Provided by: liblapack-doc_3.3.1-1_all

**NAME**

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

**SYNOPSIS**

SUBROUTINE STRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO ) CHARACTER TRANSR, UPLO INTEGER INFO, N, LDA REAL A( 0: LDA-1, 0: * ), ARF( 0: * )

**PURPOSE**

STRTTF copies a triangular matrix A from standard full format (TR) to rectangular full packed format (TF) .

**ARGUMENTS**

TRANSR (input) CHARACTER*1 = 'N': ARF in Normal form is wanted; = 'T': ARF in Transpose form is wanted. UPLO (input) CHARACTER*1 = '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) REAL array, dimension (LDA,N). On entry, the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. LDA (input) INTEGER The leading dimension of the matrix A. LDA >= max(1,N). ARF (output) REAL array, dimension (NT). NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**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 Reference ========= LAPACK routine (version 3.3.1) April 2011 STRTTF(3lapack)