--- rpl/lapack/lapack/zpftrf.f 2010/12/21 13:48:06 1.4
+++ rpl/lapack/lapack/zpftrf.f 2023/08/07 08:39:33 1.17
@@ -1,14 +1,218 @@
- SUBROUTINE ZPFTRF( TRANSR, UPLO, N, A, INFO )
+*> \brief \b ZPFTRF
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
-* -- LAPACK routine (version 3.3.0) --
+*> \htmlonly
+*> Download ZPFTRF + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZPFTRF( TRANSR, UPLO, N, A, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER TRANSR, UPLO
+* INTEGER N, INFO
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( 0: * )
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZPFTRF computes the Cholesky factorization of a complex Hermitian
+*> positive definite matrix A.
+*>
+*> The factorization has the form
+*> A = U**H * U, if UPLO = 'U', or
+*> A = L * L**H, if UPLO = 'L',
+*> where U is an upper triangular matrix and L is lower triangular.
+*>
+*> This is the block version of the algorithm, calling Level 3 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANSR
+*> \verbatim
+*> TRANSR is CHARACTER*1
+*> = 'N': The Normal TRANSR of RFP A is stored;
+*> = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of RFP A is stored;
+*> = 'L': Lower triangle of RFP A is stored.
+*> \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 ( N*(N+1)/2 );
+*> On entry, the Hermitian matrix A in RFP format. RFP format is
+*> described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
+*> then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
+*> (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
+*> the Conjugate-transpose of RFP A as defined when
+*> TRANSR = 'N'. The contents of RFP A are defined by UPLO as
+*> follows: If UPLO = 'U' the RFP A contains the nt elements of
+*> upper packed A. If UPLO = 'L' the RFP A contains the elements
+*> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
+*> 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N
+*> is odd. See the Note below for more details.
+*>
+*> On exit, if INFO = 0, the factor U or L from the Cholesky
+*> factorization RFP A = U**H*U or RFP A = L*L**H.
+*> \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, the leading minor of order i is not
+*> positive definite, and the factorization could not be
+*> completed.
+*>
+*> Further Notes on RFP Format:
+*> ============================
+*>
+*> We first consider Standard Packed Format when N is even.
+*> We give an example where N = 6.
+*>
+*> AP is Upper AP is Lower
+*>
+*> 00 01 02 03 04 05 00
+*> 11 12 13 14 15 10 11
+*> 22 23 24 25 20 21 22
+*> 33 34 35 30 31 32 33
+*> 44 45 40 41 42 43 44
+*> 55 50 51 52 53 54 55
+*>
+*> Let TRANSR = 'N'. RFP holds AP as follows:
+*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
+*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
+*> conjugate-transpose of the first three columns of AP upper.
+*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
+*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
+*> conjugate-transpose of the last three columns of AP lower.
+*> To denote conjugate we place -- above the element. This covers the
+*> case N even and TRANSR = 'N'.
+*>
+*> RFP A RFP A
+*>
+*> -- -- --
+*> 03 04 05 33 43 53
+*> -- --
+*> 13 14 15 00 44 54
+*> --
+*> 23 24 25 10 11 55
+*>
+*> 33 34 35 20 21 22
+*> --
+*> 00 44 45 30 31 32
+*> -- --
+*> 01 11 55 40 41 42
+*> -- -- --
+*> 02 12 22 50 51 52
+*>
+*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
+*> transpose of RFP A above. One therefore gets:
+*>
+*> RFP A RFP A
+*>
+*> -- -- -- -- -- -- -- -- -- --
+*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
+*> -- -- -- -- -- -- -- -- -- --
+*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
+*> -- -- -- -- -- -- -- -- -- --
+*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
+*>
+*> We next consider Standard Packed Format when N is odd.
+*> We give an example where N = 5.
+*>
+*> AP is Upper AP is Lower
+*>
+*> 00 01 02 03 04 00
+*> 11 12 13 14 10 11
+*> 22 23 24 20 21 22
+*> 33 34 30 31 32 33
+*> 44 40 41 42 43 44
+*>
+*> Let TRANSR = 'N'. RFP holds AP as follows:
+*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
+*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
+*> conjugate-transpose of the first two columns of AP upper.
+*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
+*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
+*> conjugate-transpose of the last two columns of AP lower.
+*> To denote conjugate we place -- above the element. This covers the
+*> case N odd and TRANSR = 'N'.
+*>
+*> RFP A RFP A
+*>
+*> -- --
+*> 02 03 04 00 33 43
+*> --
+*> 12 13 14 10 11 44
+*>
+*> 22 23 24 20 21 22
+*> --
+*> 00 33 34 30 31 32
+*> -- --
+*> 01 11 44 40 41 42
+*>
+*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
+*> transpose of RFP A above. One therefore gets:
+*>
+*> RFP A RFP A
+*>
+*> -- -- -- -- -- -- -- -- --
+*> 02 12 22 00 01 00 10 20 30 40 50
+*> -- -- -- -- -- -- -- -- --
+*> 03 13 23 33 11 33 11 21 31 41 51
+*> -- -- -- -- -- -- -- -- --
+*> 04 14 24 34 44 43 44 22 32 42 52
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
-* November 2010 --
+*> \ingroup complex16OTHERcomputational
+*
+* =====================================================================
+ SUBROUTINE ZPFTRF( TRANSR, UPLO, N, A, INFO )
*
+* -- 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 ..
