diff --git a/compute/pztpgqrt.c b/compute/pztpgqrt.c
index e6a9dd7aae8e09548b32c836563ef1cc26bea0ce..5b0672d031d537dcfaf402f655720a86e0a194e4 100644
--- a/compute/pztpgqrt.c
+++ b/compute/pztpgqrt.c
@@ -24,30 +24,42 @@
  **/
 #include "control/common.h"
 
-#define V(m,n) V,  m,  n
-#define T(m,n) T,  m,  n
-#define A(m,n) A,  m,  n
-#define B(m,n) B,  m,  n
+#define V1(m,n) V1,  m,  n
+#define T1(m,n) T1,  m,  n
+#define V2(m,n) V2,  m,  n
+#define T2(m,n) T2,  m,  n
+#define Q1(m,n) Q1,  m,  n
+#define Q2(m,n) Q2,  m,  n
+#if defined(CHAMELEON_COPY_DIAG)
+#define DIAG(k) DIAG, k, 0
+#else
+#define DIAG(k) V1, k, k
+#endif
 
 /***************************************************************************//**
  *  Parallel tile QR factorization - dynamic scheduling
  **/
-void morse_pztpgqrt( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, MORSE_desc_t *B,
+void morse_pztpgqrt( int L,
+                     MORSE_desc_t *V1, MORSE_desc_t *T1,
+                     MORSE_desc_t *V2, MORSE_desc_t *T2,
+                     MORSE_desc_t *Q1, MORSE_desc_t *Q2,
                      MORSE_sequence_t *sequence, MORSE_request_t *request )
 {
     MORSE_context_t *morse;
     MORSE_option_t options;
     size_t ws_worker = 0;
     size_t ws_host = 0;
+    MORSE_desc_t *DIAG = NULL;
 
     int k, m, n;
-    int ldak, ldvm, ldbm;
-    int tempkn, tempnn, tempmm, templm;
-    int ib;
+    int ldvk, ldvm;
+    int ldqk, ldqm;
+    int tempkm, tempkn, tempkk, tempnn, tempmm, templm;
+    int ib, minMT;
 
     /* Dimension of the first column */
-    int maxm  = B->m - L;
-    int maxmt = (maxm % B->mb == 0) ? (maxm / B->mb) : (maxm / B->mb + 1);
+    int maxm  = Q2->m - L;
+    int maxmt = (maxm % Q2->mb == 0) ? (maxm / Q2->mb) : (maxm / Q2->mb + 1);
     int maxmtk;
 
     morse = morse_context_self();
@@ -57,18 +69,24 @@ void morse_pztpgqrt( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, M
 
     ib = MORSE_IB;
 
+    if (V1->m > V1->n) {
+        minMT = V1->nt;
+    } else {
+        minMT = V1->mt;
+    }
+
     /*
-     * ztpmqrt = A->nb * ib
+     * ztpmqrt = Q1->nb * ib
      */
-    ws_worker = A->nb * ib;
+    ws_worker = Q1->nb * ib;
 
     /* Allocation of temporary (scratch) working space */
 #if defined(CHAMELEON_USE_CUDA)
     /* Worker space
      *
-     * ztpmqrt = 2 * A->nb * ib
+     * ztpmqrt = 2 * Q1->nb * ib
      */
-    ws_worker = chameleon_max( ws_worker, ib * A->nb * 2 );
+    ws_worker = chameleon_max( ws_worker, ib * Q1->nb * 2 );
 #endif
 
     ws_worker *= sizeof(MORSE_Complex64_t);
@@ -76,31 +94,91 @@ void morse_pztpgqrt( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, M
 
     RUNTIME_options_ws_alloc( &options, ws_worker, ws_host );
 
-    for (k = V->nt-1; k >= 0; k--) {
-        tempkn = k == A->nt-1 ? A->n-k*A->nb : A->nb;
-        ldak = BLKLDD(A, k);
+#if defined(CHAMELEON_COPY_DIAG)
+    /* necessary to avoid dependencies between tasks regarding the diag tile */
+    DIAG = (MORSE_desc_t*)malloc(sizeof(MORSE_desc_t));
+    morse_zdesc_alloc_diag(*DIAG, V1->mb, V1->nb, minMT*V1->mb, V1->nb, 0, 0, minMT*V1->mb, V1->nb, V1->p, V1->q);
+#endif
+
+    for (k = V1->nt-1; k >= 0; k--) {
+        tempkm = k == V1->mt-1 ? V1->m-k*V1->mb : V1->mb;
+        tempkk = k == V1->nt-1 ? V1->n-k*V1->nb : V1->nb;
+        tempkn = k == Q1->nt-1 ? Q1->n-k*Q1->nb : Q1->nb;
+        ldvk = BLKLDD(V1, k);
+        ldqk = BLKLDD(Q1, k);
 
