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---
:name: dtfttp
:md5sum: 5a4746cb4cd86d64545e91aae7dfdcc8
:category: :subroutine
:arguments:
- transr:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- arf:
:type: doublereal
:intent: input
:dims:
- ( n*(n+1)/2 )
- ap:
:type: doublereal
:intent: output
:dims:
- ( n*(n+1)/2 )
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DTFTTP copies a triangular matrix A from rectangular full packed\n\
* format (TF) to standard packed format (TP).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* TRANSR (input) CHARACTER*1\n\
* = 'N': ARF is in Normal format;\n\
* = 'T': ARF is in Transpose format;\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': A is upper triangular;\n\
* = 'L': A is lower triangular.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* ARF (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),\n\
* On entry, the upper or lower triangular matrix A stored in\n\
* RFP format. For a further discussion see Notes below.\n\
*\n\
* AP (output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),\n\
* On exit, the upper or lower triangular matrix A, packed\n\
* columnwise in a linear array. The j-th column of A is stored\n\
* in the array AP as follows:\n\
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\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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