Merge pull request #4087 from martin-frbg/lapack847

Improve variants of Cholesky and QR (Reference-LAPACK PR 847)

lapack-netlib/SRC/VARIANTS/Makefile

@@ -28,7 +28,7 @@ LULL = lu/LL/cgetrf.o lu/LL/dgetrf.o lu/LL/sgetrf.o lu/LL/zgetrf.o
 
 LUREC = lu/REC/cgetrf.o lu/REC/dgetrf.o lu/REC/sgetrf.o lu/REC/zgetrf.o
 
-QRLL = qr/LL/cgeqrf.o qr/LL/dgeqrf.o qr/LL/sgeqrf.o qr/LL/zgeqrf.o qr/LL/sceil.o
+QRLL = qr/LL/cgeqrf.o qr/LL/dgeqrf.o qr/LL/sgeqrf.o qr/LL/zgeqrf.o
 
 
 .PHONY: all

lapack-netlib/SRC/VARIANTS/cholesky/RL/cpotrf.f

@@ -24,7 +24,7 @@ C> \brief \b CPOTRF VARIANT: right looking block version of the algorithm, calli
 C>\details \b Purpose:
 C>\verbatim
 C>
-C> CPOTRF computes the Cholesky factorization of a real Hermitian
+C> CPOTRF computes the Cholesky factorization of a complex Hermitian
 C> positive definite matrix A.
 C>
 C> The factorization has the form

lapack-netlib/SRC/VARIANTS/cholesky/RL/zpotrf.f

@@ -24,7 +24,7 @@ C> \brief \b ZPOTRF VARIANT: right looking block version of the algorithm, calli
 C>\details \b Purpose:
 C>\verbatim
 C>
-C> ZPOTRF computes the Cholesky factorization of a real Hermitian
+C> ZPOTRF computes the Cholesky factorization of a complex Hermitian
 C> positive definite matrix A.
 C>
 C> The factorization has the form

lapack-netlib/SRC/VARIANTS/cholesky/TOP/cpotrf.f

@@ -24,7 +24,7 @@ C> \brief \b CPOTRF VARIANT: top-looking block version of the algorithm, calling
 C>\details \b Purpose:
 C>\verbatim
 C>
-C> CPOTRF computes the Cholesky factorization of a real symmetric
+C> CPOTRF computes the Cholesky factorization of a complex Hermitian
 C> positive definite matrix A.
 C>
 C> The factorization has the form
@@ -55,7 +55,7 @@ C>
 C> \param[in,out] A
 C> \verbatim
 C>          A is COMPLEX array, dimension (LDA,N)
-C>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+C>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
 C>          N-by-N upper triangular part of A contains the upper
 C>          triangular part of the matrix A, and the strictly lower
 C>          triangular part of A is not referenced.  If UPLO = 'L', the

lapack-netlib/SRC/VARIANTS/cholesky/TOP/zpotrf.f

@@ -24,7 +24,7 @@ C> \brief \b ZPOTRF VARIANT: top-looking block version of the algorithm, calling
 C>\details \b Purpose:
 C>\verbatim
 C>
-C> ZPOTRF computes the Cholesky factorization of a real symmetric
+C> ZPOTRF computes the Cholesky factorization of a complex Hermitian
 C> positive definite matrix A.
 C>
 C> The factorization has the form
@@ -55,7 +55,7 @@ C>
 C> \param[in,out] A
 C> \verbatim
 C>          A is COMPLEX*16 array, dimension (LDA,N)
-C>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
+C>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
 C>          N-by-N upper triangular part of A contains the upper
 C>          triangular part of the matrix A, and the strictly lower
 C>          triangular part of A is not referenced.  If UPLO = 'L', the

lapack-netlib/SRC/VARIANTS/qr/LL/cgeqrf.f

@@ -23,7 +23,7 @@ C> \brief \b CGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm.
 C>\details \b Purpose:
 C>\verbatim
 C>
-C> CGEQRF computes a QR factorization of a real M-by-N matrix A:
+C> CGEQRF computes a QR factorization of a complex M-by-N matrix A:
 C> A = Q * R.
 C>
 C> This is the left-looking Level 3 BLAS version of the algorithm.
@@ -172,12 +172,11 @@ C>
       EXTERNAL           CGEQR2, CLARFB, CLARFT, XERBLA
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          MAX, MIN
+      INTRINSIC          CEILING, MAX, MIN, REAL
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      REAL               SCEIL
-      EXTERNAL           ILAENV, SCEIL
+      EXTERNAL           ILAENV
 *     ..
 *     .. Executable Statements ..
 