-        maxmtk = chameleon_min( B->mt, maxmt+k ) - 1;
+        /* Equivalent to the tsmqr step on Q1,Q2 */
+        maxmtk = chameleon_min( Q2->mt, maxmt+k ) - 1;
         for (m = maxmtk; m > -1; m--) {
-            tempmm = m == B->mt-1 ? B->m-m*B->mb : B->mb;
-            templm = m == maxmtk  ? tempmm       : 0;
-            ldvm = BLKLDD(V, m);
-            ldbm = BLKLDD(B, m);
+            tempmm = m == Q2->mt-1 ? Q2->m-m*Q2->mb : Q2->mb;
+            templm = m == maxmtk ? tempmm : 0;
+            ldvm = BLKLDD(V2, m);
+            ldqm = BLKLDD(Q2, m);
+
+            for (n = k; n < Q2->nt; n++) {
+                tempnn = n == Q2->nt-1 ? Q2->n-n*Q2->nb : Q2->nb;
+                MORSE_TASK_ztpmqrt(
+                    &options,
+                    MorseLeft, MorseNoTrans,
+                    tempmm, tempnn, tempkn, templm, ib, T2->nb,
+                    V2(m, k), ldvm,
+                    T2(m, k), T2->mb,
+                    Q1(k, n), ldqk,
+                    Q2(m, n), ldqm );
+            }
+        }
 
