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---
:name: dpftri
:md5sum: 60ad689ddf94971f01ab70b0fe6ff89c
:category: :subroutine
:arguments:
- transr:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- n*(n+1)/2
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DPFTRI computes the inverse of a (real) symmetric positive definite\n\
* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T\n\
* computed by DPFTRF.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* TRANSR (input) CHARACTER*1\n\
* = 'N': The Normal TRANSR of RFP A is stored;\n\
* = 'T': The Transpose TRANSR of RFP A is stored.\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 )\n\
* On entry, the symmetric matrix A in RFP format. RFP format is\n\
* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'\n\
* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is\n\
* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is\n\
* the transpose of RFP A as defined when\n\
* TRANSR = 'N'. The contents of RFP A are defined by UPLO as\n\
* follows: If UPLO = 'U' the RFP A contains the nt elements of\n\
* upper packed A. If UPLO = 'L' the RFP A contains the elements\n\
* of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =\n\
* 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N\n\
* is odd. See the Note below for more details.\n\
*\n\
* On exit, the symmetric inverse of the original matrix, in the\n\
* same storage format.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = i, the (i,i) element of the factor U or L is\n\
* zero, and the inverse could not be computed.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* We first consider Rectangular Full Packed (RFP) Format when N is\n\
* even. We give an example where N = 6.\n\
*\n\
* AP is Upper AP is Lower\n\
*\n\
* 00 01 02 03 04 05 00\n\
* 11 12 13 14 15 10 11\n\
* 22 23 24 25 20 21 22\n\
* 33 34 35 30 31 32 33\n\
* 44 45 40 41 42 43 44\n\
* 55 50 51 52 53 54 55\n\
*\n\
*\n\
* Let TRANSR = 'N'. RFP holds AP as follows:\n\
* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last\n\
* three columns of AP upper. The lower triangle A(4:6,0:2) consists of\n\
* the transpose of the first three columns of AP upper.\n\
* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first\n\
* three columns of AP lower. The upper triangle A(0:2,0:2) consists of\n\
* the transpose of the last three columns of AP lower.\n\
* This covers the case N even and TRANSR = 'N'.\n\
*\n\
* RFP A RFP A\n\
*\n\
* 03 04 05 33 43 53\n\
* 13 14 15 00 44 54\n\
* 23 24 25 10 11 55\n\
* 33 34 35 20 21 22\n\
* 00 44 45 30 31 32\n\
* 01 11 55 40 41 42\n\
* 02 12 22 50 51 52\n\
*\n\
* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
* transpose of RFP A above. One therefore gets:\n\
*\n\
*\n\
* RFP A RFP A\n\
*\n\
* 03 13 23 33 00 01 02 33 00 10 20 30 40 50\n\
* 04 14 24 34 44 11 12 43 44 11 21 31 41 51\n\
* 05 15 25 35 45 55 22 53 54 55 22 32 42 52\n\
*\n\
*\n\
* We then consider Rectangular Full Packed (RFP) Format when N is\n\
* odd. We give an example where N = 5.\n\
*\n\
* AP is Upper AP is Lower\n\
*\n\
* 00 01 02 03 04 00\n\
* 11 12 13 14 10 11\n\
* 22 23 24 20 21 22\n\
* 33 34 30 31 32 33\n\
* 44 40 41 42 43 44\n\
*\n\
*\n\
* Let TRANSR = 'N'. RFP holds AP as follows:\n\
* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last\n\
* three columns of AP upper. The lower triangle A(3:4,0:1) consists of\n\
* the transpose of the first two columns of AP upper.\n\
* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first\n\
* three columns of AP lower. The upper triangle A(0:1,1:2) consists of\n\
* the transpose of the last two columns of AP lower.\n\
* This covers the case N odd and TRANSR = 'N'.\n\
*\n\
* RFP A RFP A\n\
*\n\
* 02 03 04 00 33 43\n\
* 12 13 14 10 11 44\n\
* 22 23 24 20 21 22\n\
* 00 33 34 30 31 32\n\
* 01 11 44 40 41 42\n\
*\n\
* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
* transpose of RFP A above. One therefore gets:\n\
*\n\
* RFP A RFP A\n\
*\n\
* 02 12 22 00 01 00 10 20 30 40 50\n\
* 03 13 23 33 11 33 11 21 31 41 51\n\
* 04 14 24 34 44 43 44 22 32 42 52\n\
*\n\
* =====================================================================\n\
*\n"
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