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---
:name: zlanhf
:md5sum: 70d3555cf9335d87bbaccab9490116b5
:category: :function
:type: doublereal
:arguments:
- norm:
:type: char
:intent: input
- transr:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublecomplex
:intent: input
:dims:
- n*(n+1)/2
- work:
:type: doublereal
:intent: workspace
:dims:
- lwork
:substitutions:
lwork: "((lsame_(&norm,\"I\")) || ((('1') || ('o')))) ? n : 0"
:fortran_help: " DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZLANHF returns the value of the one norm, or the Frobenius norm, or\n\
* the infinity norm, or the element of largest absolute value of a\n\
* complex Hermitian matrix A in RFP format.\n\
*\n\
* Description\n\
* ===========\n\
*\n\
* ZLANHF returns the value\n\
*\n\
* ZLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'\n\
* (\n\
* ( norm1(A), NORM = '1', 'O' or 'o'\n\
* (\n\
* ( normI(A), NORM = 'I' or 'i'\n\
* (\n\
* ( normF(A), NORM = 'F', 'f', 'E' or 'e'\n\
*\n\
* where norm1 denotes the one norm of a matrix (maximum column sum),\n\
* normI denotes the infinity norm of a matrix (maximum row sum) and\n\
* normF denotes the Frobenius norm of a matrix (square root of sum of\n\
* squares). Note that max(abs(A(i,j))) is not a matrix norm.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* NORM (input) CHARACTER\n\
* Specifies the value to be returned in ZLANHF as described\n\
* above.\n\
*\n\
* TRANSR (input) CHARACTER\n\
* Specifies whether the RFP format of A is normal or\n\
* conjugate-transposed format.\n\
* = 'N': RFP format is Normal\n\
* = 'C': RFP format is Conjugate-transposed\n\
*\n\
* UPLO (input) CHARACTER\n\
* On entry, UPLO specifies whether the RFP matrix A came from\n\
* an upper or lower triangular matrix as follows:\n\
*\n\
* UPLO = 'U' or 'u' RFP A came from an upper triangular\n\
* matrix\n\
*\n\
* UPLO = 'L' or 'l' RFP A came from a lower triangular\n\
* matrix\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0. When N = 0, ZLANHF is\n\
* set to zero.\n\
*\n\
* A (input) COMPLEX*16 array, dimension ( N*(N+1)/2 );\n\
* On entry, the matrix A in RFP Format.\n\
* RFP Format is described by TRANSR, UPLO and N as follows:\n\
* If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;\n\
* K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If\n\
* TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A\n\
* as defined when TRANSR = 'N'. The contents of RFP A are\n\
* defined by UPLO as follows: If UPLO = 'U' the RFP A\n\
* contains the ( N*(N+1)/2 ) elements of upper packed A\n\
* either in normal or conjugate-transpose Format. If\n\
* UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements\n\
* of lower packed A either in normal or conjugate-transpose\n\
* Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When\n\
* TRANSR is 'N' the LDA is N+1 when N is even and is N when\n\
* is odd. See the Note below for more details.\n\
* Unchanged on exit.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),\n\
* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,\n\
* WORK is not referenced.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* We first consider Standard Packed Format when N is even.\n\
* 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\
* conjugate-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\
* conjugate-transpose of the last three columns of AP lower.\n\
* To denote conjugate we place -- above the element. This covers the\n\
* case N even and TRANSR = 'N'.\n\
*\n\
* RFP A RFP A\n\
*\n\
* -- -- --\n\
* 03 04 05 33 43 53\n\
* -- --\n\
* 13 14 15 00 44 54\n\
* --\n\
* 23 24 25 10 11 55\n\
*\n\
* 33 34 35 20 21 22\n\
* --\n\
* 00 44 45 30 31 32\n\
* -- --\n\
* 01 11 55 40 41 42\n\
* -- -- --\n\
* 02 12 22 50 51 52\n\
*\n\
* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-\n\
* transpose of RFP A above. One therefore gets:\n\
*\n\
*\n\
* RFP A RFP A\n\
*\n\
* -- -- -- -- -- -- -- -- -- --\n\
* 03 13 23 33 00 01 02 33 00 10 20 30 40 50\n\
* -- -- -- -- -- -- -- -- -- --\n\
* 04 14 24 34 44 11 12 43 44 11 21 31 41 51\n\
* -- -- -- -- -- -- -- -- -- --\n\
* 05 15 25 35 45 55 22 53 54 55 22 32 42 52\n\
*\n\
*\n\
* We next consider Standard Packed Format when N is odd.\n\
* 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\
* conjugate-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\
* conjugate-transpose of the last two columns of AP lower.\n\
* To denote conjugate we place -- above the element. This covers the\n\
* case N odd and TRANSR = 'N'.\n\
*\n\
* RFP A RFP A\n\
*\n\
* -- --\n\
* 02 03 04 00 33 43\n\
* --\n\
* 12 13 14 10 11 44\n\
*\n\
* 22 23 24 20 21 22\n\
* --\n\
* 00 33 34 30 31 32\n\
* -- --\n\
* 01 11 44 40 41 42\n\
*\n\
* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-\n\
* transpose of RFP A above. One therefore gets:\n\
*\n\
*\n\
* RFP A RFP A\n\
*\n\
* -- -- -- -- -- -- -- -- --\n\
* 02 12 22 00 01 00 10 20 30 40 50\n\
* -- -- -- -- -- -- -- -- --\n\
* 03 13 23 33 11 33 11 21 31 41 51\n\
* -- -- -- -- -- -- -- -- --\n\
* 04 14 24 34 44 43 44 22 32 42 52\n\
*\n\
* =====================================================================\n\
*\n"
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