-            for (n = k; n < B->nt; n++) {
-                tempnn = n == B->nt-1 ? B->n-n*B->nb : B->nb;
+        for (m = Q1->mt - 1; m > k; m--) {
+            tempmm = m == Q1->mt-1 ? Q1->m-m*Q1->mb : Q1->mb;
+            ldvm = BLKLDD(V1, m);
+            ldqm = BLKLDD(Q1, m);
+            for (n = k; n < Q1->nt; n++) {
+                tempnn = n == Q1->nt-1 ? Q1->n-n*Q1->nb : Q1->nb;
                 MORSE_TASK_ztpmqrt(
                     &options,
-                    MorseLeft, MorseConjTrans,
-                    tempmm, tempnn, tempkn, templm, ib, T->nb,
-                    V(m, k), ldvm,
-                    T(m, k), T->mb,
-                    A(k, n), ldak,
-                    B(m, n), ldbm );
+                    MorseLeft, MorseNoTrans,
+                    tempmm, tempnn, tempkn, 0, ib, T1->nb,
+                    V1(m, k), ldvm,
+                    T1(m, k), T1->mb,
+                    Q1(k, n), ldqk,
+                    Q1(m, n), ldqm );
             }
         }
+
+#if defined(CHAMELEON_COPY_DIAG)
+        MORSE_TASK_zlacpy(
+            &options,
+            MorseLower, tempkm, tempkk, V1->nb,
+            V1(k, k), ldvk,
+            DIAG(k), ldvk );
+#if defined(CHAMELEON_USE_CUDA)
+        MORSE_TASK_zlaset(
+            &options,
+            MorseUpper, tempkm, tempkk,
+            0., 1.,
+            DIAG(k), ldvk );
+#endif
+#endif
+        for (n = k; n < Q1->nt; n++) {
+            tempnn = n == Q1->nt-1 ? Q1->n-n*Q1->nb : Q1->nb;
+            MORSE_TASK_zunmqr(
+                &options,
+                MorseLeft, MorseNoTrans,
+                tempkm, tempnn, tempkk, ib, T1->nb,
+                DIAG(k), ldvk,
+                T1(k, k), T1->mb,
+                Q1(k, n), ldqk);
+        }
     }
+
     RUNTIME_options_ws_free(&options);
     RUNTIME_options_finalize(&options, morse);
     MORSE_TASK_dataflush_all();
+
+#if defined(CHAMELEON_COPY_DIAG)
+    MORSE_Sequence_Wait(sequence);
+    morse_desc_mat_free(DIAG);
+    free(DIAG);
+#endif
+    (void)DIAG;
 }
diff --git a/compute/ztpgqrt.c b/compute/ztpgqrt.c
index 6a81d5cd53ea8a830da38ac54e66fa43c74dbdb1..e5b09415383cad31a463c81f06388aa33fda2479 100644
--- a/compute/ztpgqrt.c
+++ b/compute/ztpgqrt.c
@@ -37,68 +37,85 @@
  *******************************************************************************
  *
  * @param[in] M
- *          The number of rows of the matrices B, and V. M >= 0.
+ *          The number of rows of the matrices Q2, and V2. M >= 0.
  *
  * @param[in] N
- *          The number of columns of the matrices B, and A. N >= 0.
+ *          The number of columns of the matrices Q1, and Q1. N >= 0.
  *
  * @param[in] K
  *          The number of elementary reflectors whose product defines
  *          the matrix Q in the matrix V.
+ *          The number of rows of the matrices V1, and Q1.
+ *          The number of columns of the matrices V1, and V2.
  *
  * @param[in] L
- *          The number of rows of the upper trapezoidal part of V.
+ *          The number of rows of the upper trapezoidal part of V2.
  *          MIN(M,N) >= L >= 0.  See Further Details.
  *
- * @param[in] V
+ * @param[in] V1
  *          The i-th row must contain the vector which defines the
  *          elementary reflector H(i), for i = 1,2,...,k, as returned by
- *          MORSE_ztpqrt() in the first k rows of its array argument V.
- *          V is matrx of size M-by-K. The first M-L rows
+ *          MORSE_ztpqrt().
+ *          V1 is a matrix of size K-by-K.
+ *
+ * @param[in] LDV1
+ *          The leading dimension of the array V1. LDV1 >= max(1,K).
+ *
+ * @param[int] descT1
+ *          The auxiliary factorization data generated by the call to
+ *          MORSE_zgeqrf() on V1.
+ *
+ * @param[in] V2
+ *          The i-th row must contain the vector which defines the
+ *          elementary reflector H(i), for i = 1,2,...,k, as returned by
+ *          MORSE_ztpqrt() in the first k rows of its array argument V2.
+ *          V2 is a matrix of size M-by-K. The first M-L rows
  *          are rectangular, and the last L rows are upper trapezoidal.
  *
