ctpttf-f(3)

ctpttf.f –

Synopsis

Functions/Subroutines

subroutine ctpttf (TRANSR, UPLO, N, AP, ARF, INFO)
CTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Function/Subroutine Documentation

subroutine ctpttf (characterTRANSR, characterUPLO, integerN, complex, dimension( 0: * )AP, complex, dimension( 0: * )ARF, integerINFO)

CTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Purpose:

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

Parameters:

TRANSR

 TRANSR is CHARACTER*1
 = 'N': ARF in Normal format is wanted;
 = 'C': ARF in Conjugate-transpose format is wanted.

UPLO

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

 N is INTEGER
 The order of the matrix A. N >= 0.

 AP is COMPLEX array, dimension ( N*(N+1)/2 ),
 On entry, 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.

ARF

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

INFO

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Further Details:

 We first consider Standard Packed 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
 conjugate-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
 conjugate-transpose of the last three columns of AP lower.
 To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
 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 next consider Standard Packed 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
 conjugate-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
 conjugate-transpose of the last two columns of AP lower.
 To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
 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

Definition at line 208 of file ctpttf.f.

Author

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