--- rpl/lapack/lapack/zhetri2x.f 2011/07/24 10:31:39 1.1
+++ rpl/lapack/lapack/zhetri2x.f 2023/08/07 08:39:25 1.13
@@ -1,11 +1,126 @@
+*> \brief \b ZHETRI2X
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHETRI2X + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N, NB
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHETRI2X computes the inverse of a COMPLEX*16 Hermitian indefinite matrix
+*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
+*> ZHETRF.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the details of the factorization are stored
+*> as an upper or lower triangular matrix.
+*> = 'U': Upper triangular, form is A = U*D*U**H;
+*> = 'L': Lower triangular, form is A = L*D*L**H.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the NNB diagonal matrix D and the multipliers
+*> used to obtain the factor U or L as computed by ZHETRF.
+*>
+*> On exit, if INFO = 0, the (symmetric) inverse of the original
+*> matrix. If UPLO = 'U', the upper triangular part of the
+*> inverse is formed and the part of A below the diagonal is not
+*> referenced; if UPLO = 'L' the lower triangular part of the
+*> inverse is formed and the part of A above the diagonal is
+*> not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges and the NNB structure of D
+*> as determined by ZHETRF.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3)
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> Block size
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
+*> inverse could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16HEcomputational
+*
+* =====================================================================
SUBROUTINE ZHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO )
*
-* -- LAPACK routine (version 3.3.1) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
-*
-* -- Written by Julie Langou of the Univ. of TN --
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -16,58 +131,10 @@
COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* )
* ..
*
-* Purpose
-* =======
-*
-* ZHETRI2X computes the inverse of a COMPLEX*16 Hermitian indefinite matrix
-* A using the factorization A = U*D*U**H or A = L*D*L**H computed by
-* ZHETRF.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the details of the factorization are stored
-* as an upper or lower triangular matrix.
-* = 'U': Upper triangular, form is A = U*D*U**H;
-* = 'L': Lower triangular, form is A = L*D*L**H.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA,N)
-* On entry, the NNB diagonal matrix D and the multipliers
-* used to obtain the factor U or L as computed by ZHETRF.
-*
-* On exit, if INFO = 0, the (symmetric) inverse of the original
-* matrix. If UPLO = 'U', the upper triangular part of the
-* inverse is formed and the part of A below the diagonal is not
-* referenced; if UPLO = 'L' the lower triangular part of the
-* inverse is formed and the part of A above the diagonal is
-* not referenced.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* IPIV (input) INTEGER array, dimension (N)
-* Details of the interchanges and the NNB structure of D
-* as determined by ZHETRF.
-*
-* WORK (workspace) COMPLEX*16 array, dimension (N+NNB+1,NNB+3)
-*
-* NB (input) INTEGER
-* Block size
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
-* inverse could not be computed.
-*
* =====================================================================
*
* .. Parameters ..