- * @param[in] LDV
- *          The leading dimension of the array V. LDV >= max(1,K).
+ * @param[in] LDV2
+ *          The leading dimension of the array V2. LDV2 >= max(1,M).
  *
- * @param[int] descT
- *          On exit, auxiliary factorization data, required by MORSE_zgeqrs to
- *          solve the system of equations, or by any function to apply the Q.
+ * @param[int] descT2
+ *          The auxiliary factorization data, generated by the call to
+ *          MORSE_ztpqrt() on V1 and V2, and associated to V2.
  *
- * @param[in,out] A
- *          A is COMPLEX*16 array, dimension (LDA,N)
- *          On entry, the K-by-N matrix A.
- *          On exit, A is overwritten by the corresponding block of
- *          Q*A.  See Further Details.
+ * @param[in,out] Q1
+ *          Q1 is COMPLEX*16 array, dimension (LDQ1,N)
+ *          On entry, the K-by-N matrix Q1.
+ *          On exit, Q1 is overwritten by the corresponding block of
+ *          Q*Q1.  See Further Details.
  *
- * @param[in] LDA
- *          The leading dimension of the array A. LDA >= max(1,K).
+ * @param[in] LDQ1
+ *          The leading dimension of the array Q1. LDQ1 >= max(1,K).
  *
- * @param[in,out] B
- *          On entry, the pentagonal M-by-N matrix B.
- *          On exit, B contains Q.
+ * @param[in,out] Q2
+ *          On entry, the pentagonal M-by-N matrix Q2.
+ *          On exit, Q2 contains Q.
  *
- * @param[in] LDB
- *          The leading dimension of the array B.  LDB >= max(1,M).
+ * @param[in] LDQ2
+ *          The leading dimension of the array Q2.  LDQ2 >= max(1,M).
  *
  * @par Further Details:
  * =====================
  *
  *  The input matrix Q is a (K+M)-by-N matrix
  *
- *               Q = [ A ]
- *                   [ B ]
+ *               Q = [ Q1 ]
+ *                   [ Q2 ]
  *
- *  where A is an identity matrix, and B is a M-by-N matrix of 0.
- *  V a matrix of householder reflectors with a pentagonal shape consisting of a
- *  (M-L)-by-K rectangular matrix V1 on top of a L-by-N
- *  Upper trapezoidal matrix V2:
+ *  where Q1 is an identity matrix, and Q2 is a M-by-N matrix of 0.
+ *  V is a matrix of householder reflectors with a pentagonal shape consisting
+ *  of a K-by-K rectangular matrix V1 on top of a matrix V2 composed of
+ *  (M-L)-by-K rectangular part on top of a L-by-N upper trapezoidal matrix:
  *
- *               V = [ V1 ]  <- (M-L)-by-N rectangular
- *                   [ V2 ]  <-     L-by-N upper trapezoidal.
+ *               V = [ V1  ]  <-     K-by-K rectangular
+ *                   [ V2a ]  <- (M-L)-by-K rectangular
+ *                   [ V2b ]  <-     L-by-K upper trapezoidal.
  *
- *  The upper trapezoidal matrix V2 consists of the first L rows of a
- *  K-by-K upper triangular matrix, where 0 <= L <= MIN(M,K).  If L=0,
- *  V is rectangular M-by-K; if M=L=K, V is upper triangular.
+ *  The upper trapezoidal part of the matrix V2 consists of the first L rows of
+ *  a K-by-K upper triangular matrix, where 0 <= L <= MIN(M,K).  If L=0, V2 is
+ *  rectangular M-by-K; if M=L=K, V2 is upper triangular. Those are the two
+ *  cases only handled for now.
  *
  *******************************************************************************
  *
@@ -117,17 +134,17 @@
  *
  ******************************************************************************/
 int MORSE_ztpgqrt( int M, int N, int K, int L,
-                   MORSE_Complex64_t *V, int LDV,
-                   MORSE_desc_t *descT,
-                   MORSE_Complex64_t *A, int LDA,
-                   MORSE_Complex64_t *B, int LDB )
+                   MORSE_Complex64_t *V1, int LDV1, MORSE_desc_t *descT1,
+                   MORSE_Complex64_t *V2, int LDV2, MORSE_desc_t *descT2,
+                   MORSE_Complex64_t *Q1, int LDQ1,
+                   MORSE_Complex64_t *Q2, int LDQ2 )
 {
     int NB;
     int status;
     MORSE_context_t *morse;
     MORSE_sequence_t *sequence = NULL;
     MORSE_request_t request = MORSE_REQUEST_INITIALIZER;
-    MORSE_desc_t descA, descB, descV;
+    MORSE_desc_t descQ1, descQ2, descV1, descV2;
     int minMK = chameleon_min( M, K );
 
