--- rpl/lapack/lapack/dpftri.f 2010/08/07 13:22:23 1.2
+++ rpl/lapack/lapack/dpftri.f 2011/11/21 22:19:37 1.8
@@ -1,12 +1,200 @@
- SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
+*> \brief \b DPFTRI
+*
+* =========== DOCUMENTATION ===========
*
-* -- LAPACK routine (version 3.2.2) --
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
-* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
-* -- June 2010 --
+*> \htmlonly
+*> Download DPFTRI + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER TRANSR, UPLO
+* INTEGER INFO, N
+* .. Array Arguments ..
+* DOUBLE PRECISION A( 0: * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DPFTRI computes the inverse of a (real) symmetric positive definite
+*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
+*> computed by DPFTRF.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANSR
+*> \verbatim
+*> TRANSR is CHARACTER*1
+*> = 'N': The Normal TRANSR of RFP A is stored;
+*> = 'T': The Transpose TRANSR of RFP A is stored.
+*> \endverbatim
+*>
+*> \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] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 )
+*> On entry, the symmetric 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 = 'T' then RFP is
+*> the 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 =
+*> 'T'. 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, the symmetric inverse of the original matrix, in the
+*> same storage format.
+*> \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 (i,i) element of the factor U or L is
+*> zero, and the inverse could not be computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> We first consider Rectangular Full Packed (RFP) 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
+*> the 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
+*> the transpose of the last three columns of AP lower.
+*> 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 = 'T'. RFP A in both UPLO cases is just the
+*> 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 then consider Rectangular Full Packed (RFP) 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
+*> the 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
+*> the transpose of the last two columns of AP lower.
+*> 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 = 'T'. RFP A in both UPLO cases is just the
+*> 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
+*>
+* =====================================================================
+ SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
*
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER TRANSR, UPLO
@@ -15,133 +203,6 @@
DOUBLE PRECISION A( 0: * )
* ..
*
-* Purpose
-* =======
-*
-* DPFTRI computes the inverse of a (real) symmetric positive definite
-* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
-* computed by DPFTRF.
-*
-* Arguments
-* =========
-*
-* TRANSR (input) CHARACTER
-* = 'N': The Normal TRANSR of RFP A is stored;
-* = 'T': The Transpose TRANSR of RFP A is stored.
-*
-* UPLO (input) CHARACTER
-* = '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.
-*
-* A (input/output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 )
-* On entry, the symmetric 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 = 'T' then RFP is
-* the 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 =
-* 'T'. 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, the symmetric inverse of the original matrix, in the
-* same storage format.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, the (i,i) element of the factor U or L is
-* zero, and the inverse could not be computed.
-*
-* Further Details
-* ===============
-*
-* We first consider Rectangular Full Packed (RFP) 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
-* the 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
-* the transpose of the last three columns of AP lower.
-* 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 = 'T'. RFP A in both UPLO cases is just the
-* 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 then consider Rectangular Full Packed (RFP) 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
-* the 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
-* the transpose of the last two columns of AP lower.
-* 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 = 'T'. RFP A in both UPLO cases is just the
-* 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 ..
@@ -184,13 +245,13 @@
* Quick return if possible
*
IF( N.EQ.0 )
- + RETURN
+ $ RETURN
*
* Invert the triangular Cholesky factor U or L.
*
CALL DTFTRI( TRANSR, UPLO, 'N', N, A, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
*
* If N is odd, set NISODD = .TRUE.
* If N is even, set K = N/2 and NISODD = .FALSE.
