         CALL DLARNV( 2, ISEED, M, A( 1, J ) )
+      END DO
+      CALL DLACPY( 'Full', M, N, A, M, AF, M )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL DGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
+*
+*     Generate the m-by-m matrix Q
+*
+      CALL DLASET( 'Full', M, M, ZERO, ONE, Q, M )
+      CALL DGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL DLASET( 'Full', M, N, ZERO, ZERO, R, M )
+      CALL DLACPY( 'Upper', M, N, AF, M, R, M )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
+      ANORM = DLANGE( '1', M, N, A, M, RWORK )
+      RESID = DLANGE( '1', M, N, R, M, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL DLASET( 'Full', M, M, ZERO, ONE, R, M )
+      CALL DSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M )
+      RESID = DLANSY( '1', 'Upper', M, R, M, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL DLARNV( 2, ISEED, M, C( 1, J ) )
+      END DO
+      CNORM = DLANGE( '1', M, N, C, M, RWORK)
+      CALL DLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as Q*C
+*
+      CALL DGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL DGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = DLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL DLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as QT*C
+*
+      CALL DGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = DLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M
+         CALL DLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = DLANGE( '1', N, M, D, N, RWORK)
+      CALL DLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL DGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL DGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = DLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL DLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL DGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL DGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = DLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+*
+      RETURN
+      END
+
diff --git a/TESTING/LIN/dqrt05.f b/TESTING/LIN/dqrt05.f
new file mode 100644
index 00000000..d3a793f0
--- /dev/null
+++ b/TESTING/LIN/dqrt05.f
@@ -0,0 +1,219 @@
+      SUBROUTINE DQRT05(M,N,L,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, L, NB, LDT
+*     .. Return values ..
+      DOUBLE PRECISION RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  DQRT05 tests DTPQRT and DTPMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in lower part of the test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  L       (input) INTEGER
+*          The number of rows of the upper trapezoidal part the
+*          lower test matrix.  0 <= L <= M.
+*          
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= N.
+*
+*  RESULT  (output) DOUBLE PRECISION array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*      
+*     ..
+*     .. Local allocatable arrays 
+      DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      DOUBLE PRECISION ONE, ZERO
+      PARAMETER( ZERO = 0.0, ONE = 1.0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, M2
+      DOUBLE PRECISION   ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
+      LOGICAL  LSAME
+      EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /
+*      
+      EPS = DLAMCH( 'Epsilon' )
+      K = N
+      M2 = M+N
+      LWORK = M2*M2*NB
+*
+*     Dynamically allocate all arrays
+*
+      ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
+     $           WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 
+     $           D(N,M2),DF(N,M2) )
+*
+*     Put random stuff into A
+*
+      LDT=NB
+      CALL DLASET( 'Full', M2, N, ZERO, ZERO, A, M2 )
+      DO J=1,N
+         CALL DLARNV( 2, ISEED, J, A( 1, J ) )
+         CALL DLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) )
+         CALL DLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) )
+      END DO
+*
+*     Copy the matrix A to the array AF.
+*
+      CALL DLACPY( 'Full', M2, N, A, M2, AF, M2 )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL DTPQRT( M,N,L,NB,AF,M2,AF(N+1,1),M2,T,LDT,WORK,INFO)
+*
+*     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
+*
+      CALL DLASET( 'Full', M2, M2, ZERO, ONE, Q, M2 )
+      CALL DGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL DLASET( 'Full', M2, N, ZERO, ZERO, R, M2 )
+      CALL DLACPY( 'Upper', M2, N, AF, M2, R, M2 )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL DGEMM( 'T', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
+      ANORM = DLANGE( '1', M2, N, A, M2, RWORK )
+      RESID = DLANGE( '1', M2, N, R, M2, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL DLASET( 'Full', M2, M2, ZERO, ONE, R, M2 )
+      CALL DSYRK( 'U', 'C', M2, M2, -ONE, Q, M2, ONE, R, M2 )
+      RESID = DLANSY( '1', 'Upper', M2, R, M2, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL DLARNV( 2, ISEED, M2, C( 1, J ) )
+      END DO
+      CNORM = DLANGE( '1', M2, N, C, M2, RWORK)
+      CALL DLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as Q*C
+*
+      CALL DTPMQRT( 'L','N', M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $               CF(N+1,1),M2,WORK,INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL DGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 )
+      RESID = DLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL DLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as QT*C
+*
+      CALL DTPMQRT( 'L','T',M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $              CF(N+1,1),M2,WORK,INFO) 
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL DGEMM('T','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
+      RESID = DLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M2
+         CALL DLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = DLANGE( '1', N, M2, D, N, RWORK)
+      CALL DLACPY( 'Full', N, M2, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL DTPMQRT('R','N',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL DGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
+      RESID = DLANGE('1',N, M2,DF,N,RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL DLACPY('Full',N,M2,D,N,DF,N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL DTPMQRT('R','T',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)     
+       
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL DGEMM( 'N', 'T', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
+      RESID = DLANGE( '1', N, M2, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+      RETURN
+      END
+
diff --git a/TESTING/LIN/sqrt04.f b/TESTING/LIN/sqrt04.f
new file mode 100644
index 00000000..7db31249
--- /dev/null
+++ b/TESTING/LIN/sqrt04.f
@@ -0,0 +1,213 @@
+      SUBROUTINE SQRT04(M,N,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, NB, LDT
+*     .. Return values ..