     morse = morse_context_self();
@@ -153,18 +170,26 @@ int MORSE_ztpgqrt( int M, int N, int K, int L,
         morse_error("MORSE_ztpgqrt", "illegal value of N");
         return -4;
     }
-    if (LDV < chameleon_max(1, M)) {
-        morse_error("MORSE_ztpgqrt", "illegal value of LDV");
+    if (K != N) {
+        morse_error("MORSE_ztpgqrt", "illegal value of K and N. K must be equal to N");
+        return -3;
+    }
+    if (LDV1 < chameleon_max(1, K)) {
+        morse_error("MORSE_ztpgqrt", "illegal value of LDV1");
         return -6;
     }
-    if (LDA < chameleon_max(1, K)) {
-        morse_error("MORSE_ztpgqrt", "illegal value of LDA");
+    if (LDV2 < chameleon_max(1, M)) {
+        morse_error("MORSE_ztpgqrt", "illegal value of LDV2");
         return -9;
     }
-    if (LDB < chameleon_max(1, M)) {
-        morse_error("MORSE_ztpgqrt", "illegal value of LDB");
+    if (LDQ1 < chameleon_max(1, K)) {
+        morse_error("MORSE_ztpgqrt", "illegal value of LDQ1");
         return -11;
     }
+    if (LDQ2 < chameleon_max(1, M)) {
+        morse_error("MORSE_ztpgqrt", "illegal value of LDQ2");
+        return -13;
+    }
 
     /* Quick return */
     if (minMK == 0)
@@ -183,34 +208,41 @@ int MORSE_ztpgqrt( int M, int N, int K, int L,
     morse_sequence_create(morse, &sequence);
 