@@ -231,9 +292,9 @@
*
CALL DLAUUM( 'L', N1, A( 0 ), N, INFO )
CALL DSYRK( 'L', 'T', N1, N2, ONE, A( N1 ), N, ONE,
- + A( 0 ), N )
+ $ A( 0 ), N )
CALL DTRMM( 'L', 'U', 'N', 'N', N2, N1, ONE, A( N ), N,
- + A( N1 ), N )
+ $ A( N1 ), N )
CALL DLAUUM( 'U', N2, A( N ), N, INFO )
*
ELSE
@@ -244,9 +305,9 @@
*
CALL DLAUUM( 'L', N1, A( N2 ), N, INFO )
CALL DSYRK( 'L', 'N', N1, N2, ONE, A( 0 ), N, ONE,
- + A( N2 ), N )
+ $ A( N2 ), N )
CALL DTRMM( 'R', 'U', 'T', 'N', N1, N2, ONE, A( N1 ), N,
- + A( 0 ), N )
+ $ A( 0 ), N )
CALL DLAUUM( 'U', N2, A( N1 ), N, INFO )
*
END IF
@@ -262,9 +323,9 @@
*
CALL DLAUUM( 'U', N1, A( 0 ), N1, INFO )
CALL DSYRK( 'U', 'N', N1, N2, ONE, A( N1*N1 ), N1, ONE,
- + A( 0 ), N1 )
+ $ A( 0 ), N1 )
CALL DTRMM( 'R', 'L', 'N', 'N', N1, N2, ONE, A( 1 ), N1,
- + A( N1*N1 ), N1 )
+ $ A( N1*N1 ), N1 )
CALL DLAUUM( 'L', N2, A( 1 ), N1, INFO )
*
ELSE
@@ -274,9 +335,9 @@
*
CALL DLAUUM( 'U', N1, A( N2*N2 ), N2, INFO )
CALL DSYRK( 'U', 'T', N1, N2, ONE, A( 0 ), N2, ONE,
- + A( N2*N2 ), N2 )
+ $ A( N2*N2 ), N2 )
CALL DTRMM( 'L', 'L', 'T', 'N', N2, N1, ONE, A( N1*N2 ),
- + N2, A( 0 ), N2 )
+ $ N2, A( 0 ), N2 )
CALL DLAUUM( 'L', N2, A( N1*N2 ), N2, INFO )
*
END IF
@@ -299,9 +360,9 @@
*
CALL DLAUUM( 'L', K, A( 1 ), N+1, INFO )
CALL DSYRK( 'L', 'T', K, K, ONE, A( K+1 ), N+1, ONE,
- + A( 1 ), N+1 )
+ $ A( 1 ), N+1 )
CALL DTRMM( 'L', 'U', 'N', 'N', K, K, ONE, A( 0 ), N+1,
- + A( K+1 ), N+1 )
+ $ A( K+1 ), N+1 )
CALL DLAUUM( 'U', K, A( 0 ), N+1, INFO )
*
ELSE
@@ -312,9 +373,9 @@
*
CALL DLAUUM( 'L', K, A( K+1 ), N+1, INFO )
CALL DSYRK( 'L', 'N', K, K, ONE, A( 0 ), N+1, ONE,
- + A( K+1 ), N+1 )
+ $ A( K+1 ), N+1 )
CALL DTRMM( 'R', 'U', 'T', 'N', K, K, ONE, A( K ), N+1,
- + A( 0 ), N+1 )
+ $ A( 0 ), N+1 )
CALL DLAUUM( 'U', K, A( K ), N+1, INFO )
*
END IF
@@ -331,9 +392,9 @@
*
CALL DLAUUM( 'U', K, A( K ), K, INFO )
CALL DSYRK( 'U', 'N', K, K, ONE, A( K*( K+1 ) ), K, ONE,
- + A( K ), K )
+ $ A( K ), K )
CALL DTRMM( 'R', 'L', 'N', 'N', K, K, ONE, A( 0 ), K,
- + A( K*( K+1 ) ), K )
+ $ A( K*( K+1 ) ), K )
CALL DLAUUM( 'L', K, A( 0 ), K, INFO )
*
ELSE
@@ -344,9 +405,9 @@
*
CALL DLAUUM( 'U', K, A( K*( K+1 ) ), K, INFO )
CALL DSYRK( 'U', 'T', K, K, ONE, A( 0 ), K, ONE,
- + A( K*( K+1 ) ), K )
+ $ A( K*( K+1 ) ), K )
CALL DTRMM( 'L', 'L', 'T', 'N', K, K, ONE, A( K*K ), K,
- + A( 0 ), K )
+ $ A( 0 ), K )
CALL DLAUUM( 'L', K, A( K*K ), K, INFO )
*
END IF