+      REAL RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  SQRT04 tests SGEQRT and SGEMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= Min(M,N).
+*
+*  RESULT  (output) REAL array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*
+*     ..
+*     .. Local allocatable arrays 
+      REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      REAL ONE, ZERO
+      PARAMETER( ZERO = 0.0, ONE = 1.0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, L
+      REAL   ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      REAL SLAMCH 
+      REAL SLANGE, SLANSY
+      LOGICAL  LSAME
+      EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC  MAX, MIN      
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /      
+*      
+      EPS = SLAMCH( 'Epsilon' )
+      K = MIN(M,N)
+      L = MAX(M,N)
+      LWORK = MAX(2,L)*MAX(2,L)*NB
+*
+*     Dynamically allocate local arrays
+*
+      ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 
+     $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 
+     $           D(N,M), DF(N,M) )
+*
+*     Put random numbers into A and copy to AF
+*
+      LDT=NB
+      DO J=1,N
+         CALL SLARNV( 2, ISEED, M, A( 1, J ) )
+      END DO
+      CALL SLACPY( 'Full', M, N, A, M, AF, M )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL SGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
+*
+*     Generate the m-by-m matrix Q
+*
+      CALL SLASET( 'Full', M, M, ZERO, ONE, Q, M )
+      CALL SGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL SLASET( 'Full', M, N, ZERO, ZERO, R, M )
+      CALL SLACPY( 'Upper', M, N, AF, M, R, M )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
+      ANORM = SLANGE( '1', M, N, A, M, RWORK )
+      RESID = SLANGE( '1', M, N, R, M, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL SLASET( 'Full', M, M, ZERO, ONE, R, M )
+      CALL SSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M )
+      RESID = SLANSY( '1', 'Upper', M, R, M, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL SLARNV( 2, ISEED, M, C( 1, J ) )
+      END DO
+      CNORM = SLANGE( '1', M, N, C, M, RWORK)
+      CALL SLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as Q*C
+*
+      CALL SGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL SGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = SLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL SLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as QT*C
+*
+      CALL SGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = SLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M
+         CALL SLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = SLANGE( '1', N, M, D, N, RWORK)
+      CALL SLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL SGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL SGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = SLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL SLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL SGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL SGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = SLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+*
+      RETURN
+      END
+
diff --git a/TESTING/LIN/sqrt05.f b/TESTING/LIN/sqrt05.f
new file mode 100644
index 00000000..cbc458b5
--- /dev/null
+++ b/TESTING/LIN/sqrt05.f
@@ -0,0 +1,221 @@
+      SUBROUTINE SQRT05(M,N,L,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, L, NB, LDT
+*     .. Return values ..
+      REAL RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  SQRT05 tests STPQRT and STPMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in lower part of the test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  L       (input) INTEGER
+*          The number of rows of the upper trapezoidal part the
+*          lower test matrix.  0 <= L <= M.
+*          
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= N.
+*
+*  RESULT  (output) REAL array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*      
+*     ..
+*     .. Local allocatable arrays 
+      REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      REAL ZERO, ONE
+      PARAMETER( ZERO = 0.0, ONE = 1.0 )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, M2
+      REAL   ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      REAL SLAMCH 
+      REAL SLANGE, SLANSY
+      LOGICAL  LSAME
+      EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /
+*      
+      EPS = SLAMCH( 'Epsilon' )
+      K = N
+      M2 = M+N
+      LWORK = M2*M2*NB
+*
+*     Dynamically allocate all arrays
+*
+      ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
+     $           WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 
+     $           D(N,M2),DF(N,M2) )
+*
+*     Put random stuff into A
+*
+      LDT=NB
+      CALL SLASET( 'Full', M2, N, ZERO, ZERO, A, M2 )
+      DO J=1,N
+         CALL SLARNV( 2, ISEED, J, A( 1, J ) )
+         CALL SLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) )
+         CALL SLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) )
+      END DO
+*
+*     Copy the matrix A to the array AF.