 /*    if ( MORSE_TRANSLATION == MORSE_OUTOFPLACE ) {*/
-        morse_zooplap2tile( descV, V, NB, NB, LDB, K, 0, 0, M, K, sequence, &request,
-                            morse_desc_mat_free(&(descV)) );
-        morse_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, K, N, sequence, &request,
-                            (morse_desc_mat_free(&(descV)),
-                             morse_desc_mat_free(&(descA))) );
-        morse_zooplap2tile( descB, B, NB, NB, LDB, N, 0, 0, M, N, sequence, &request,
-                            (morse_desc_mat_free(&(descV)),
-                             morse_desc_mat_free(&(descA)),
-                             morse_desc_mat_free(&(descB))) );
+        morse_zooplap2tile( descV1, V1, NB, NB, LDV1, K, 0, 0, M, K, sequence, &request,
+                            morse_desc_mat_free(&(descV1)) );
+        morse_zooplap2tile( descV2, V2, NB, NB, LDV2, K, 0, 0, M, K, sequence, &request,
+                            (morse_desc_mat_free(&(descV1)),
+                             morse_desc_mat_free(&(descV2))) );
+        morse_zooplap2tile( descQ1, Q1, NB, NB, LDQ1, N, 0, 0, K, N, sequence, &request,
+                            (morse_desc_mat_free(&(descV1)),
+                             morse_desc_mat_free(&(descV2)),
+                             morse_desc_mat_free(&(descQ1))) );
+        morse_zooplap2tile( descQ2, Q2, NB, NB, LDQ2, N, 0, 0, M, N, sequence, &request,
+                            (morse_desc_mat_free(&(descV1)),
+                             morse_desc_mat_free(&(descV2)),
+                             morse_desc_mat_free(&(descQ1)),
+                             morse_desc_mat_free(&(descQ2))) );
 /*    } else {*/
-/*        morse_ziplap2tile( descA, A, NB, NB, LDA, N, 0, 0, M, N,*/
+/*        morse_ziplap2tile( descQ1, Q1, NB, NB, LDQ1, N, 0, 0, M, N,*/
 /*                            sequence, &request);*/
 /*    }*/
 
     /* Call the tile interface */
-    MORSE_ztpgqrt_Tile_Async(L, &descV, descT, &descA, &descB, sequence, &request);
+    MORSE_ztpgqrt_Tile_Async(L, &descV1, descT1, &descV2, descT2, &descQ1, &descQ2, sequence, &request);
 
 /*    if ( MORSE_TRANSLATION == MORSE_OUTOFPLACE ) {*/
-        morse_zooptile2lap(descA, A, NB, NB, LDA, N, sequence, &request);
-        morse_zooptile2lap(descB, B, NB, NB, LDB, N, sequence, &request);
+        morse_zooptile2lap(descQ1, Q1, NB, NB, LDQ1, N, sequence, &request);
+        morse_zooptile2lap(descQ2, Q2, NB, NB, LDQ2, N, sequence, &request);
         morse_sequence_wait(morse, sequence);
-        morse_desc_mat_free(&descV);
-        morse_desc_mat_free(&descA);
-        morse_desc_mat_free(&descB);
+        morse_desc_mat_free(&descV1);
+        morse_desc_mat_free(&descV2);
+        morse_desc_mat_free(&descQ1);
+        morse_desc_mat_free(&descQ2);
 /*    } else {*/
-/*        morse_ziptile2lap( descV, V, NB, NB, LDV, K,  sequence, &request);*/
-/*        morse_ziptile2lap( descA, A, NB, NB, LDA, N,  sequence, &request);*/
-/*        morse_ziptile2lap( descB, B, NB, NB, LDB, N,  sequence, &request);*/
+/*        morse_ziptile2lap( descV1, V1, NB, NB, LDV1, K,  sequence, &request);*/
+/*        morse_ziptile2lap( descV2, V2, NB, NB, LDV2, K,  sequence, &request);*/
+/*        morse_ziptile2lap( descQ1, Q1, NB, NB, LDQ1, N,  sequence, &request);*/
+/*        morse_ziptile2lap( descQ2, Q2, NB, NB, LDQ2, N,  sequence, &request);*/
 /*        morse_sequence_wait(morse, sequence);*/
 /*    }*/
 
