Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  copies  a  triangular  matrix  A  from rectangular full packed format (TF) to
standard packed format (TP)

```

#### SYNOPSIS

```       SUBROUTINE STFTTP( TRANSR, UPLO, N, ARF, AP, INFO )

CHARACTER      TRANSR, UPLO

INTEGER        INFO, N

REAL           AP( 0: * ), ARF( 0: * )

```

#### PURPOSE

```       STFTTP copies a triangular matrix A from rectangular full packed format (TF)  to  standard
packed format (TP).

```

#### ARGUMENTS

```        TRANSR   (input) CHARACTER*1
= 'N':  ARF is in Normal format;
= 'T':  ARF is in Transpose format;

UPLO    (input) CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.

N       (input) INTEGER
The order of the matrix A. N >= 0.

ARF     (input) REAL array, dimension ( N*(N+1)/2 ),
On entry, the upper or lower triangular matrix A stored in
RFP format. For a further discussion see Notes below.

AP      (output) REAL array, dimension ( N*(N+1)/2 ),
On exit, the upper or lower triangular matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

```

#### FURTHERDETAILS

```        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

LAPACK routine (version 3.3.1)             April 2011                            STFTTP(3lapack)
```