+*
+      CALL SLACPY( 'Full', M2, N, A, M2, AF, M2 )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL STPQRT( M,N,L,NB,AF,M2,AF(N+1,1),M2,T,LDT,WORK,INFO)
+*
+*     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
+*
+      CALL SLASET( 'Full', M2, M2, ZERO, ONE, Q, M2 )
+      CALL SGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL SLASET( 'Full', M2, N, ZERO, ZERO, R, M2 )
+      CALL SLACPY( 'Upper', M2, N, AF, M2, R, M2 )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL SGEMM( 'T', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
+      ANORM = SLANGE( '1', M2, N, A, M2, RWORK )
+      RESID = SLANGE( '1', M2, N, R, M2, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL SLASET( 'Full', M2, M2, ZERO, ONE, R, M2 )
+      CALL SSYRK( 'U', 'C', M2, M2, -ONE, Q, M2, ONE, 
+     $            R, M2 )
+      RESID = SLANSY( '1', 'Upper', M2, R, M2, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL SLARNV( 2, ISEED, M2, C( 1, J ) )
+      END DO
+      CNORM = SLANGE( '1', M2, N, C, M2, RWORK)
+      CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as Q*C
+*
+      CALL STPMQRT( 'L','N', M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $               CF(N+1,1),M2,WORK,INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL SGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 )
+      RESID = SLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as QT*C
+*
+      CALL STPMQRT( 'L','T',M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $              CF(N+1,1),M2,WORK,INFO) 
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL SGEMM('T','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
+      RESID = SLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M2
+         CALL SLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = SLANGE( '1', N, M2, D, N, RWORK)
+      CALL SLACPY( 'Full', N, M2, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL STPMQRT('R','N',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL SGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
+      RESID = SLANGE('1',N, M2,DF,N,RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL SLACPY('Full',N,M2,D,N,DF,N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL STPMQRT('R','T',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)     
+       
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL SGEMM( 'N', 'T', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
+      RESID = SLANGE( '1', N, M2, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+      RETURN
+      END
+
diff --git a/TESTING/LIN/zqrt04.f b/TESTING/LIN/zqrt04.f
new file mode 100644
index 00000000..6cfc3544
--- /dev/null
+++ b/TESTING/LIN/zqrt04.f
@@ -0,0 +1,214 @@
+      SUBROUTINE ZQRT04(M,N,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, NB, LDT
+*     .. Return values ..
+      DOUBLE PRECISION RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  ZQRT04 tests ZGEQRT and ZGEMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= Min(M,N).
+*
+*  RESULT  (output) DOUBLE PRECISION array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*
+*     ..
+*     .. Local allocatable arrays 
+      COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      DOUBLE PRECISION ZERO
+      COMPLEX*16 ONE, CZERO
+      PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, L
+      DOUBLE PRECISION   ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION DLAMCH 
+      DOUBLE PRECISION ZLANGE, ZLANSY
+      LOGICAL  LSAME
+      EXTERNAL DLAMCH, ZLANGE, ZLANSY, LSAME
+*     ..
+*     .. Intrinsic Functions ..
