--- rpl/lapack/lapack/zhptrd.f 2010/01/26 15:22:45 1.1.1.1
+++ rpl/lapack/lapack/zhptrd.f 2023/08/07 08:39:26 1.18
@@ -1,9 +1,157 @@
+*> \brief \b ZHPTRD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHPTRD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHPTRD( UPLO, N, AP, D, E, TAU, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION D( * ), E( * )
+* COMPLEX*16 AP( * ), TAU( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHPTRD reduces a complex Hermitian matrix A stored in packed form to
+*> real symmetric tridiagonal form T by a unitary similarity
+*> transformation: Q**H * A * Q = T.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] AP
+*> \verbatim
+*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
+*> On entry, the upper or lower triangle of the Hermitian matrix
+*> A, packed columnwise in a linear array. The j-th column of A
+*> is stored in the array AP as follows:
+*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
+*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
+*> On exit, if UPLO = 'U', the diagonal and first superdiagonal
+*> of A are overwritten by the corresponding elements of the
+*> tridiagonal matrix T, and the elements above the first
+*> superdiagonal, with the array TAU, represent the unitary
+*> matrix Q as a product of elementary reflectors; if UPLO
+*> = 'L', the diagonal and first subdiagonal of A are over-
+*> written by the corresponding elements of the tridiagonal
+*> matrix T, and the elements below the first subdiagonal, with
+*> the array TAU, represent the unitary matrix Q as a product
+*> of elementary reflectors. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (N)
+*> The diagonal elements of the tridiagonal matrix T:
+*> D(i) = A(i,i).
+*> \endverbatim
+*>
+*> \param[out] E
+*> \verbatim
+*> E is DOUBLE PRECISION array, dimension (N-1)
+*> The off-diagonal elements of the tridiagonal matrix T:
+*> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is COMPLEX*16 array, dimension (N-1)
+*> The scalar factors of the elementary reflectors (see Further
+*> Details).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16OTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> If UPLO = 'U', the matrix Q is represented as a product of elementary
+*> reflectors
+*>
+*> Q = H(n-1) . . . H(2) H(1).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - tau * v * v**H
+*>
+*> where tau is a complex scalar, and v is a complex vector with
+*> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
+*> overwriting A(1:i-1,i+1), and tau is stored in TAU(i).
+*>
+*> If UPLO = 'L', the matrix Q is represented as a product of elementary
+*> reflectors
+*>
+*> Q = H(1) H(2) . . . H(n-1).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - tau * v * v**H
+*>
+*> where tau is a complex scalar, and v is a complex vector with
+*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
+*> overwriting A(i+2:n,i), and tau is stored in TAU(i).
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZHPTRD( UPLO, N, AP, D, E, TAU, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -14,85 +162,6 @@
COMPLEX*16 AP( * ), TAU( * )
* ..
*
-* Purpose
-* =======
-*
-* ZHPTRD reduces a complex Hermitian matrix A stored in packed form to
-* real symmetric tridiagonal form T by a unitary similarity
-* transformation: Q**H * A * Q = T.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of A is stored;
-* = 'L': Lower triangle of A is stored.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
-* On entry, the upper or lower triangle of the Hermitian matrix
-* A, packed columnwise in a linear array. The j-th column of A
-* is stored in the array AP as follows:
-* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
-* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
-* On exit, if UPLO = 'U', the diagonal and first superdiagonal
-* of A are overwritten by the corresponding elements of the
-* tridiagonal matrix T, and the elements above the first
-* superdiagonal, with the array TAU, represent the unitary
-* matrix Q as a product of elementary reflectors; if UPLO
-* = 'L', the diagonal and first subdiagonal of A are over-
-* written by the corresponding elements of the tridiagonal
-* matrix T, and the elements below the first subdiagonal, with
-* the array TAU, represent the unitary matrix Q as a product
-* of elementary reflectors. See Further Details.
-*
-* D (output) DOUBLE PRECISION array, dimension (N)
-* The diagonal elements of the tridiagonal matrix T:
-* D(i) = A(i,i).