@@ -205,13 +204,13 @@ C>
 *
 *     So here 4 x 4 is the last T stored in the workspace
 *
-      NT = K-SCEIL(REAL(K-NX)/REAL(NB))*NB
+      NT = K-CEILING(REAL(K-NX)/REAL(NB))*NB
 
 *
 *     optimal workspace = space for dlarfb + space for normal T's + space for the last T
 *
       LLWORK = MAX (MAX((N-M)*K, (N-M)*NB), MAX(K*NB, NB*NB))
-      LLWORK = SCEIL(REAL(LLWORK)/REAL(NB))
+      LLWORK = CEILING(REAL(LLWORK)/REAL(NB))
 
       IF( K.EQ.0 ) THEN
 
@@ -230,7 +229,7 @@ C>
 
       ELSE
 
-          LBWORK = SCEIL(REAL(K)/REAL(NB))*NB
+          LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
           WORK( 1 ) = LWKOPT
 

lapack-netlib/SRC/VARIANTS/qr/LL/dgeqrf.f

@@ -172,12 +172,11 @@ C>
       EXTERNAL           DGEQR2, DLARFB, DLARFT, XERBLA
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          MAX, MIN
+      INTRINSIC          CEILING, MAX, MIN, REAL
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      REAL               SCEIL
-      EXTERNAL           ILAENV, SCEIL
+      EXTERNAL           ILAENV
 *     ..
 *     .. Executable Statements ..
 
@@ -205,13 +204,13 @@ C>
 *
 *     So here 4 x 4 is the last T stored in the workspace
 *
-      NT = K-SCEIL(REAL(K-NX)/REAL(NB))*NB
+      NT = K-CEILING(REAL(K-NX)/REAL(NB))*NB
 
 *
 *     optimal workspace = space for dlarfb + space for normal T's + space for the last T
 *
       LLWORK = MAX (MAX((N-M)*K, (N-M)*NB), MAX(K*NB, NB*NB))
-      LLWORK = SCEIL(REAL(LLWORK)/REAL(NB))
+      LLWORK = CEILING(REAL(LLWORK)/REAL(NB))
 
       IF( K.EQ.0 ) THEN
 
@@ -230,7 +229,7 @@ C>
 
       ELSE
 
-          LBWORK = SCEIL(REAL(K)/REAL(NB))*NB
+          LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
           WORK( 1 ) = LWKOPT
 

lapack-netlib/SRC/VARIANTS/qr/LL/sceil.f

@@ -1,86 +0,0 @@
-C> \brief \b SCEIL
-*
-*  =========== DOCUMENTATION ===========
-*
-* Online html documentation available at
-*            http://www.netlib.org/lapack/explore-html/
-*
-*  Definition:
-*  ===========
-*
-*       REAL FUNCTION SCEIL( A )
-*
-*       .. Scalar Arguments ..
-*       REAL A
-*       ..
-*
-*    =====================================================================
-*
-*       .. Intrinsic Functions ..
-* 	      INTRINSIC          INT
-*       ..
-*       .. Executable Statements ..*
-*
-*       IF (A-INT(A).EQ.0) THEN
-*           SCEIL = A
-*       ELSE IF (A.GT.0) THEN
-*           SCEIL = INT(A)+1;
-*       ELSE
-*           SCEIL = INT(A)
-*       END IF
-*
-*       RETURN
-*
-*       END
-*  Purpose
-*  =======
-*
-C>\details \b Purpose:
-C>\verbatim
-C>\endverbatim
-*
-*  Arguments:
-*  ==========
-*
-*
-*  Authors:
-*  ========
-*
-C> \author Univ. of Tennessee
-C> \author Univ. of California Berkeley
-C> \author Univ. of Colorado Denver
-C> \author NAG Ltd.
-*
-C> \date December 2016
-*
-C> \ingroup variantsOTHERcomputational
-*
-*  =====================================================================
-      REAL FUNCTION SCEIL( A )
-*
-*  -- LAPACK computational routine --
-*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
-*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*
-*     .. Scalar Arguments ..*
-      REAL A
-*     ..
-*
-*  =====================================================================
-*
-*     .. Intrinsic Functions ..
-	      INTRINSIC          INT
-*     ..
-*     .. Executable Statements ..*
-*
-      IF (A-INT(A).EQ.0) THEN
-          SCEIL = A
-      ELSE IF (A.GT.0) THEN
-          SCEIL = INT(A)+1;
-      ELSE
-          SCEIL = INT(A)
-      END IF
-
-      RETURN
-*
-      END