+      INTRINSIC  MAX, MIN      
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /      
+*      
+      EPS = DLAMCH( 'Epsilon' )
+      K = MIN(M,N)
+      L = MAX(M,N)
+      LWORK = MAX(2,L)*MAX(2,L)*NB
+*
+*     Dynamically allocate local arrays
+*
+      ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 
+     $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 
+     $           D(N,M), DF(N,M) )
+*
+*     Put random numbers into A and copy to AF
+*
+      LDT=NB
+      DO J=1,N
+         CALL ZLARNV( 2, ISEED, M, A( 1, J ) )
+      END DO
+      CALL ZLACPY( 'Full', M, N, A, M, AF, M )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL ZGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
+*
+*     Generate the m-by-m matrix Q
+*
+      CALL ZLASET( 'Full', M, M, CZERO, ONE, Q, M )
+      CALL ZGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL ZLASET( 'Full', M, N, CZERO, CZERO, R, M )
+      CALL ZLACPY( 'Upper', M, N, AF, M, R, M )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL ZGEMM( 'C', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
+      ANORM = ZLANGE( '1', M, N, A, M, RWORK )
+      RESID = ZLANGE( '1', M, N, R, M, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL ZLASET( 'Full', M, M, CZERO, ONE, R, M )
+      CALL ZHERK( 'U', 'C', M, M, DREAL(-ONE), Q, M, DREAL(ONE), R, M )
+      RESID = ZLANSY( '1', 'Upper', M, R, M, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL ZLARNV( 2, ISEED, M, C( 1, J ) )
+      END DO
+      CNORM = ZLANGE( '1', M, N, C, M, RWORK)
+      CALL ZLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as Q*C
+*
+      CALL ZGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL ZGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = ZLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL ZLACPY( 'Full', M, N, C, M, CF, M )
+*
+*     Apply Q to C as QT*C
+*
+      CALL ZGEMQRT( 'L', 'C', M, N, K, NB, AF, M, T, NB, CF, M, 
+     $             WORK, LWORK, INFO)
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL ZGEMM( 'C', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
+      RESID = ZLANGE( '1', M, N, CF, M, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M
+         CALL ZLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = ZLANGE( '1', N, M, D, N, RWORK)
+      CALL ZLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL ZGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL ZGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = ZLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL ZLACPY( 'Full', N, M, D, N, DF, N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL ZGEMQRT( 'R', 'C', N, M, K, NB, AF, M, T, NB, DF, N, 
+     $             WORK, LWORK, INFO)      
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL ZGEMM( 'N', 'C', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
+      RESID = ZLANGE( '1', N, M, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+*
+      RETURN
+      END
+
diff --git a/TESTING/LIN/zqrt05.f b/TESTING/LIN/zqrt05.f
new file mode 100644
index 00000000..8fb61566
--- /dev/null
+++ b/TESTING/LIN/zqrt05.f
@@ -0,0 +1,222 @@
+      SUBROUTINE ZQRT05(M,N,L,NB,RESULT)
+*
+*  -- LAPACK test routine (version 3.?) --
+*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+*     August 2011
+*
+      IMPLICIT NONE
+*     .. Scalar Arguments ..
+      INTEGER LWORK, M, N, L, NB, LDT
+*     .. Return values ..
+      DOUBLE PRECISION RESULT(6)
+*
+*  Purpose
+*  =======
+*
+*  ZQRT05 tests ZTPQRT and ZTPMQRT.
+*
+*  Arguments
+*  =========
+*
+*  M       (input) INTEGER
+*          Number of rows in lower part of the test matrix.
+*
+*  N       (input) INTEGER
+*          Number of columns in test matrix.
+*
+*  L       (input) INTEGER
+*          The number of rows of the upper trapezoidal part the
+*          lower test matrix.  0 <= L <= M.
+*          
+*  NB      (input) INTEGER
+*          Block size of test matrix.  NB <= N.
+*
+*  RESULT  (output) DOUBLE PRECISION array, dimension (6)
+*          Results of each of the six tests below.
+*
+*          RESULT(1) = | A - Q R |
+*          RESULT(2) = | I - Q^H Q |
+*          RESULT(3) = | Q C - Q C |
+*          RESULT(4) = | Q^H C - Q^H C |
+*          RESULT(5) = | C Q - C Q | 
+*          RESULT(6) = | C Q^H - C Q^H |
+*
+*  =====================================================================
+*      
+*     ..
+*     .. Local allocatable arrays 
+      COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:),
+     $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
+     $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
+*
+*     .. Parameters ..
+      DOUBLE PRECISION ZERO
+      COMPLEX*16 ONE, CZERO
+      PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
+*     ..
+*     .. Local Scalars ..
+      INTEGER INFO, J, K, M2
+      DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
+*     ..
+*     .. Local Arrays ..
+      INTEGER            ISEED( 4 )
+*     ..
+*     .. External Functions ..
+      DOUBLE PRECISION DLAMCH 
+      DOUBLE PRECISION ZLANGE, ZLANSY
+      LOGICAL  LSAME
+      EXTERNAL DLAMCH, ZLANGE, ZLANSY, LSAME
+*     ..
+*     .. Data statements ..
+      DATA ISEED / 1988, 1989, 1990, 1991 /
+*      
+      EPS = DLAMCH( 'Epsilon' )
+      K = N
+      M2 = M+N
+      LWORK = M2*M2*NB
+*
+*     Dynamically allocate all arrays
+*
+      ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2),
+     $           WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 
+     $           D(N,M2),DF(N,M2) )
+*
+*     Put random stuff into A
+*
+      LDT=NB
+      CALL ZLASET( 'Full', M2, N, CZERO, CZERO, A, M2 )
+      DO J=1,N
+         CALL ZLARNV( 2, ISEED, J, A( 1, J ) )
+         CALL ZLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) )
+         CALL ZLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) )
+      END DO
+*
+*     Copy the matrix A to the array AF.