@@ -231,16 +263,6 @@ int MORSE_ztpgqrt( int M, int N, int K, int L,
  *
  *******************************************************************************
  *
- * @param[in,out] A
- *          On entry, the M-by-N matrix A.
- *          On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N
- *          upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the
- *          diagonal represent the unitary matrix Q as a product of elementary reflectors stored
- *          by tiles.
- *
- * @param[out] T
- *          On exit, auxiliary factorization data, required by MORSE_zgeqrs to solve the system
- *          of equations.
  *
  *******************************************************************************
  *
@@ -257,7 +279,10 @@ int MORSE_ztpgqrt( int M, int N, int K, int L,
  * @sa MORSE_zgeqrs_Tile
  *
  ******************************************************************************/
-int MORSE_ztpgqrt_Tile( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, MORSE_desc_t *B )
+int MORSE_ztpgqrt_Tile( int L,
+                        MORSE_desc_t *V1, MORSE_desc_t *T1,
+                        MORSE_desc_t *V2, MORSE_desc_t *T2,
+                        MORSE_desc_t *Q1, MORSE_desc_t *Q2 )
 {
     MORSE_context_t *morse;
     MORSE_sequence_t *sequence = NULL;
@@ -270,10 +295,10 @@ int MORSE_ztpgqrt_Tile( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A
         return MORSE_ERR_NOT_INITIALIZED;
     }
     morse_sequence_create(morse, &sequence);
-    MORSE_ztpgqrt_Tile_Async(L, V, T, A, B, sequence, &request);
+    MORSE_ztpgqrt_Tile_Async(L, V1, T1, V2, T2, Q1, Q2, sequence, &request);
     morse_sequence_wait(morse, sequence);
-    RUNTIME_desc_getoncpu(A);
-    RUNTIME_desc_getoncpu(B);
+    RUNTIME_desc_getoncpu(Q1);
+    RUNTIME_desc_getoncpu(Q2);
 
     status = sequence->status;
     morse_sequence_destroy(morse, sequence);
@@ -309,7 +334,10 @@ int MORSE_ztpgqrt_Tile( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A
  * @sa MORSE_zgeqrs_Tile_Async
  *
  ******************************************************************************/
-int MORSE_ztpgqrt_Tile_Async( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, MORSE_desc_t *B,
+int MORSE_ztpgqrt_Tile_Async( int L,
+                              MORSE_desc_t *V1, MORSE_desc_t *T1,
+                              MORSE_desc_t *V2, MORSE_desc_t *T2,
+                              MORSE_desc_t *Q1, MORSE_desc_t *Q2,
                               MORSE_sequence_t *sequence, MORSE_request_t *request )
 {
     MORSE_context_t *morse;
@@ -334,37 +362,47 @@ int MORSE_ztpgqrt_Tile_Async( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_des
         return morse_request_fail(sequence, request, MORSE_ERR_SEQUENCE_FLUSHED);
 
     /* Check descriptors for correctness */
-    if (morse_desc_check(V) != MORSE_SUCCESS) {
-        morse_error("MORSE_ztpgqrt_Tile", "invalid third descriptor");
+    if (morse_desc_check(V1) != MORSE_SUCCESS) {
+        morse_error("MORSE_ztpgqrt_Tile", "invalid V1 descriptor");
+        return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
+    }
+    if (morse_desc_check(T1) != MORSE_SUCCESS) {
+        morse_error("MORSE_ztpgqrt_Tile", "invalid T1 descriptor");
+        return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
+    }
+    if (morse_desc_check(V2) != MORSE_SUCCESS) {
+        morse_error("MORSE_ztpgqrt_Tile", "invalid V2 descriptor");
         return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
     }
-    if (morse_desc_check(T) != MORSE_SUCCESS) {
-        morse_error("MORSE_ztpgqrt_Tile", "invalid third descriptor");
+    if (morse_desc_check(T2) != MORSE_SUCCESS) {
+        morse_error("MORSE_ztpgqrt_Tile", "invalid T2 descriptor");
         return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
     }
-    if (morse_desc_check(A) != MORSE_SUCCESS) {
-        morse_error("MORSE_ztpgqrt_Tile", "invalid first descriptor");
+    if (morse_desc_check(Q1) != MORSE_SUCCESS) {
+        morse_error("MORSE_ztpgqrt_Tile", "invalid Q1 descriptor");
         return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
     }
-    if (morse_desc_check(B) != MORSE_SUCCESS) {
-        morse_error("MORSE_ztpgqrt_Tile", "invalid second descriptor");
+    if (morse_desc_check(Q2) != MORSE_SUCCESS) {
+        morse_error("MORSE_ztpgqrt_Tile", "invalid Q2 descriptor");
         return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
     }
     /* Check input arguments */
-    if (A->nb != A->mb) {
+    if (Q1->nb != Q1->mb) {
         morse_error("MORSE_ztpgqrt_Tile", "only square tiles supported");
         return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
     }
-    if (((B->m - L) % B->mb) != 0) {
+    if (((Q2->m - L) % Q2->mb) != 0) {
         morse_error("MORSE_ztpgqrt_Tile", "Triangular part must be aligned with tiles");
         return morse_request_fail(sequence, request, MORSE_ERR_ILLEGAL_VALUE);
     }
 