CHARACTER TRANSR, UPLO
INTEGER N, INFO
@@ -16,161 +220,6 @@
* .. Array Arguments ..
COMPLEX*16 A( 0: * )
*
-* Purpose
-* =======
-*
-* ZPFTRF computes the Cholesky factorization of a complex Hermitian
-* positive definite matrix A.
-*
-* The factorization has the form
-* A = U**H * U, if UPLO = 'U', or
-* A = L * L**H, if UPLO = 'L',
-* where U is an upper triangular matrix and L is lower triangular.
-*
-* This is the block version of the algorithm, calling Level 3 BLAS.
-*
-* Arguments
-* =========
-*
-* TRANSR (input) CHARACTER*1
-* = 'N': The Normal TRANSR of RFP A is stored;
-* = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of RFP A is stored;
-* = 'L': Lower triangle of RFP A is stored.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) COMPLEX array, dimension ( N*(N+1)/2 );
-* On entry, the Hermitian matrix A in RFP format. RFP format is
-* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
-* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
-* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
-* the Conjugate-transpose of RFP A as defined when
-* TRANSR = 'N'. The contents of RFP A are defined by UPLO as
-* follows: If UPLO = 'U' the RFP A contains the nt elements of
-* upper packed A. If UPLO = 'L' the RFP A contains the elements
-* of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
-* 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N
-* is odd. See the Note below for more details.
-*
-* On exit, if INFO = 0, the factor U or L from the Cholesky
-* factorization RFP A = U**H*U or RFP A = L*L**H.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, the leading minor of order i is not
-* positive definite, and the factorization could not be
-* completed.
-*
-* Further Notes on RFP Format:
-* ============================
-*
-* We first consider Standard Packed Format when N is even.
-* We give an example where N = 6.
-*
-* AP is Upper AP is Lower
-*
-* 00 01 02 03 04 05 00
-* 11 12 13 14 15 10 11
-* 22 23 24 25 20 21 22
-* 33 34 35 30 31 32 33
-* 44 45 40 41 42 43 44
-* 55 50 51 52 53 54 55
-*
-*
-* Let TRANSR = 'N'. RFP holds AP as follows:
-* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
-* three columns of AP upper. The lower triangle A(4:6,0:2) consists of
-* conjugate-transpose of the first three columns of AP upper.
-* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
-* three columns of AP lower. The upper triangle A(0:2,0:2) consists of
-* conjugate-transpose of the last three columns of AP lower.
-* To denote conjugate we place -- above the element. This covers the
-* case N even and TRANSR = 'N'.
-*
-* RFP A RFP A
-*
-* -- -- --
-* 03 04 05 33 43 53
-* -- --
-* 13 14 15 00 44 54
-* --
-* 23 24 25 10 11 55
-*
-* 33 34 35 20 21 22
-* --
-* 00 44 45 30 31 32
-* -- --
-* 01 11 55 40 41 42
-* -- -- --
-* 02 12 22 50 51 52
-*
-* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
-* transpose of RFP A above. One therefore gets:
-*
-*
-* RFP A RFP A
-*
-* -- -- -- -- -- -- -- -- -- --
-* 03 13 23 33 00 01 02 33 00 10 20 30 40 50
-* -- -- -- -- -- -- -- -- -- --
-* 04 14 24 34 44 11 12 43 44 11 21 31 41 51
-* -- -- -- -- -- -- -- -- -- --
-* 05 15 25 35 45 55 22 53 54 55 22 32 42 52
-*
-*
-* We next consider Standard Packed Format when N is odd.
-* We give an example where N = 5.
-*
-* AP is Upper AP is Lower
-*
-* 00 01 02 03 04 00
-* 11 12 13 14 10 11
-* 22 23 24 20 21 22
-* 33 34 30 31 32 33
-* 44 40 41 42 43 44
-*
-*
-* Let TRANSR = 'N'. RFP holds AP as follows:
-* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
-* three columns of AP upper. The lower triangle A(3:4,0:1) consists of
-* conjugate-transpose of the first two columns of AP upper.
-* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
-* three columns of AP lower. The upper triangle A(0:1,1:2) consists of
-* conjugate-transpose of the last two columns of AP lower.
-* To denote conjugate we place -- above the element. This covers the
-* case N odd and TRANSR = 'N'.
-*
-* RFP A RFP A
-*
-* -- --
-* 02 03 04 00 33 43
-* --
-* 12 13 14 10 11 44
-*
-* 22 23 24 20 21 22
-* --
-* 00 33 34 30 31 32
-* -- --
-* 01 11 44 40 41 42
-*
-* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
-* transpose of RFP A above. One therefore gets:
-*
-*
-* RFP A RFP A
-*
-* -- -- -- -- -- -- -- -- --
-* 02 12 22 00 01 00 10 20 30 40 50
-* -- -- -- -- -- -- -- -- --
-* 03 13 23 33 11 33 11 21 31 41 51
-* -- -- -- -- -- -- -- -- --
-* 04 14 24 34 44 43 44 22 32 42 52
-*
* =====================================================================
*
* .. Parameters ..