+*
+      CALL ZLACPY( 'Full', M2, N, A, M2, AF, M2 )
+*
+*     Factor the matrix A in the array AF.
+*
+      CALL ZTPQRT( M,N,L,NB,AF,M2,AF(N+1,1),M2,T,LDT,WORK,INFO)
+*
+*     Generate the (M+N)-by-(M+N) matrix Q by applying H to I
+*
+      CALL ZLASET( 'Full', M2, M2, CZERO, ONE, Q, M2 )
+      CALL ZGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2,
+     $              WORK, INFO )
+*
+*     Copy R
+*
+      CALL ZLASET( 'Full', M2, N, CZERO, CZERO, R, M2 )
+      CALL ZLACPY( 'Upper', M2, N, AF, M2, R, M2 )
+*
+*     Compute |R - Q'*A| / |A| and store in RESULT(1)
+*
+      CALL ZGEMM( 'C', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 )
+      ANORM = ZLANGE( '1', M2, N, A, M2, RWORK )
+      RESID = ZLANGE( '1', M2, N, R, M2, RWORK )
+      IF( ANORM.GT.ZERO ) THEN
+         RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2))
+      ELSE
+         RESULT( 1 ) = ZERO
+      END IF
+*
+*     Compute |I - Q'*Q| and store in RESULT(2)
+*
+      CALL ZLASET( 'Full', M2, M2, CZERO, ONE, R, M2 )
+      CALL ZHERK( 'U', 'C', M2, M2, DREAL(-ONE), Q, M2, DREAL(ONE), 
+     $            R, M2 )
+      RESID = ZLANSY( '1', 'Upper', M2, R, M2, RWORK )
+      RESULT( 2 ) = RESID / (EPS*MAX(1,M2))
+*
+*     Generate random m-by-n matrix C and a copy CF
+*
+      DO J=1,N
+         CALL ZLARNV( 2, ISEED, M2, C( 1, J ) )
+      END DO
+      CNORM = ZLANGE( '1', M2, N, C, M2, RWORK)
+      CALL ZLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as Q*C
+*
+      CALL ZTPMQRT( 'L','N', M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $               CF(N+1,1),M2,WORK,INFO)
+*
+*     Compute |Q*C - Q*C| / |C|
+*
+      CALL ZGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 )
+      RESID = ZLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 3 ) = ZERO
+      END IF
+*
+*     Copy C into CF again
+*
+      CALL ZLACPY( 'Full', M2, N, C, M2, CF, M2 )
+*
+*     Apply Q to C as QT*C
+*
+      CALL ZTPMQRT( 'L','C',M,N,K,L,NB,AF(N+1,1),M2,T,LDT,CF,M2,
+     $              CF(N+1,1),M2,WORK,INFO) 
+*
+*     Compute |QT*C - QT*C| / |C|
+*
+      CALL ZGEMM('C','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2)
+      RESID = ZLANGE( '1', M2, N, CF, M2, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM)
+      ELSE
+         RESULT( 4 ) = ZERO
+      END IF     
+*
+*     Generate random n-by-m matrix D and a copy DF
+*
+      DO J=1,M2
+         CALL ZLARNV( 2, ISEED, N, D( 1, J ) )
+      END DO
+      DNORM = ZLANGE( '1', N, M2, D, N, RWORK)
+      CALL ZLACPY( 'Full', N, M2, D, N, DF, N )
+*
+*     Apply Q to D as D*Q
+*
+      CALL ZTPMQRT('R','N',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)
+*
+*     Compute |D*Q - D*Q| / |D|
+*
+      CALL ZGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N)
+      RESID = ZLANGE('1',N, M2,DF,N,RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 5 ) = ZERO
+      END IF
+*
+*     Copy D into DF again
+*
+      CALL ZLACPY('Full',N,M2,D,N,DF,N )
+*
+*     Apply Q to D as D*QT
+*
+      CALL ZTPMQRT('R','C',N,M,N,L,NB,AF(N+1,1),M2,T,LDT,DF,N,
+     $             DF(1,N+1),N,WORK,INFO)     
+       
+*
+*     Compute |D*QT - D*QT| / |D|
+*
+      CALL ZGEMM( 'N', 'C', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N )
+      RESID = ZLANGE( '1', N, M2, DF, N, RWORK )
+      IF( CNORM.GT.ZERO ) THEN
+         RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM)
+      ELSE
+         RESULT( 6 ) = ZERO
+      END IF
+*
+*     Deallocate all arrays
+*
+      DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
+      RETURN
+      END
+