lapack-netlib/SRC/VARIANTS/qr/LL/sgeqrf.f

@@ -172,12 +172,11 @@ C>
       EXTERNAL           SGEQR2, SLARFB, SLARFT, XERBLA
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          MAX, MIN
+      INTRINSIC          CEILING, MAX, MIN, REAL
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      REAL               SCEIL
-      EXTERNAL           ILAENV, SCEIL
+      EXTERNAL           ILAENV
 *     ..
 *     .. Executable Statements ..
 
@@ -205,13 +204,13 @@ C>
 *
 *     So here 4 x 4 is the last T stored in the workspace
 *
-      NT = K-SCEIL(REAL(K-NX)/REAL(NB))*NB
+      NT = K-CEILING(REAL(K-NX)/REAL(NB))*NB
 
 *
 *     optimal workspace = space for dlarfb + space for normal T's + space for the last T
 *
       LLWORK = MAX (MAX((N-M)*K, (N-M)*NB), MAX(K*NB, NB*NB))
-      LLWORK = SCEIL(REAL(LLWORK)/REAL(NB))
+      LLWORK = CEILING(REAL(LLWORK)/REAL(NB))
 
       IF( K.EQ.0 ) THEN
 
@@ -230,7 +229,7 @@ C>
 
       ELSE
 
-          LBWORK = SCEIL(REAL(K)/REAL(NB))*NB
+          LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
           WORK( 1 ) = LWKOPT
 

lapack-netlib/SRC/VARIANTS/qr/LL/zgeqrf.f

@@ -23,7 +23,7 @@ C> \brief \b ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm.
 C>\details \b Purpose:
 C>\verbatim
 C>
-C> ZGEQRF computes a QR factorization of a real M-by-N matrix A:
+C> ZGEQRF computes a QR factorization of a complex M-by-N matrix A:
 C> A = Q * R.
 C>
 C> This is the left-looking Level 3 BLAS version of the algorithm.
@@ -172,12 +172,11 @@ C>
       EXTERNAL           ZGEQR2, ZLARFB, ZLARFT, XERBLA
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          MAX, MIN
+      INTRINSIC          CEILING, MAX, MIN, REAL
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      REAL               SCEIL
-      EXTERNAL           ILAENV, SCEIL
+      EXTERNAL           ILAENV
 *     ..
 *     .. Executable Statements ..
 
@@ -205,13 +204,13 @@ C>
 *
 *     So here 4 x 4 is the last T stored in the workspace
 *
-      NT = K-SCEIL(REAL(K-NX)/REAL(NB))*NB
+      NT = K-CEILING(REAL(K-NX)/REAL(NB))*NB
 
 *
 *     optimal workspace = space for dlarfb + space for normal T's + space for the last T
 *
       LLWORK = MAX (MAX((N-M)*K, (N-M)*NB), MAX(K*NB, NB*NB))
-      LLWORK = SCEIL(REAL(LLWORK)/REAL(NB))
+      LLWORK = CEILING(REAL(LLWORK)/REAL(NB))
 
       IF( K.EQ.0 ) THEN
 
@@ -230,7 +229,7 @@ C>
 
       ELSE
 
-          LBWORK = SCEIL(REAL(K)/REAL(NB))*NB
+          LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
           WORK( 1 ) = LWKOPT