     /* if (morse->householder == MORSE_FLAT_HOUSEHOLDER) { */
-    morse_pztpgqrt(L, V, T, A, B, sequence, request);
+    morse_pzlaset( MorseUpperLower, 0., 1., Q1, sequence, request );
+    morse_pzlaset( MorseUpperLower, 0., 0., Q2, sequence, request );
+    morse_pztpgqrt( L, V1, T1, V2, T2, Q1, Q2, sequence, request );
     /* } */
     /* else { */
-    /*    morse_pztpgqrtrh(A, T, MORSE_RHBLK, sequence, request); */
+    /*    morse_pztpgqrtrh(Q1, T, MORSE_RHBLK, sequence, request); */
     /* } */
 
     return MORSE_SUCCESS;
diff --git a/control/compute_z.h b/control/compute_z.h
index 122120e48999160fafb1e01aef495670fe363dba..bb930ba0ff84322f11b7c5969ea268ae7a91b831 100644
--- a/control/compute_z.h
+++ b/control/compute_z.h
@@ -134,7 +134,7 @@ void morse_pzsyrk(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MO
 void morse_pzsyr2k(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_Complex64_t beta, MORSE_desc_t *C, MORSE_sequence_t *sequence, MORSE_request_t *request);
 void morse_pzsytrf(MORSE_enum uplo, MORSE_desc_t *A, MORSE_sequence_t *sequence, MORSE_request_t *request);
 void morse_pztile2band(MORSE_enum uplo, MORSE_desc_t *A, MORSE_desc_t *descAB, MORSE_sequence_t *sequence, MORSE_request_t *request);
-void morse_pztpgqrt( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_sequence_t *sequence, MORSE_request_t *request );
+void morse_pztpgqrt( int L, MORSE_desc_t *V1, MORSE_desc_t *T1, MORSE_desc_t *V2, MORSE_desc_t *T2, MORSE_desc_t *Q1, MORSE_desc_t *Q2, MORSE_sequence_t *sequence, MORSE_request_t *request );
 void morse_pztpqrt( int L, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_desc_t *T, MORSE_sequence_t *sequence, MORSE_request_t *request );
 void morse_pztradd(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_Complex64_t beta, MORSE_desc_t *B, MORSE_sequence_t *sequence, MORSE_request_t *request);
 void morse_pztrmm(MORSE_enum side, MORSE_enum uplo, MORSE_enum transA, MORSE_enum diag, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_sequence_t *sequence, MORSE_request_t *request);
diff --git a/include/morse_z.h b/include/morse_z.h
index 2718a6bea1c82411a0c4c401821f0b5be940f90d..65f911f00a7f257fea0d897da102c1c8294ef9fa 100644
--- a/include/morse_z.h
+++ b/include/morse_z.h
@@ -102,7 +102,7 @@ int MORSE_zsyrk(MORSE_enum uplo, MORSE_enum trans, int N, int K, MORSE_Complex64
 int MORSE_zsyr2k(MORSE_enum uplo, MORSE_enum trans, int N, int K, MORSE_Complex64_t alpha, MORSE_Complex64_t *A, int LDA, MORSE_Complex64_t *B, int LDB, MORSE_Complex64_t beta, MORSE_Complex64_t *C, int LDC);
 int MORSE_zsysv(MORSE_enum uplo, int N, int NRHS, MORSE_Complex64_t *A, int LDA, MORSE_Complex64_t *B, int LDB);
 int MORSE_zsytrs(MORSE_enum uplo, int N, int NRHS, MORSE_Complex64_t *A, int LDA, MORSE_Complex64_t *B, int LDB);
-int MORSE_ztpgqrt( int M, int N, int K, int L, MORSE_Complex64_t *V, int LDV, MORSE_desc_t *descT, MORSE_Complex64_t *A, int LDA, MORSE_Complex64_t *B, int LDB );
+int MORSE_ztpgqrt( int M, int N, int K, int L, MORSE_Complex64_t *V1, int LDV1, MORSE_desc_t *descT1, MORSE_Complex64_t *V2, int LDV2, MORSE_desc_t *descT2, MORSE_Complex64_t *Q1, int LDQ1, MORSE_Complex64_t *Q2, int LDQ2 );
 int MORSE_ztpqrt( int M, int N, int L, MORSE_Complex64_t *A, int LDA, MORSE_Complex64_t *B, int LDB, MORSE_desc_t *descT );
 int MORSE_ztradd(MORSE_enum uplo, MORSE_enum trans, int M, int N, MORSE_Complex64_t alpha, MORSE_Complex64_t *A, int LDA, MORSE_Complex64_t beta, MORSE_Complex64_t *B, int LDB);
 int MORSE_ztrmm(MORSE_enum side, MORSE_enum uplo, MORSE_enum transA, MORSE_enum diag, int N, int NRHS, MORSE_Complex64_t alpha, MORSE_Complex64_t *A, int LDA, MORSE_Complex64_t *B, int LDB);
@@ -181,7 +181,7 @@ int MORSE_zsyrk_Tile(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha,
 int MORSE_zsyr2k_Tile(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_Complex64_t beta, MORSE_desc_t *C);
 int MORSE_zsysv_Tile(MORSE_enum uplo, MORSE_desc_t *A, MORSE_desc_t *B);
 int MORSE_zsytrs_Tile(MORSE_enum uplo, MORSE_desc_t *A, MORSE_desc_t *B);
-int MORSE_ztpgqrt_Tile( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, MORSE_desc_t *B );
+int MORSE_ztpgqrt_Tile( int L, MORSE_desc_t *V1, MORSE_desc_t *T1, MORSE_desc_t *V2, MORSE_desc_t *T2, MORSE_desc_t *Q1, MORSE_desc_t *Q2 );
 int MORSE_ztpqrt_Tile( int L, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_desc_t *T );
 int MORSE_ztradd_Tile(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_Complex64_t beta, MORSE_desc_t *B);
 int MORSE_ztrmm_Tile(MORSE_enum side, MORSE_enum uplo, MORSE_enum transA, MORSE_enum diag, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_desc_t *B);
@@ -257,7 +257,7 @@ int MORSE_zsytrs_Tile_Async(MORSE_enum uplo, MORSE_desc_t *A, MORSE_desc_t *B, M
 int MORSE_zsymm_Tile_Async(MORSE_enum side, MORSE_enum uplo, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_Complex64_t beta, MORSE_desc_t *C, MORSE_sequence_t *sequence, MORSE_request_t *request);
 int MORSE_zsyrk_Tile_Async(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_Complex64_t beta, MORSE_desc_t *C, MORSE_sequence_t *sequence, MORSE_request_t *request);
 int MORSE_zsyr2k_Tile_Async(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_Complex64_t beta, MORSE_desc_t *C, MORSE_sequence_t *sequence, MORSE_request_t *request);
-int MORSE_ztpgqrt_Tile_Async( int L, MORSE_desc_t *V, MORSE_desc_t *T, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_sequence_t *sequence, MORSE_request_t *request );
+int MORSE_ztpgqrt_Tile_Async( int L, MORSE_desc_t *V1, MORSE_desc_t *T1, MORSE_desc_t *V2, MORSE_desc_t *T2, MORSE_desc_t *Q1, MORSE_desc_t *Q2, MORSE_sequence_t *sequence, MORSE_request_t *request );
 int MORSE_ztpqrt_Tile_Async( int L, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_desc_t *T, MORSE_sequence_t *sequence, MORSE_request_t *request );
 int MORSE_ztradd_Tile_Async(MORSE_enum uplo, MORSE_enum trans, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_Complex64_t beta, MORSE_desc_t *B, MORSE_sequence_t *sequence, MORSE_request_t *request);
 int MORSE_ztrmm_Tile_Async(MORSE_enum side, MORSE_enum uplo, MORSE_enum transA, MORSE_enum diag, MORSE_Complex64_t alpha, MORSE_desc_t *A, MORSE_desc_t *B, MORSE_sequence_t *sequence, MORSE_request_t *request);