@@ -214,7 +263,7 @@
* Quick return if possible
*
IF( N.EQ.0 )
- + RETURN
+ $ RETURN
*
* If N is odd, set NISODD = .TRUE.
* If N is even, set K = N/2 and NISODD = .FALSE.
@@ -254,14 +303,14 @@
*
CALL ZPOTRF( 'L', N1, A( 0 ), N, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE, A( 0 ), N,
- + A( N1 ), N )
+ $ A( N1 ), N )
CALL ZHERK( 'U', 'N', N2, N1, -ONE, A( N1 ), N, ONE,
- + A( N ), N )
+ $ A( N ), N )
CALL ZPOTRF( 'U', N2, A( N ), N, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
*
ELSE
*
@@ -271,14 +320,14 @@
*
CALL ZPOTRF( 'L', N1, A( N2 ), N, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'L', 'L', 'N', 'N', N1, N2, CONE, A( N2 ), N,
- + A( 0 ), N )
+ $ A( 0 ), N )
CALL ZHERK( 'U', 'C', N2, N1, -ONE, A( 0 ), N, ONE,
- + A( N1 ), N )
+ $ A( N1 ), N )
CALL ZPOTRF( 'U', N2, A( N1 ), N, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
*
END IF
*
@@ -294,14 +343,14 @@
*
CALL ZPOTRF( 'U', N1, A( 0 ), N1, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE, A( 0 ), N1,
- + A( N1*N1 ), N1 )
+ $ A( N1*N1 ), N1 )
CALL ZHERK( 'L', 'C', N2, N1, -ONE, A( N1*N1 ), N1, ONE,
- + A( 1 ), N1 )
+ $ A( 1 ), N1 )
CALL ZPOTRF( 'L', N2, A( 1 ), N1, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
*
ELSE
*
@@ -311,14 +360,14 @@
*
CALL ZPOTRF( 'U', N1, A( N2*N2 ), N2, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'R', 'U', 'N', 'N', N2, N1, CONE, A( N2*N2 ),
- + N2, A( 0 ), N2 )
+ $ N2, A( 0 ), N2 )
CALL ZHERK( 'L', 'N', N2, N1, -ONE, A( 0 ), N2, ONE,
- + A( N1*N2 ), N2 )
+ $ A( N1*N2 ), N2 )
CALL ZPOTRF( 'L', N2, A( N1*N2 ), N2, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
*
END IF
*
@@ -340,14 +389,14 @@
*
CALL ZPOTRF( 'L', K, A( 1 ), N+1, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'R', 'L', 'C', 'N', K, K, CONE, A( 1 ), N+1,
- + A( K+1 ), N+1 )
+ $ A( K+1 ), N+1 )
CALL ZHERK( 'U', 'N', K, K, -ONE, A( K+1 ), N+1, ONE,
- + A( 0 ), N+1 )
+ $ A( 0 ), N+1 )
CALL ZPOTRF( 'U', K, A( 0 ), N+1, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
*
ELSE
*
@@ -357,14 +406,14 @@
*
CALL ZPOTRF( 'L', K, A( K+1 ), N+1, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'L', 'L', 'N', 'N', K, K, CONE, A( K+1 ),
- + N+1, A( 0 ), N+1 )
+ $ N+1, A( 0 ), N+1 )
CALL ZHERK( 'U', 'C', K, K, -ONE, A( 0 ), N+1, ONE,
- + A( K ), N+1 )
+ $ A( K ), N+1 )
CALL ZPOTRF( 'U', K, A( K ), N+1, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
*
END IF
*
@@ -380,14 +429,14 @@
*
CALL ZPOTRF( 'U', K, A( 0+K ), K, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'L', 'U', 'C', 'N', K, K, CONE, A( K ), N1,
- + A( K*( K+1 ) ), K )
+ $ A( K*( K+1 ) ), K )
CALL ZHERK( 'L', 'C', K, K, -ONE, A( K*( K+1 ) ), K, ONE,
- + A( 0 ), K )
+ $ A( 0 ), K )
CALL ZPOTRF( 'L', K, A( 0 ), K, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
*
ELSE
*
@@ -397,14 +446,14 @@
*
CALL ZPOTRF( 'U', K, A( K*( K+1 ) ), K, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL ZTRSM( 'R', 'U', 'N', 'N', K, K, CONE,
- + A( K*( K+1 ) ), K, A( 0 ), K )
+ $ A( K*( K+1 ) ), K, A( 0 ), K )
CALL ZHERK( 'L', 'N', K, K, -ONE, A( 0 ), K, ONE,
- + A( K*K ), K )
+ $ A( K*K ), K )
CALL ZPOTRF( 'L', K, A( K*K ), K, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
*
END IF
*