- REAL ONE
+ DOUBLE PRECISION ONE
COMPLEX*16 CONE, ZERO
PARAMETER ( ONE = 1.0D+0,
$ CONE = ( 1.0D+0, 0.0D+0 ),
@@ -145,7 +212,7 @@
INFO = 0
*
* Splitting Workspace
-* U01 is a block (N,NB+1)
+* U01 is a block (N,NB+1)
* The first element of U01 is in WORK(1,1)
* U11 is a block (NB+1,NB+1)
* The first element of U11 is in WORK(N+1,1)
@@ -161,7 +228,7 @@
CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO )
*
* inv(D) and inv(D)*inv(U)
-*
+*
K=1
DO WHILE ( K .LE. N )
IF( IPIV( K ).GT.0 ) THEN
@@ -172,13 +239,13 @@
ELSE
* 2 x 2 diagonal NNB
T = ABS ( WORK(K+1,1) )
- AK = REAL ( A( K, K ) ) / T
- AKP1 = REAL ( A( K+1, K+1 ) ) / T
+ AK = DBLE ( A( K, K ) ) / T
+ AKP1 = DBLE ( A( K+1, K+1 ) ) / T
AKKP1 = WORK(K+1,1) / T
D = T*( AK*AKP1-ONE )
WORK(K,INVD) = AKP1 / D
WORK(K+1,INVD+1) = AK / D
- WORK(K,INVD+1) = -AKKP1 / D
+ WORK(K,INVD+1) = -AKKP1 / D
WORK(K+1,INVD) = DCONJG (WORK(K,INVD+1) )
K=K+2
END IF
@@ -195,7 +262,7 @@
NNB=CUT
ELSE
COUNT = 0
-* count negative elements,
+* count negative elements,
DO I=CUT+1-NNB,CUT
IF (IPIV(I) .LT. 0) COUNT=COUNT+1
END DO
@@ -205,7 +272,7 @@
CUT=CUT-NNB
*
-* U01 Block
+* U01 Block
*
DO I=1,CUT
DO J=1,NNB
@@ -268,7 +335,7 @@
I=I+2
END IF
END DO
-*
+*
* U11**H*invD1*U11->U11
*
CALL ZTRMM('L','U','C','U',NNB, NNB,
@@ -312,7 +379,7 @@
END DO
*
* Apply PERMUTATIONS P and P**H: P * inv(U**H)*inv(D)*inv(U) *P**H
-*
+*
I=1
DO WHILE ( I .LE. N )
IF( IPIV(I) .GT. 0 ) THEN
@@ -322,9 +389,9 @@
ELSE
IP=-IPIV(I)
I=I+1
- IF ( (I-1) .LT. IP)
+ IF ( (I-1) .LT. IP)
$ CALL ZHESWAPR( UPLO, N, A, LDA, I-1 ,IP )
- IF ( (I-1) .GT. IP)
+ IF ( (I-1) .GT. IP)
$ CALL ZHESWAPR( UPLO, N, A, LDA, IP ,I-1 )
ENDIF
I=I+1
@@ -338,7 +405,7 @@
CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO )
*
* inv(D) and inv(D)*inv(U)
-*
+*
K=N
DO WHILE ( K .GE. 1 )
IF( IPIV( K ).GT.0 ) THEN
@@ -349,13 +416,13 @@
ELSE
* 2 x 2 diagonal NNB
T = ABS ( WORK(K-1,1) )
- AK = REAL ( A( K-1, K-1 ) ) / T
- AKP1 = REAL ( A( K, K ) ) / T
+ AK = DBLE ( A( K-1, K-1 ) ) / T
+ AKP1 = DBLE ( A( K, K ) ) / T
AKKP1 = WORK(K-1,1) / T
D = T*( AK*AKP1-ONE )
WORK(K-1,INVD) = AKP1 / D
WORK(K,INVD) = AK / D
- WORK(K,INVD+1) = -AKKP1 / D
+ WORK(K,INVD+1) = -AKKP1 / D
WORK(K-1,INVD+1) = DCONJG (WORK(K,INVD+1) )
K=K-2
END IF
@@ -372,7 +439,7 @@
NNB=N-CUT
ELSE
COUNT = 0
-* count negative elements,
+* count negative elements,
DO I=CUT+1,CUT+NNB
IF (IPIV(I) .LT. 0) COUNT=COUNT+1
END DO
@@ -439,7 +506,7 @@
I=I-2
END IF
END DO
-*
+*
* L11**H*invD1*L11->L11
*
CALL ZTRMM('L',UPLO,'C','U',NNB, NNB,
@@ -457,7 +524,7 @@
*
CALL ZGEMM('C','N',NNB,NNB,N-NNB-CUT,CONE,A(CUT+NNB+1,CUT+1)
$ ,LDA,WORK,N+NB+1, ZERO, WORK(U11+1,1), N+NB+1)
-
+
*
* L11 = L11**H*invD1*L11 + U01**H*invD*U01
*
@@ -495,7 +562,7 @@
END DO
*
* Apply PERMUTATIONS P and P**H: P * inv(U**H)*inv(D)*inv(U) *P**H
-*
+*
I=N
DO WHILE ( I .GE. 1 )
IF( IPIV(I) .GT. 0 ) THEN