-*
-* E (output) DOUBLE PRECISION array, dimension (N-1)
-* The off-diagonal elements of the tridiagonal matrix T:
-* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
-*
-* TAU (output) COMPLEX*16 array, dimension (N-1)
-* The scalar factors of the elementary reflectors (see Further
-* Details).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
-* Further Details
-* ===============
-*
-* If UPLO = 'U', the matrix Q is represented as a product of elementary
-* reflectors
-*
-* Q = H(n-1) . . . H(2) H(1).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a complex scalar, and v is a complex vector with
-* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
-* overwriting A(1:i-1,i+1), and tau is stored in TAU(i).
-*
-* If UPLO = 'L', the matrix Q is represented as a product of elementary
-* reflectors
-*
-* Q = H(1) H(2) . . . H(n-1).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a complex scalar, and v is a complex vector with
-* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
-* overwriting A(i+2:n,i), and tau is stored in TAU(i).
-*
* =====================================================================
*
* .. Parameters ..
@@ -147,12 +216,12 @@
AP( I1+N-1 ) = DBLE( AP( I1+N-1 ) )
DO 10 I = N - 1, 1, -1
*
-* Generate elementary reflector H(i) = I - tau * v * v'
+* Generate elementary reflector H(i) = I - tau * v * v**H
* to annihilate A(1:i-1,i+1)
*
ALPHA = AP( I1+I-1 )
CALL ZLARFG( I, ALPHA, AP( I1 ), 1, TAUI )
- E( I ) = ALPHA
+ E( I ) = DBLE( ALPHA )
*
IF( TAUI.NE.ZERO ) THEN
*
@@ -165,23 +234,23 @@
CALL ZHPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
$ 1 )
*
-* Compute w := y - 1/2 * tau * (y'*v) * v
+* Compute w := y - 1/2 * tau * (y**H *v) * v
*
ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, AP( I1 ), 1 )
CALL ZAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
*
* Apply the transformation as a rank-2 update:
-* A := A - v * w' - w * v'
+* A := A - v * w**H - w * v**H
*
CALL ZHPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP )
*
END IF
AP( I1+I-1 ) = E( I )
- D( I+1 ) = AP( I1+I )
+ D( I+1 ) = DBLE( AP( I1+I ) )
TAU( I ) = TAUI
I1 = I1 - I
10 CONTINUE
- D( 1 ) = AP( 1 )
+ D( 1 ) = DBLE( AP( 1 ) )
ELSE
*
* Reduce the lower triangle of A. II is the index in AP of
@@ -192,12 +261,12 @@
DO 20 I = 1, N - 1
I1I1 = II + N - I + 1
*
-* Generate elementary reflector H(i) = I - tau * v * v'
+* Generate elementary reflector H(i) = I - tau * v * v**H
* to annihilate A(i+2:n,i)
*
ALPHA = AP( II+1 )
CALL ZLARFG( N-I, ALPHA, AP( II+2 ), 1, TAUI )
- E( I ) = ALPHA
+ E( I ) = DBLE( ALPHA )
*
IF( TAUI.NE.ZERO ) THEN
*
@@ -210,25 +279,25 @@
CALL ZHPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1,
$ ZERO, TAU( I ), 1 )
*
-* Compute w := y - 1/2 * tau * (y'*v) * v
+* Compute w := y - 1/2 * tau * (y**H *v) * v
*
ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, AP( II+1 ),
$ 1 )
CALL ZAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 )
*
* Apply the transformation as a rank-2 update:
-* A := A - v * w' - w * v'
+* A := A - v * w**H - w * v**H
*
CALL ZHPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1,
$ AP( I1I1 ) )
*
END IF
AP( II+1 ) = E( I )
- D( I ) = AP( II )
+ D( I ) = DBLE( AP( II ) )
TAU( I ) = TAUI
II = I1I1
20 CONTINUE
- D( N ) = AP( II )
+ D( N ) = DBLE( AP( II ) )
END IF
*
RETURN