spftri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by SPFTRF
SUBROUTINE SPFTRI(TRANSR, UPLO, N, A, INFO) CHARACTER*1 TRANSR, UPLO INTEGER INFO, N REAL A(0:*) SUBROUTINE SPFTRI_64(TRANSR, UPLO, N, A, INFO) CHARACTER*1 TRANSR, UPLO INTEGER*8 INFO, N REAL A(0:*) F95 INTERFACE SUBROUTINE PFTRI(TRANSR, UPLO, N, A, INFO) INTEGER :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO REAL, DIMENSION(:) :: A SUBROUTINE PFTRI_64(TRANSR, UPLO, N, A, INFO) INTEGER(8) :: N, INFO CHARACTER(LEN=1) :: TRANSR, UPLO REAL, DIMENSION(:) :: A C INTERFACE #include <sunperf.h> void spftri (char transr, char uplo, int n, float *a, int *info); void spftri_64 (char transr, char uplo, long n, float *a, long *info);
Oracle Solaris Studio Performance Library spftri(3P)
NAME
spftri - compute the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization computed by SPFTRF
SYNOPSIS
SUBROUTINE SPFTRI(TRANSR, UPLO, N, A, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER INFO, N
REAL A(0:*)
SUBROUTINE SPFTRI_64(TRANSR, UPLO, N, A, INFO)
CHARACTER*1 TRANSR, UPLO
INTEGER*8 INFO, N
REAL A(0:*)
F95 INTERFACE
SUBROUTINE PFTRI(TRANSR, UPLO, N, A, INFO)
INTEGER :: N, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
REAL, DIMENSION(:) :: A
SUBROUTINE PFTRI_64(TRANSR, UPLO, N, A, INFO)
INTEGER(8) :: N, INFO
CHARACTER(LEN=1) :: TRANSR, UPLO
REAL, DIMENSION(:) :: A
C INTERFACE
#include <sunperf.h>
void spftri (char transr, char uplo, int n, float *a, int *info);
void spftri_64 (char transr, char uplo, long n, float *a, long *info);
PURPOSE
spftri computes the inverse of a real (symmetric) positive definite
matrix A using the Cholesky factorization A = U**T*U or A = L*L**T com-
puted by SPFTRF.
ARGUMENTS
TRANSR (input)
TRANSR is CHARACTER*1
= 'N': The Normal TRANSR of RFP A is stored;
= 'T': The Transpose TRANSR of RFP A is stored.
UPLO (input)
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input)
N is INTEGER
The order of the matrix A. N >= 0.
A (input/output)
A is REAL 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 con-
tents 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 = 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)
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.
FURTHER NOTES ON RFP FORMAT
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
7 Nov 2015 spftri(3P)